text:
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Sonu S. Varghese
Steven H. Frankel1
e-mail: firstname.lastname@example.com
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
Numerical Modeling of Pulsatile
Turbulent Flow in Stenotic
Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the
Reynolds-averaged Navier-Stokes equation approach. The commercially available com-
putational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two
different experiments were modeled involving pulsatile flow through axisymmetric
stenoses. Four different turbulence models were employed to study their influence on the
results. It was found that the low Reynolds number k–? turbulence model was in much
better agreement with previous experimental measurements than both the low and high
Reynolds number versions of the RNG (renormalization-group theory) k–? turbulence
model and the standard k–? model, with regard to predicting the mean flow distal to the
stenosis including aspects of the vortex shedding process and the turbulent flow field. All
models predicted a wall shear stress peak at the throat of the stenosis with minimum
values observed distal to the stenosis where flow separation occurred.
Blood flow under pathological conditions, such as atherosclero-
sis, involves a narrowing of the artery lumen, referred to as a
stenosis, which together with flow pulsatility can result in the
periodic generation of turbulence despite the relatively low Rey-
nolds numbers of such flows ?the typical Reynolds number range
is from 1 to 4000 in small arterioles and large vessels, respectively
?1??. This can affect flow resistance and mixing rates and impact
platelet coagulation rates ?2,3?. The fact that the vessels involve
compliant walls also affects flow stability and the generation of
turbulence. Because of the difficulties in making in vivo measure-
ments of local velocity profiles and wall shear stresses in pulsatile
flow, computational fluid dynamics ?CFD? has begun to play a
major role in improving our understanding of biofluid flows in
general, and blood flow in arteries in particular ?1,4?. Recent CFD
work has addressed pulsatile flows in stenotic vessels accounting
for fluid-structure interactions, non-Newtonian effects, and irregu-
lar geometry ?3,5,6? but the nature and effects of turbulence have
not been addressed in these studies.
Stenotic flows involve low Reynolds number, pulsatile flow
through a restriction ?most resembling a converging-diverging
nozzle in the idealized case?. They feature flow separation, strong
shear layers, recirculation, reattachment, and turbulence. It has
been observed that flow separation occurs in the expansion region
for Re?10 for a 70% ?by area? stenosis. The critical upstream Re
for turbulence is 300 and intensity levels reach about 100% of
upstream velocity values and remain high for about 1.5–6 diam-
eters downstream. Pulsatility creates a periodic generation of tur-
bulence, which is greatest during the deceleration of systole and
least during the upstroke of systole. A reduced wall shear stress
has been associated with this transition to turbulence. For stenoses
greater than 75%, turbulence effects are very large and create
significant flow resistance and pressure loss ?1?.
Turbulence in blood flow influences many physiological pro-
cesses. In addition to flow resistance, turbulence affects the shear
stress acting on the blood vessel wall, tensile stress in the endot-
helial cell membrane, mass transport from the blood to the vessel
wall, atheroscle-rosis, blood clot formation, blood rheology
through deformability of red blood cells, the hematocrit ?volume
fraction of red blood cells in blood?, cell division and surface cell
loss, as well as internal cell motion due to pressure and shear
stress ?7?. Of particular interest here is the effect of the shear
strain rate of the blood on the endothelial cells which line the
blood vessel walls, which is thought to be a contributing factor in
atherosclerosis ?8?.
Experimental studies of pulsatile flow through stenotic vessels
have been limited to laboratory studies for obvious reasons. Ojha
et al. ?9? studied pulsatile flow through constricted tubes using a
photochromic technique. It was found that with mild stenoses vor-
tical and helical structures were observed during the deceleration
phase near the reattachment point. With moderate constrictions,
transition to turbulence associated with the breakdown of waves
and streamwise vortices occurred. Intense wall shear stress fluc-
tuations were also observed near the reattachment point with in-
creases in instantaneous wall shear stress as much as by a factor of
8. The vortical structures occurred due to jet instability during the
deceleration phase and were not shed from stenosis. Interactions
between the imposed flow oscillation and the turbulence in the
viscous sublayer were strongest during the deceleration phase.
Giddens and co-workers constructed a plexiglass model of an
axisymmetric stenotic blood vessel experiencing pulsatile flow
and measured instantaneous core velocity, ensemble-averaged ve-
locity profiles, and wall shear stress using laser Doppler velocim-
etry ?10–12?. For a 75% stenosis, turbulence was found to exist
during parts of the cycle. Issues related to velocity decomposition
to account for the time-varying mean and the presence of coherent
vortical structures via a triple decomposition were discussed, as
well as the effect of the apparent stresses. They reported that
vessel wall thickening may depend on the instantaneous wall
shear stress being low during the entire cycle rather than just the
There have been several recent numerical studies investigating
steady and pulsatile flow through stenotic vessels addressing sev-
eral of the above issues. These issues include fluid-structure inter-
action and rheology effects. Bathe and Kamm ?13? conducted a
finite-element analysis to examine fluid-structure interaction of
pulsatile flow through a compliant stenotic artery. They used the
commercial software package ADINA to develop an axisymmetric
model of the flow and vessel. They observed an increase in the
pressure drop and wall shear stress associated with the flow as
1?Author to whom correspondence should be addressed.
Contributed by the Bioengineering Division for publication in the JOURNAL OF
BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Divi-
sion January 28, 2002; revision received February 10, 2003. Associate Editor: J. E.
Moore, Jr.
Copyright © 2003 by ASMEJournal of Biomechanical Engineering
AUGUST 2003, Vol. 125 Õ 445
Page 2
they increased the degree of stenosis. They also reported an in-
crease in the inner wall hoop stretch and compressive stresses on
the lesion, as well as additional decreases in vessel area during
peak flow times. Turbulence effects were not considered in their
study. Tang et al. ?5? also considered fluid-structure interactions of
steady flow through an axisymmetric stenotic vessel using the
commercial code ADINA. They observed complex flow patterns
and high shear stresses at the throat of the stenosis, as well as
compressive stresses inside the tube. Turbulence was not ad-
dressed. Qiu and Tarbell ?14? used FIDAP to study pulsatile flow in
a compliant curved tube model of a coronary artery. They report
that in addition to the wall shear stress, the stress phase angle
between the circumferential strain in the artery wall and the wall
shear stress is important for locating possible coronary atheroscle-
rosis. Buchanan et al. ?6? studied rheological effects on pulsatile
laminar flow through an axisymmetric stenosed tube and found
that they could affect wall shear stress quantities.
Many turbulent flows that occur both naturally ?such as blood
flow in arteries? and artificially ?fluid pumped through a channel
by a reciprocating device? are inherently unsteady. The unsteadi-
ness may be due to an imposed boundary condition or due to
fluctuations in the driving force, or even a combination of both.
This imposition can alter the flow physics to such an extent that it
can even cause relaminarization of an initially turbulent flow.
Unsteady flow can be periodic or aperiodic in nature. If the
mean quantity is nonzero, the unsteadiness is pulsatile or else it is
purely oscillatory flow. A flow subject to a homogeneous, time
varying pressure gradient is equivalent to a flow in which the time
varying component of the pressure is replaced by an equivalent
oscillation in the boundary condition, via a transformation of vari-
able ?15?. However, this is not true for aperiodic flow, as in the
case of flow accelerating at a constriction.
Many authors have investigated the effect of unsteadiness on
the structure of turbulence, but the possible effects of unsteadiness
on time-mean flow characteristics have been disputed between
two groups of authors who have conducted experimental investi-
gations on the structure of turbulent pulsatile flows. The results of
Ramaprian and Tu ?16,17? and Mizushina et al. ?18? indicated
small modifications of the time-mean characteristics of pulsatile
turbulent flow ?such as time-averaged velocity, Reynolds stress
distribution, etc.? when the pulsation frequency was sufficiently
close to the bursting frequency of turbulence or when the pulsa-
tion amplitude was large. The second group of authors, which
include Ohmi et al. ?19–21?, Kita et al. ?22?, and Tardu et al.
?23,24?, indicated that there was no such effect of unsteadiness on
the time-mean characteristics of pulsatile turbulent flows for full
ranges of the flow parameters such as the pulsation frequency,
amplitude, or Reynolds numbers. Most recently, He and Jackson
?25? provided a thorough review of the literature on experimental
studies of turbulence in transient pipe flow. In their study, they
find that the turbulence intensity is attenuated during the acceler-
ating phase of the transient flow and increased during the decel-
erating phase. This behavior was attributed to time delays in the
response of turbulence production and energy redistribution, as
well as propagation of turbulence radially.
Recently, Scotti and Piomelli ?15? conducted direct numerical
simulations ?DNS? and large eddy simulations ?LES? of pulsatile
turbulent channel flow subjected to an unsteady pressure gradient.
In DNS, numerically accurate and complete resolution of all spa-
tial and temporal flow scales is required and no turbulence model
is used. In LES, numerically accurate resolution of the large scales
is required and the effect of the small scales, which are not sup-
ported by the computational grid, on the resolved scales is mod-
eled using a sub-grid-scale turbulence model. Both techniques re-
sult in simulations that should enable capture of unsteady scale-
dependent vortex dynamics, transition, and turbulence. Scotti and
Piomelli ?15? showed that fluctuations generated in the near-wall
region did not propagate beyond a certain distance from the wall,
which depended on the imposed oscillation frequency. Because of
the instantaneous nature of the simulations, coherent flow struc-
tures, including streaks and spots, were able to be identified. In a
related study, Scotti and Piomelli ?26? employed the Reynolds
averaged Navier-Stokes ?RANS? equations to assess the capabili-
ties of three turbulence models for the same flow. In the RANS
approach, only the mean flow is computed, with the effect of all
the turbulent eddies being modeled. The authors found that all the
turbulence models were in reasonable agreement with the DNS
and LES for the velocity profiles over the cycle, but the models
differed when it came to other turbulence parameters.
Fig. 1
Ahmed and Giddens †11‡, where LÄ4.0? and DÄ2.0?, and the
"b… sharp-edged stenosis of Ojha et al. †9‡, where LÄ1.5 mm
and DÄ5.0 mm. For both geometries, the normalized distance
from the stenosis center is given by ZÄZ?ÕD.
Stenosis geometries for the "a… smooth stenosis of
Table 1Closure coefficients for the k–? models
Low Re RNG
Table 2
k–? model
Closure coefficients for the low Reynolds number
Low Re k–?
2.0 2.06.0 0.52
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Bluestein et al. ?27? correlated platelet deposition in a model
stenosis with flow dynamics using a steady flow numerical model
at different Rynolds numbers. They employed the two equation
standard k–? turbulence model and observed a single closed vor-
tex within the recirculation region. In a later study, Bluestein et al.
?2? used the two equation low Reynolds number k–? turbulence
model ?similar to that used in the present study? to simulate steady
flow through a stenosis. In this case they observed the process of
vortex shedding in the separated flow region downstream of the
stenosis which was also confirmed by digital particle image ve-
locimetry. They proposed that the development of vortical struc-
tures in the flow field near the walls for high Reynolds numbers
leads to enhanced platelet deposition.
More recently, Mallinger and Drikakis ?28? and Mittal et al.
?29? have conducted DNS and LES, respectively, of pulsatile
stenotic flow. Drikakis et al. observed asymmetries in the form of
helical disturbances develop in the distal region of the stenosis,
while Mittal et al. found evidence of turbulence further down-
Fig. 2
Reynolds number RNG k–? model and normalized by the mean inlet velocity.
The distances are in normalized units "normalized by diameter…. Only a third of
the actual number of grid points used is shown and profiles are offset by 5
units in the x direction. "a… Smooth stenosis. The profiles were obtained during
peak inlet flow. "b… Sharp-edged stenosis. The profiles were obtained during
minimum flow conditions at the inlet.
Grid refinement tests. The velocity profiles were obtained using the low
Fig. 3
distal to the smooth stenosis with the experimental profiles of Ahmed and
Giddens †10‡, for steady flow at inlet ReÄ500
Comparison of computed velocity profiles at different axial locations
Table 3Key flow parameters used for the two stenotic flow simulations
? ?rad/s?
D (m)
? ?kg/m3? ? ?Pa–s?
Ahmed and Giddens
Ojha et al.
3.6014 ? 10?3
1.43 ? 10?3
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stream of the stenosis. These studies highlight the utility of con-
ducting three-dimensional transient simulations of pulsatile
stenotic flows to identify important flow features not captured in
more traditional RANS studies of the type reported here. Our own
recent DNS studies have also revealed the development of asym-
metries in the distal region ?30?.
In this study, the pulsatile stenotic flow experiments of Giddens
et al. ?11? and Ojha et al. ?9? are simulated, within the framework
of two-equation RANS turbulence models. The capabilities of
four different models in predicting the flow features that were
observed in the experiments are assessed. Various issues involved
in the modeling, such as near-wall treatment and grid-
independence are also discussed.
Turbulence Models
The Reynolds averaged Navier-Stokes ?RANS? equations rep-
resent transport equations for the mean flow quantities only, with
the effect of all the turbulent eddies being modeled. In time-
dependent simulations, such as those performed during this study,
a computational advantage is that the time step is determined by
the global unsteadiness in the mean flow, rather than by the tur-
bulence ?31?.
In unsteady turbulent flows, instantaneous flow variables in the
Navier-Stokes equations such as axial velocity, u, can be ex-
pressed in terms of an ensemble-averaged quantity, u ¯, and a fluc-
tuation from this average, u?. Likewise for other scalar quantities
like pressure. Applying this decomposition to the Navier-Stokes
equations yields the RANS equations. The incompressible form of
these equations can be written in the Cartesian form as:
?u ¯i
Du ¯i
?p ¯
?u ¯i
?xj??u ¯j
?xj??ui?uj??, (2)
where D( )/Dt??( )/?t?uj??( )/?xj? and ? is the kinematic vis-
As seen above, averaging the equations of motion gives rise to
new terms such as, ?ui?uj?. Also known as the Reynolds stress
tensor, it is the time-averaged rate of momentum transfer due to
turbulence ?32?. It is expressed in terms of ?T, the kinematic eddy
viscosity, and the mean strain rate tensor, Sijas:
?u ¯i
?xj??u ¯j
?xi??2?TSij. (3)
A turbulence model can be used to model the cross correlations
which arise from the nonlinear terms in the governing equations
and thereby close the equations. Four different two-equation tur-
bulence models, readily available in FLUENT were used in this
study. The models use different transport equations for turbulent
kinetic energy ?TKE?, k, and dissipation rate, ?, or pseudovortic-
ity, ?. The turbulent transport equation for the TKE can be de-
scribed as:
?u ¯i
Fig. 4
used by Ahmed and Giddens is also shown. A flat inlet velocity profile was
used for the simulation. "b… Comparison of computed velocity profiles at differ-
ent axial locations distal to the stenosis with the experimental profiles of
Ahmed and Giddens †11‡ for pulsatile flow with mean inlet ReÄ600. Velocity
profiles are compared during peak inlet flow conditions "T2….
"a… Flow inlet waveform for the smooth stenosis. The inlet waveform
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For the k–? models, the Boussinesq approximation is used to
determine the eddy viscosity as ?T?C?(k2/?) and in Eq. ?4?,
The transport equation for ? is:
?u ¯i
?xj?, (7)
where ??????T/??. The closure coefficients for the different
models are given in Table 1.
The value of R in Eq. ?7? for the standard k–? is 0. The stan-
dard model is widely used despite known limitations, especially in
the prediction of complex flows involving strong pressure gradi-
Fig. 5
inlet velocity. The distances are in normalized units "by diameter away from the center of the stenosis… and the
profiles are offset by 5 units in the x direction.
Velocity profiles for the smooth stenosis at different phases in the flow cycle, normalized by the mean
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ents, separation, and strong streamline curvature. The RNG k–?
model is similar to the standard k–? model and is derived from
the instantaneous Navier-Stokes equations, using a mathematical
technique called renormalization group ?RNG? theory ?33–35?. It
features slightly modified modeling constants and includes an ad-
ditional term in the ? equation ?Eq. ?7??, introduced by R as:
, (8)
where ??(k/?)?2SijSji, ?0?4.38, and ??0.012. This term im-
proves the accuracy for rapidly strained flows.
For the low Reynolds number variation of the RNG k–? model,
?k??????? ˆ in Eqs. ?4? and ?7?. A differential equation is used
for the turbulent viscosity:
? ˆ
d? ˆ,(9)
where C??100 and ? is given by the relation
? ˆ. (10)
During the computation, Eq. ?9? is integrated to accurately obtain
the variation of effective turbulent transport with the effective
Reynolds number, allowing the model to better predict low Rey-
nolds number and near-wall flow behavior. In the high Reynolds
number limit, the model reverts to the high Reynolds number
form of the RNG model ?31?.
The fourth turbulence model used for this study was the low
Reynolds number variation of the k–? model. The standard k–?
model is an empirical model based on modeled transport equa-
tions for the turbulent kinetic energy k as given in Eq. ?4? with
D??0*f?*k?, (11)
?xj, (13)
Fig. 6
The stream function increment is 0.0015 sÀ1. The axial distance is indicated in normalized units Z "normalized by diameter….
Streamlines for the smooth stenosis from the low Reynolds number RNG k–? model at different phases in the flow cycle.
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and the specific dissipation rate ?(??/k) ?32?. The transport
equation for ? is
?u ¯i
where ??????T/??. The eddy viscosity for the low Reynolds
number variation is computed as ?T??*(k/?). The auxiliary re-
lations are described as
??, (17)
?u ¯i
?xj??u ¯j
Closure coefficients for this model can be found in Table 2. The
low Reynolds number variation of the k–? model has been
shown to demonstrate superior performance for wall bounded low
Reynolds number flows. Wilcox ?32? also showed that the low
Reynolds number k–? model has potential to predict transitional
flows quite well, though the model has tended to predict excessive
and early separation ?31?. More details on all of the discussed
models can be found in books on turbulent flows and modeling
Numerical Modeling
Analytical solutions of the governing equations of fluid dynam-
ics are rare, especially as the dimensionality of the problem in-
creases. Analytic solutions for laminar pipe flow are available in
the form of the Hagen-Poseiulle solution. Many investigators have
conducted theoretical studies of both pulsatile and oscillatory pipe
flows. Womersley ?37? introduced a nondimensional frequency
parameter, ?, and proposed a solution for the time-dependent axial
velocity for fully developed pulsatile laminar flow in a circular
pipe which is a function of radial location and time and takes the
following form:
Fig. 7
streamfunction increment is 0.0018 sÀ1.
Streamlines for the smooth stenosis from the low Reynolds number k–? model at different phases in the flow cycle. The
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Fig. 8
phases in the flow cycle. The distances are in normalized units "by diameter
away from the center of the stenosis… and the profiles are offset by 5 units in
the x direction.
Turbulence intensity profiles for the smooth stenosis at different
Fig. 9
distance is indicated in normalized units, Z.
Axial wall shear stress profiles for the smooth stenosis case at different phases in the flow cycle. The axial
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where a is the pipe radius, J0( ), is the Bessel function of type 0,
? is the angular frequency of the pulsation, ? is a nondimensional
parameter called the Womersley number where ??a?(?/?), P is
the pressure gradient, ? is the density, and ? is the kinematic
Investigators focusing on turbulent pulsatile flow have concen-
trated on the effect of pulsation frequency in terms of ? ?or the
frequency? with the effect of turbulence being modeled using both
time-dependent and time-independent eddy viscosity concepts
?38?. The RANS equations represent transport equations for the
mean flow quantities only, with the effect of all the turbulent
eddies being modeled, as discussed in the previous section. How-
ever, finding an analytic solution is difficult and so numerical
solutions are usually relied upon.
In this study, the commercially available CFD code FLUENT,
Version 6.0, was used to solve the incompressible RANS equa-
tions together with a two-equation turbulence model. The dis-
cretized equations were solved in a segregated manner using the
PISO ?pressure implicit splitting of operators? algorithm, which is
useful for stability in unsteady flow calculations and to achieve
proper pressure-velocity coupling. The grids used for the calcula-
tions was generated using GAMBIT, the preprocessor for FLUENT.
An important consideration for turbulence modeling is near-
wall treatment and this can be carried out in FLUENT by using the
wall function approach or the enhanced wall treatment. In the wall
function approach, the viscosity affected near-wall region is not
resolved with the near-wall mesh being relatively coarse. Here,
the solution is determined by empirically based wall functions and
it is important that the first grid point off the wall not get into the
wall layer. Wall functions become much less reliable in the pres-
ence of separated flow ?32?. The enhanced wall treatment gener-
ally requires a very fine near-wall mesh capable of resolving the
viscous sublayer, with the first grid point off the wall being within
the region y??1, the distance being measured in wall units,
y?(??u?y/?) ?where u?is the friction velocity?. The latter ap-
proach is more suited for low-Reynolds number flows though it
obviously requires a greater amount of computational resources.
The enhanced wall treatment approach was employed for all the
cases reported in this study.
For the time periodic calculations, the time period, T, was cal-
culated in terms of the angular frequency, ?, as T?2?/?. The
time step was then calculated by dividing the time period with the
number of iterations required for convergence during each step. In
FLUENT, an unsteady formulation was used and a temporally peri-
odic boundary condition was applied to the inlet of the tube by
creating a user defined function ?UDF? for the sinusoidal velocity
of the form
where U0is the mean velocity and Umis taken as a fraction of
U0. This resulted in a time-periodic calculation and by varying
the total number of iterations during each run, flow characteristics
at different positions on the periodic cycle were obtained during
the post-processing step.
The turbulence intensity and hydraulic diameter were also
specified as inlet boundary conditions according to:
uavg?0.16?ReDH??1/8, (21)
where ReDHis the Reynolds number based on hydraulic diameter
?the main vessel diameter, D, in the present stenotic flow cases?, ?
and ? the fluid density and viscosity, respectively. More details on
turbulent flow parameters as well as modeling guidelines can be
found in Refs. ?31,32,36?.
Description of Modeled Experiments
Pulsating Turbulent Flow Through a Smooth Stenosis.
experimental investigation of Ahmed and Giddens ?11? consider-
ing pulsatile flow through an axisymmetric smooth stenosis was
studied here. The geometry used was similar to theirs with the
stenosis shape given by a cosine function as shown in Fig. 1a. If
r0is the radius of the nonstenotic part of the tube, S(x), gives the
shape of the stenosis as:
where s0is the % stenosis severity with x1and x2(x1?x?x2)
specifying the position and length of the stenosis. A 75% axisym-
metric stenosis was used in this model. Pulsatile flow was studied
at a mean Reynolds number of 600 and a Womersley number of
??D/2?(?/?)?7.5, similar to the experiments. Other param-
eters used in Eqs. ?20? and ?21? can be found in Table 3.
Pulsating Turbulent Flow Through a Sharp-Edged Stenosis.
The experimental investigation of Ojha et al. ?9? on pulsatile flow
through an axisymmetric sharp-edged stenosis was studied here.
The 75% axisymmetric stenosis case in their study was modeled
and the geometry used is shown in Fig. 1b. The Womersely pa-
rameter was ??7.5. The mean and modulation Reynolds numbers
were 575 and 360, respectively, matching the experiments. The
other parameters used in Eqs. ?20? and ?21? can be found in
Table 3.
Grid Refinement Study.
formed for the cases reported in this study. Figure 2 shows two
typical grid independence studies that were conducted for both
stenosis models using the low Reynolds number RNG k–? model.
The profiles were obtained during minimum flow conditions at the
inlet. Grids consisting of 30, 60, and 120 points in the radial
direction were used in this study ?the number of points in the
Grid refinement studies were per-
Fig. 10
ferent from the waveform used for the smooth stenosis…. A flat
inlet velocity profile was used for the simulation.
Flow inlet waveform for the sharp-edged stenosis "dif-
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streamwise direction was correspondingly varied in order to avoid
skewness of the elements? and the profiles obtained on the two
finer grids, corresponding to 60 and 120 radial points, fall on top
of each other. The results shown in the following sections ?for
both the stenosis models? were all obtained using the grid with 60
points in the radial direction. Simulations with the low Reynolds
number k–? model took approximately 16 h to converge with
two parallel processors. Computational times for simulations with
the k–? models were approximately 19 to 22 h with the low
Reynolds number k–? model requiring the maximum.
Pulsating Turbulent Flow Through the Smooth Stenosis.
FLUENT calculations were also performed for the 75% axisymmet-
ric stenosis model of Giddens and co-workers ?10–12?. As part of
Fig. 11
mean inlet velocity. The distances are in normalized units "by diameter away from the center of the stenosis… and
the profiles are offset by 5 units in the x direction.
Velocity profiles for the sharp-edged stenosis at different phases in the flow cycle, normalized by the
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a validation process, steady flow computations were performed at
a mean inlet Reynolds number of 500 and the velocity profiles
distal to the stenosis were compared to the data in Ref. ?10?,
shown in Fig. 3. A parabolic inlet velocity profile was specified
2.5 diameters upstream of the stenosis throat for this case. The
figure shows the low Reynolds number k–? model performing
better than its counterparts in the region immedietly downstream
of the stenosis. Far downstream, all the models show poor agree-
ment with the experimental data, though the low Reynolds num-
ber k–? model better predicts the jetlike flow at the center of the
The previously described pulsatile flow conditions were chosen
to mimic the experiments of Ahmed and Giddens ?11?. The flow
input waveform and the times at which the results will be pre-
sented are indicated in Fig. 4a along with the waveform used in
the experiments. A flat inlet velocity profile was specified 2.5
diameters upstream of the stenosis throat. Computed velocity pro-
files were compared with the experimental data during peak inlet
flow as shown in Fig. 4b. All the four models show poor agree-
ment with the experiments especially in predicting flow separation
far downstream of the stenosis during this time. Although, as for
the steady flow case, the low Reynolds number k–? model better
predicts the jetlike flow behavior further downstream from the
stenosis. Part of the discrepancy in the profiles may be due to the
differences between the inlet waveforms, highlighted in Fig. 4a,
as well as the nature and location of the inlet velocity profile
specified for these computations. In the experiments the entrance
length of the tube prior to the constriction was 96 diameters ?11?.
Figure 5 shows the velocity profiles computed by all the turbu-
lence models at various distal locations ?distances being measured
from the stenosis throat?. The low Reynolds number k–? model
predicts more jetlike behavior immediately downstream of the
stenosis throat than any of the three k–? models. Similar to the
experiments, a permanent recirculation region is not observed in
any of the present results. The profiles during acceleration ?time
T1) and peak flow (T2) indicate that the flow is mostly in the
forward direction during these times. During deceleration (T4)
and minimum flow (T5), the profiles are more inflectional in
nature, which could lead to instabilities further downstream.
The streamlines computed by the low Reynolds number RNG
model and the low Reynolds number k–? model in Figs. 6 and 7,
respectively, indicate a region of flow reversal upstream of the
stenosis during parts of the cycle, consistent with the reverse flow
observed byAhmed and Giddens. The low Reynolds number k–?
model predicts strong vortex formation in the jetlike region during
the deceleration phase, when an adverse pressure gradient exists
across the vessel, similar to the vortex formation observed in the
experiments. The three k–? models fail to predict this behavior.
Turbulence intensity profiles shown in Fig. 8 once again high-
light the differences between the three k–? models and the low
Reynolds number k–? model. The low Reynolds number k–?
model predicts lower turbulence intensities than the other models
immediately downstream of the stenosis during both peak and
minimum flow (T2 and T5, respectively?. Further downstream,
around Z?4.0, the low Reynolds number k–? model predicts
higher intensity, due to the breakdown of vortices in that region.
However, all the turbulence models predict low levels of turbu-
lence intensities across the distal section of the stenotic vessel. In
the experiments, high turbulence levels were observed at Z
Axial profiles of wall shear stress ?WSS? in the vicinity and
distal to the stenosis are plotted in Fig. 9 at different phases of the
flow cycle and the levels can be seen to be fluctuating throughout
the cycle. Again, peak WSS levels are observed at the stenosis,
consistent with the high velocities associated with flow accelera-
tion through the restriction. The highest values are observed dur-
ing the acceleration phase and the early part of the deceleration
phase. The maximum value occurs at time T2 ?peak flow? similar
to experimental observations at the same phase. Negative values
of the WSS can be observed during the deceleration phase consis-
tent with the presence of flow reversal. Consistent with the experi-
ments, the magnitude of shear stress is relatively insignificant af-
ter Z?4.0.
Pulsating Turbulent Flow Through the Sharp-Edged Steno-
Ojha et al. ?9? described a moderate stenosis to be one for
which turbulence is generated in a large portion of the region
distal to the stenosis, but which does not result in a physiologi-
cally significant reduction in blood flow. The 75% axisymmetric
stenosis geometry they studied falls within this category. Their
experiments also indicated transition to turbulence for the same
case. FLUENT was used here to model this experiment with param-
eters described in the previous section. The flow input waveform
shown in Fig. 10 is different from the one used in the computa-
tions for the smooth stenosis. A flat inlet velocity profile was
specified 2.5 diameters upstream of the stenosis throat. In the
experiments the test section was located 160 diameters down-
stream from the entrance ?9?.
Velocity profiles at different phases of the flow cycle, as calcu-
lated by all the models, are presented at various axial locations
distal to the stenosis ?the distance being measured from the center
of the stenosis? in Fig. 11. The profiles predicted by the three
variations of the k–? model are almost the same throughout the
cycle. However, the low Reynolds number variation of the k–?
model predicts a more jetlike flow immediately downstream of the
stenosis with higher velocities at the center of the tube, similar to
the experiments. All the models show that towards the end of the
acceleration phase, at peak flow (T2), the velocity profiles be-
come more inflectional in nature, which can cause instabilities in
the flow. As the flow becomes more unstable, a region of reversed
flow starts to develop immediately downstream of the stenosis.
Variations in the size of the flow separation regions distal to the
stenosis are also observed between the turbulence models, espe-
cially during the deceleration phase ?time T4) and minimum flow
(T5). It should be noted that a direct comparison with the photo-
chromic measurements of Ojha et al. ?9?, which represent instan-
taneous velocity profiles, is not possible here because our predic-
tions are of the ensemble-averaged flow field.
Fig. 12
edged stenosis. Waveforms computed by the four turbulence
models are compared to the experimental data.
Centerline velocity waveforms at ZÄ0.6 for the sharp-
Journal of Biomechanical Engineering
AUGUST 2003, Vol. 125 Õ 455
Page 12
Figure 12 compares computed centerline velocities, obtained
during one cycle at Z?0.6, with data from the experiments. None
of the turbulence models are able to predict the variations in the
centerline velocity at that location which is close to the stenosis
Streamlines computed by the low Reynolds number variation of
the RNG model and the low Reynolds number k–? model at
different phases of the flow cycle during one time period are
shown in Figs. 13 and 14, respectively. Streamlines computed by
the other k–? models are not shown here due to their similarity
with the low Reynolds number RNG model. The streamline plots
show that a region of reversed flow starts to develop immediately
downstream of the stenosis at peak flow. Later in the deceleration
phase, and into the early part of the acceleration phase, this re-
versed flow region continues to grow, until it almost completely
disappears during the middle of acceleration. Both models predict
a permanent region of flow reversal immediately distal to the
stenosis as well as a recirculation region in the region proximal to
the stenosis during deceleration when an adverse pressure gradient
results across the model, similar to that observed by Ojha et al.
The reattachment point as well as the size of the separation
zone fluctuated throughout the cycle. During deceleration, around
time T4, the low Reynolds number k–? model predicts the size
of the separation zone to be between 0.35R and 0.4R ?where R is
the radius of the vessel? from the exit of the stenosis to around
Z?2.5, beyond which it starts to taper. This corresponds well to
the separation zone thickness of 0.38R measured in the experi-
ments. At the same time, the k–? models predict separation zones
that are smaller in size ?about 0.2R). In the experiments, as the
flow accelerated, the thickness of the separation zone was found
to reduce along the tube in a wavelike manner from the edge of
the stenosis, quite similar to computations by the k–? model.
During the middle of acceleration, when conditions are least
favourable for separation ?around time T1), the model again was
in better agreement, predicting a thickness value of approximately
0.25R within Z?2.0, while the k–? models predict a smaller
zone that is only about half the size. Towards the end of the
acceleration phase, near peak flow, the separation boundary moves
closer to the wall and eventually disappears between Z?3.0 and
Z?4.0, while at the same time, the k–? model predicts the gen-
eration of waves and streamwise vortices in the high shear layer,
between Z?1.0 and Z?1.6, agreeing very well with the experi-
mental values of Z?3.7 and Z?1.4, respectively. This is not the
case for the other models.
Turbulence intensity profiles at peak and minimum flow times
are shown in Fig. 15 ?profiles at other times are not shown here
Fig. 13
cycle. The stream function increment is 0.000425 sÀ1. The axial distance is indicated in normalized units Z "normalized by
Streamlines for the sharp-edged stenosis from the low Reynolds number RNG k–? model at different phases in the flow
456 Õ Vol. 125, AUGUST 2003
Transactions of the ASME
Page 13
due to their similarities with profiles in corresponding phases of
the cycle?, further highlighting the differences between the models
used for the calculation. While the k–? models predict higher
intensities in the jetlike region immediately downstream of the
stenosis, the low Reynolds number k–? model predicts higher
values further downstream after approximately Z?2.8, which cor-
responds to the region in which the structures start to breakdown
and transition to turbulence occurs. The latter is more consistent
with the experimental observations. However, high turbulence
levels observed in the region between Z?4.5 and Z?7.5 are not
predicted by any of the models.
All the turbulence models predict peak wall shear stress ?WSS?
levels at the stenosis, consistent with the high velocities associated
with flow acceleration through the restriction as seen in Fig. 16.
The maximum value occurs at time T2 when there is maximum
flow into the tube and the minimum value occurs at time T5,
during minimum flow conditions. Due to the geometry of the
constriction employed in this study, the WSS increases as the fluid
enters the constriction and then decreases as the fluid flows
through the region of minimum area only to increase again upon
entering the diverging section, resulting in the two peaks observed
in the figures. The low Reynolds number k–? model again differs
from the results of the other models, especially in the region 0.5
?Z?3.3, where flow separation and reattachment occurs, as was
observed for the smooth stenosis.
Several previous studies have employed numerical models to
predict pulsatile flows in stenotic vessels ?5,6,13?. None of these
studies addressed the issue of turbulence. The two main experi-
mental studies which considered pulsatile flow through stenotic
vessels clearly observed the presence of transitional or turbulent
flow distal to the stenosis ?9,11?. Previous experimental studies of
pulsatile turbulent flow through unrestricted channels or tubes
have shown that turbulence levels are highest during the decelera-
tion phase of the cycle ?25?. Taken together these previous studies
suggest that numerical studies of turbulent pulsatile flow are war-
ranted. Our own studies that were carried out for nonseparated
flows ?not discussed here? have shown that the turbulence inten-
sity is indeed greater during deceleration, while it diminishes dur-
ing acceleration. The characteristics which are observed for
simple confined pulsatile flows exist even in the presence of a
Fig. 14
The stream function increment is 0.00054 sÀ1.
Streamlines for the sharp-edged stenosis from the low Reynolds number k–? model at different phases in the flow cycle.
Journal of Biomechanical Engineering
AUGUST 2003, Vol. 125 Õ 457
Page 14
stenosis, where the free jet that forms combines with these to
create a highly unstable flow resulting in cyclic and localized
For both stenosis geometries considered here, the turbulence
models predicted that the flow starts to become unstable around
peak flow, with velocity profiles becoming more inflectional in
nature. A region of reversed flow continues to grow throughout
the deceleration phase. The flow remains quite stable throughout
the acceleration phase. The low Reynolds number k–? model
was found to be in better agreement with the experiments as to the
prediction of the location and sizes of reversed flow regions that
occured distal to the stenosis throughout the cycle, than any of the
k–? models, especially in the case of the sharp-edged stenosis.
The models in this study predict highly inflectional velocity
profiles, especially during the deceleration phase, which may
cause Kelvin-Helmholtz-type instabilities to be generated at dif-
ferent locations distal to the stenosis. These disturbances could
grow during parts of the cycle that are conducive to their growth
leading to localized turbulence at these times. The low Reynolds
number k–? model appears to be able to capture the generation
of streamwise vortices in the high shear layer and the resulting
unsteady vortex shedding distal to the stenosis. This in turn led to
the model predicting higher turbulence intensities at locations fur-
ther downstream of the stenosis due to vortex interactions during
the deceleration phase, consistent with experiments, while its
counterparts predicted higher turbulence levels only in the jetlike
region immediately distal to the stenosis. Unsteady behavior along
the tube wall is interesting due to their possible interactions with
the vessel wall ?11?. The vortex shedding process was also ob-
served by Bluestein et al. in their studies of steady flow and the
vortical structures were related to increased platelet deposition
?2?. In this context, unsteady vortex shedding observed in this
study would be very relevant to mural platelet deposition along a
stenotic vessel and warrants a thorough investigation.
The turbulence models predict maximum values of wall shear
stress at the stenosis during acceleration when the velocity is high-
est at this location, followed by regions of negative WSS when
separated flow occurs. The WSS levels fluctuate throughout the
cycle and as in the experiments, the WSS remains low at locations
where higher turbulence levels are predicted, especially during the
deceleration part of the cycle. This is important in the context of
studying the effect of turbulence on wall shear stress and the
resulting arterial wall thickening. The results also show that de-
tails of the stenosis geometry also affect the nature of variations in
the wall shear stress along the stenosis and distal to it.
In this study, enhanced wall functions were employed along
with the turbulence models in order to better resolve the near wall
region. These are more suited for low Reynolds number flows
with complex near wall phenomena. However, this approach is
more computationally intensive because it generally requires a
very fine near wall mesh, that can resolve the viscous sublayer.
Grid resolution requirements were found to be demanding for
these type of turbulence model calculations as opposed to the
standard wall function approach with turbulence models. The lat-
ter approach utilizes relatively less computational resources, as
the viscosity affected near wall region is not resolved and the
Fig. 15
are in normalized units "by diameter away from the center of the stenosis… and the profiles are offset by 25 units in the
x direction.
Turbulence intensity profiles for the sharp-edged stenosis at different phases in the flow cycle. The distances
458 Õ Vol. 125, AUGUST 2003
Transactions of the ASME
Page 15
mesh is relatively coarse. A point to note here is that while em-
ploying standard wall functions, the grid must not get into the wall
layer. However, standard wall functions generally perform poorly
for low Reynolds number type of flows ?32,39?.
Large discrepancies were observed when comparing the com-
puted results with available experimental data. Part of this may be
attributed to the choice of upstream location and shape of inlet
velocity profile specified for the computations, factors which
could play an important role in such studies. The flow physics,
required accuracy, computational resources and turnaround time
constraints also play a major role in the selection of turbulence
model and near wall treatment as well as the computational grid
employed for these type of computations. Improvements in the
capabilities of turbulence models could also be made by perform-
ing DNS or LES of pulsatile, stenotic flows ?28,29?.
Numerical predictions for turbulent pulsatile flow through two
different axisymmetric stenoses were obtained within the frame-
work of two-equation turbulence models. The low Reynolds num-
ber k–? model was found to be in better qualitative and quanti-
tative agreement with the two experiments studied, in contrast to
the standard k–? model, the RNG k–? model or even the low
Reynolds number RNG k–? model. Many of the recent numerical
studies conducted in the biomechanical engineering community
have employed commercial CFD codes. Most commercial CFD
codes offer a variety of turbulence models from which one can
choose. Therefore, it is important to provide some guidance to the
community as to which models are appropriate for use in model-
ing pulsatile turbulent stenotic flows as well as other issues in-
volved in the modeling such as near-wall treatment. The results
obtained in this study could be useful in developing a viable low
Reynolds number turbulence model for predicting transition and
intermittency, the latter being the fraction of time that the flow is
turbulent, in stenotic flows. For now, it appears that the low Rey-
nolds number k–? model seems to be better capable of predicting
such flows with its ability to predict low Reynolds number tran-
sitional flows. Various factors such as computational resources,
flow physics and accuracy required will also have to be consid-
ered for such studies.
Financial support for this work was provided through the B.F.S.
Schaeffer Award.
Fig. 16
distance is indicated in normalized units, Z.
Axial wall shear stress profiles for the sharp-edged stenosis at different phases in the flow cycle. The axial
Journal of Biomechanical Engineering
AUGUST 2003, Vol. 125 Õ 459


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Cutting back?
I have one violet that developes new leaves and flowers on the same stems. In other words, the flowers don't just dry up after blooming producing a stem that just pulls away later, but the flowers dry up and I still have the tiny but well developed leaves left on the end of the sturdy stem. Do I cut these stems away after the flowers die back? If so, where do I make the cuts? Thanks.
Hi Miss Linda,
You can cut away the stem entirely and trash it or you can grow a new violet from it! I put in a link with photos showing how to do that. Some violets that won't grow true from a leaf will do so from a sucker or blossom stem. I'm trying that for the first time right now myself and the stem is growing little roots.
Here is a link that might be useful: Propagation By Blossom Stems


text:
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Man convicted in 'Biden defense' gun case
Jeffrey Barton took the vice president's advice to fire shotgun blasts for protection.
Gun owners should support background checks
The priority of Congress should be to keep guns away from criminals. The best way to do this is by expanding criminal background checks.
The myth behind defensive gun ownership
Guns are more likely to do harm than good.
Gun-control supporters win in Wash.
About 60 percent of the state's voters support universal background checks for gun buyers.
2 die at Canada's Parliament
Officials identify the gunman as Michael Zehaf-Bibeau but gave no immediate details.
Gabby Giffords gets mean
Her frustration with lawmakers' failure to advance gun control is playing out in her 2014 efforts.
NRA goes big in key 2014 races
The gun rights group says it plans to spend big in the final weeks before the midterm elections.
Holder presses delay on Fast and Furious documents
The attorney general again asks the court to delay the transfer of disputed documents.
Guns 'R' Us
What a 9-year-old's Uzi accident tells us about gun rights in America.
What mass murderers are thinking
Once upon a time people thought I might be one, and I came to love the notoriety.
Six Flags sorry for shirt ban
The amusement park apologizes for not allowing in an ex-Marine with a rifle shown on his shirt.
Dem pushes Ferguson gun bill
The legislation would focus on stopping a program providing machine guns to law enforcement.
D.C. seeks stay of gun ruling
Motion raises specter of presidential assassinations
D.C. gun provision struck down
A ban on carrying handguns outside the home is unconstitutional, a federal judge rules.
Police: Man with gun tried to enter House office
The man, who is not a Capitol Hill employee, was carrying a 9mm Ruger.
Hill staffer denies guilt in gun case
A lawyer for U.S. Rep. Tom Marino's press secretary calls the gun incident unintentional.
Hill hopeful hosts 'ATF' fundraiser
Former NFL quarterback Andrew Walter offers supporters a chance to shoot guns at his event.
Scarborough slams Christie on guns
The governor says that it would be "hypocritical" to meet with Sandy Hook families.
Senate supports sportsmen bill
The package is a political boon to the host of red-state Democrats up for reelection.
Christie responds to gun veto critics
"I understand their argument, I hear their argument, I don't agree with their argument," he says.


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obe Abe's The Ruined Map has haunted me since I first read it over twenty years ago. The book, first published in Japan in 1967, has had a lingering, disquieting effect that has colored my fiction, and to some extent, my view of the world.
The story starts out traditionally enough in the vein of the hard-boiled detective story: a private investigator meets with a young, beer-swilling woman at her home. Her husband has been missing for six months, vanishing on his way to a train station to deliver some documents. All her efforts to find him, and those of her brother, have been futile. The only clue she presents is a book of matches from a local coffee shop.
Like most PIs, the nameless narrator tries to dissuade her from spending money she doesn't have looking for a man who likely ran off with a bar hostesses. She insists that he was really going to deliver documents, because he came back a few minutes after leaving to get a paper clip to secure them. The PI is not convinced it wasn't a ruse, and, watching her open another beer, starts to wonder about her motives.
The matchbox clue, of course, leads to other clues about the missing husband's life: blackmail, amateur pornography, and assorted illegal activities dealing with secondhand cars, fuel, and trucking. Along the way we encounter intriguing and repulsive characters at an automated sake bar where the blood sport is killing cockroaches, or at a nightly caravan of unlicensed food stalls that regularly turns violent, or at a "nude encounter" establishment. As the PI investigates, making copious written and mental notes on the case, he becomes entangled in the lives of those he investigates. Always a fatal mistake for a PI.
Kobo Abe (1924-1993) is best known for his 1962 Woman in the Dunes, made famous as much by the movie of the same title. Many of his stories deal with the theme of descent, sometimes in a physical sense (as in Woman, when the main character is tossed down into the bottom of a sand pit, and in The Ark Sakura, when the main character is held captive in an underground cavern), as well as psychological descent, as in The Ruined Map. Kobo Abe's work has become so entwined with my fiction sensibilities as to make it impossible not to be influenced by him at nearly every turn. I hope that is not a fatal mistake for a writer.
Like most aspiring writers, when I first started writing seriously I read many books on the fiction process, as if there were a magic formula. The only such book I have read more than once, and still go back to on occasion, is The Art of Fiction by John Gardner. It was in this book that I first heard of Kobo Abe's The Ruined Map. In his book, Gardner claimed that "All great writing is in a sense imitation of great writing." No matter how oddly constructed (and he put The Ruined Map in that category) or innovative, a great novel will leave the writer with the feeling of "that was a novel."
I read many of the books Gardner recommended based on that feeling: Under the Volcano, Moby Dick, those by Italo Calvino and John Fowles. But it was The Ruined Map that captured my imagination, and it is still the only novel I have read more than twice. My first reading of The Ruined Map was a couple of years before I went to Japan for the first time. Arriving there in the mid-80s to teach English and edit technical documents, the Japan I found most intriguing, most seductive, was the Japan in The Ruined Map.
The ancient soaring temples, the neonic urban landscapes, the beauty of the gardens and tea ceremony, did little for me. The Japan I wanted to find was that of dingy coffee shops with surly waitresses, tiny hole-in-the-wall joints serving sake and shochu (a grain alcohol), and food stalls set up under railroad tracks. I wanted to meet a few of the homeless men who lived in boxes. I wanted to run into urban street thugs and the occasional yakuza. And I did find that Japan--it wasn't hard--and that's what I reveled in during my stay.
Whenever I read The Ruined Map again, I find bits and pieces of the novel that have crept into my own fiction. Of course, when I was writing it, I don't recall that I consciously picked up Kobo Abe's world and dumped it in my fiction, rather it's become my world too. For example, in my novel The Fourth Treasure, one of the characters lives in an old, eccentric apartment building that has the same eerie feel of the wife's apartment in The Ruined Map. Also, one of the main characters is a private investigator who becomes entangled in the case of a missing calligraphy student (although he manages to avoid it being a fatal mistake.)
The ending of The Ruined Map is still somewhat mysterious to me, even after many readings. But I think a clue to the ending, which begins with a word-for-word repetition of the first page and a half of the very start of the novel, is found in the first chapter. The wife of the missing man tells the PI: "a single map for life is all you need…The world is a forest, a woods, full of wild beasts and poisonous insects. You should go only through places where everyone goes, places that are considered absolutely safe." But what if that map is ruined?
Upon finishing The Ruined Map, the feeling is always there: "that's a novel."
Todd Shimoda is the author of 365 Views of Mt. Fuji and The Fourth Treasure, forthcoming from Nan A. Talese/Doubleday in April 2002.


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Email Alerts
Five minute interview: Craig Whitney, Axway
MicroScope puts its questions to Craig Whitney, vice-president and managing director of Axway What is the best/worst advice you have received and from whom? Always have a 'plan B' – from a former manager. Stuff happens, so be prepared for it. Wh... News | 20 Oct 2009
HP warns datacentre budgets will take time to return
Those expecting a return to pre-recessionary ordering patterns from data centre customers might have to wait slightly longer than they were expecting. News | 16 Sep 2009
SAP reveals lax user attitude to data management
The mantra about IT being able to help businesses make the right decisions in recession has been embraced by users but is still not being acted on. News | 15 Jul 2009
Cloud backup positioned as SME headache solver
Although there has been some questions raised about the satisfaction levels surrounding SME customer experiences with the cloud those promoting backup services believe the market remains strong. News | 13 Jul 2009
ThinkGrid unveils cloud storage offering
Cloud specialist ThinkGrid has taken the wraps off a hosted storage service that provides a range of data tools that are designed to help those struggling to keep on top of their data. News | 06 Jul 2009
Disaster recovery plans failing to cover virtualised systems
Disaster recovery has climbed up the agenda in customerboardrooms but a more needs to be done to ensure that customers are taking thesafety of their data more seriously. According to the results of the latest Symantec disaster recovery survey thenumb... News | 03 Jul 2009
NetApp splashes out $1.5bn to pick up Data Domain
NetApp has put $1.5bn on the table to buy de-duplication specialist Data Domain as consolidation among storage vendors continues unabated. News | 21 May 2009
NetApp heralds mid market channel focus
NetApp has heralded its 1,000th reseller as evidence of its ability to service the mid market with its MSE product line. News | 07 Apr 2009
Hitachi GST builds division on Fabrik acquisition
Hitachi Global Storage Technologies has completed the acquisition of external storage specialist Fabrik to form the basis of a branded business division. Fabrik produces a range of products that provide external backup for both Mac and PC environmen... News | 06 Apr 2009
Cisco partners must skill up for data centre push
Cisco is urging partners to start skilling up to meet demand for its Unified Computing System (UCS), a new computing architecture launched yesterday that knits together compute, network, storage access and virtualisation into a modular system. News | 17 Mar 2009


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Activities and Examples: Using Data in the Classroom Today
This collection contains links to on-line activites for teaching STEM concepts with data of all types and examples that describe ways in which on-line, published, and student-collected data are currently used in teaching and learning.
This collection includes both data activities identified from across the web as well as a local example collection.
The initial example collection was created in collaboration with the Geological Society of America where the examples were given in a poster session "Using Data to Teach Earth Processes: An Illustrated Community Discussion" sponsored by the NAGT On the Cutting Edge program. We invite you to contribute additional examples in any of the STEM disciplines.
Each example includes a description of the activity, its learning goals, the context in which it is used, information on the needed data, tools, and activities and suggestions for evaluation.
Inquiry Level
Special Interest
- Student Selected Problem 2 matches
- Local Issue 11 matches
- Global/National Issue 16 matches
- Real-Time Data 11 matches
- Small Group 2 matches
- Quantitative 31 matches
- Computer-Based 28 matches
- GIS 13 matches
- Remote Sensing 2 matches
- Google Earth 3 matches
- Hazards 18 matches
- Visualization 23 matches
- Data, models, or simulations 39 matches
- Complex Systems 13 matches
- Field-Based Teaching and Learning 9 matches
- Geo2YC- OLD DO NOT USE 1 match
- 2YC 1 match
Results 21 - 30 of 195 matches
The Modern Atmospheric CO2 Record part of Starting Point-Teaching Entry Level Geoscience:Teaching with Data:Examples
Students compare carbon dioxide (CO2) data from Mauna Loa Observatory, Barrow (Alaska), and the South Pole over the past 40 years to help them better understand what controls atmospheric CO2. -
Calculating Pressures and Temperatures of Petrologic Events: Geothermobarometry part of Cutting Edge:Courses:Petrology:Teaching Examples
In this lab exercise, students examine one or more metamorphic rocks and use various approaches to estimating and calculating the pressure-temperature conditions at which the rocks equilibrated. The exercise ...
Harker Diagrams part of Integrating Research and Education:EarthChem:Compositional Diversity in Volcanic Suites
Kent Ratajeski Department of Earth Sciences, Montana State University, Bozeman, MT Published Oct. 26, 2004. Description In this exercise, students use whole-rock major- and trace-element compositions of volcanic ...
Global Temperatures part of Starting Point-Teaching Entry Level Geoscience:Teaching with Data:Examples
Students analyze the global temperature record from 1867 to the present. Long-term trends and shorter-term fluctuations are both evaluated. -
Carbon Dioxide Exercise part of Starting Point-Teaching Entry Level Geoscience:Interactive Lectures:Examples
Students work in groups, plotting carbon dioxide concentrations over time on overheads and estimating the rate of change over five years. -
Time Scales of Climate Change part of Cutting Edge:Rates and Time:Teaching Activities
This activity introduces students to the fact that climate change occurs at timescales of 1 year to 108 years and there are various drivers to explain these changes. It addresses how scientists detect these scales ...
Serpentine Seamounts in the Mariana Forearc: Shallow Material Releases from Downgoing Plates part of MARGINS Data in the Classroom:MARGINS Mini-Lessons
A set of maps, images and .kmz files for use in lectures and discussions on forearc serpentine volcanism in the Mariana subduction system.
Volcanoes Around the Globe part of Cutting Edge:Visualization:Examples
Undergraduate non-majors use the Arcview geographic information system (GIS) to explore volcanic hazards and the geochemistry of volcanic rocks. Students explore geochemical data from the GEOROC global database and ...
Geologic Structures Lab part of Cutting Edge:Introductory Courses:Activities
In class activity involving a thought exercise about rock rheology, discussion and drawing of simple brittle and ductile structures, and then reading an article about how the depth of the brittle-ductile transition ...
Exploring Seafloor Topography part of Earth Exploration Toolbook:Sea Floor
DATA: Digital Elevation Model Data. TOOL: GeoMapApp. SUMMARY: Explore a timeline about how we have learned about the oceans. Construct a profile across the Atlantic Ocean and create 3-D visualizations of the seafloor.


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White God
Imagine an "R" rated "Lassie" by way of "Spartacus." That's Kornél Mundruczó's "White God," a brutal but stirring fantasy about street dogs rising up against…
Imagine an "R" rated "Lassie" by way of "Spartacus." That's Kornél Mundruczó's "White God," a brutal but stirring fantasy about street dogs rising up against…
In this exuberant but ultimately simpleminded comedy, a car wash owner (Kevin Hart) helps a wimpy hedge fund manager (Will Ferrell) get ready for prison…
"The Ballad of Narayama" is a Japanese film of great beauty and elegant artifice, telling a story of startling cruelty. What a space it opens…
Patrice Leconte's "Monsieur Hire" is a tragedy about loneliness and erotomania, told about two solitary people who have nothing else in common. It involves a…
Chaz Ebert to be a guest at The Dinner Party in Chicago on April 6th.
A gallery of photos, videos and links illustrating Chaz's journey relating to Roger's legacy in the two years since his death.
Chaz Ebert to be a guest at The Dinner Party in Chicago on April 6th.
A gallery of photos, videos and links illustrating Chaz's journey relating to Roger's legacy in the two years since his death.
An FFC reviews Jodoroswky's The Dance of Reality.
Our Far-Flung Correspondent Brings Explosive Polish 1980s Sci-Fi to NYC
NBC's American Odyssey attempts to woo viewers who have given up on the networks for cable but it misses its mark.
The video of 2014's memorable "Remembering Roger" panel at Ebertfest.
Words like "disaffected," "distanced" and "deadpan" flew from my mind onto my note pad while I was watching "The Doom Generation." This is the kind of movie where the filmmaker hopes to shock you with sickening carnage and violent amorality, while at the same time holding himself carefully aloof from it with his style.
He would be more honest and probably make a better movie if he got down in the trenches with the rest of us.
There is an attitude in Gregg Araki's film that I've sensed in a lot of work recently: The desire by the filmmaker to have his cake and eat it, too. He wants to make a blood-soaked, disgusting, disturbing movie about characters of low intelligence and little personal worth, but he's not willing to cop to that, and so by giving them smarmy pop-culture references and nihilistic dialogue, and filling the edges of his frame with satirical in-jokes and celebrity walk-ons (Margaret Cho, Heidi Fleiss), he's keeping himself at arm's length. Hey, if we're dumb enough to be offended by his sleazefest, that's our problem; Araki is, you see, a stylist, who can use concepts like iconography and irony to weasel away from his material.
Note carefully that I do not object to the content of his movie, but to the attitude. Content is neutral until shaped by approach and style. This is a road picture about Amy and Jordan, young druggies who get involved with a drifter named Xavier who challenges their ideas about sex, both gay and straight, while involving them on a blood-soaked cross-country odyssey. The movie opens as the drifter "inadvertently" (Araki's word, in the press kit) blows off the head of a Korean convenience store owner. The head lands in the hot dog relish and keeps right on screaming. Ho, ho.
It continues as the "enigmatic Xavier" (I am again quoting from the wonderfully revealing press kit) "has such rotten karma that every time they stop the car for fries and Diet Cokes, someone ends up dying in one gruesome way or another." Wait, there's more: "As the youthful band of outsiders continues their travels through the wasteland of America, Amy finds herself (having sex with) both Jordan and Xavier, forging a triangle of love, sex and desperation too pure for this world." Now let's deconstruct that. (1) The correct word is "its," not "their." (2) "Band of outsiders" is an insider reference to "A Band Apart," the name of Quentin Tarantino's production company, which itself is a pun on the title of a film by Godard. (3) Is it remotely possible that America is a "wasteland" because Amy, Jordan and Xavier kill someone every time they stop for fries and a soda? That wouldn't have occurred to this movie. (4) The clause "someone ends up dying" is a passive way to avoid saying that the three characters kill them. This is precisely the same construction used by many serial killers and heads of state, who use language to separate themselves from the consequences of their actions.
Finally, (5) The notion that the threesome is "too pure for this world," which presumably gives them the right to kill store owners and other bystanders, is in its classic form pure fascist twaddle about the uebermensch or superman, whose moral superiority gives him the right to murder.
Araki may not have been thinking of Leopold and Loeb when he made his movie, but I was when I watched it.
Two of the best movies I've seen in recent years covered material similar to "The Doom Generation." They were "Kalifornia" and "Natural Born Killers." Both were about cross-country odysseys involving young lover; killers. Both dealt thoughtfully with their characters, and the consequences of their actions. Both had a point of view, and a moral position. "Bonnie and Clyde" (1967), Terence Malick's "Badlands" (1974) and both versions of "Gun Crazy" also had doomed young lovers on the run. All of these films were honest enough to be about what they were about - to acknowledge their subject matter.
But Gregg Araki has maybe seen too many movies, and is eager to have us know that he is above his subject matter. He's like the sideshow impresario whose taste is too good to enter his own tent.
For him, I recommend several viewings of "Henry: Portrait of a Serial Killer," a brilliant film that deals with a character very much like Xavier, and is not too shy to deal with him - to see him as he is, and accept the consequences.
Was I unfair to quote so liberally from the press kit? I used it because it praises the film so openly in terms that reveal its underlying dishonesty. Directors may not write their press kits, but they are responsible for them. Further reading from the kit: "The Doom Generation"' is the Alienated Teen Pic to End All Alienated Teen Pics - and, oh yeah, it's a comedy and a love story, too." Oh, yeah.
A film teacher looks back on "The Breakfast Club," partly through the eyes of her students.
The conversation about Woody Allen's personal and professional lives intertwining continues, but to what end?
As we mourn Abrams' macho Star Trek obliteration, it's a good time to revisit that most Star Trek-ian of accomplishme...
A piece on the use of animals in film in light of "White God".


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The Church Hill Free Medical Clinic will hold a fund-raiser at Leaping Lizards Family Entertainment Center Thursday, April 3. The event will be held from 4 to 7 p.m.Comments
A meditation on Colossians 1:9-10aComments
A meditation on Acts 9:17-18.Comments
In late October 1929, a group of 125 residents stood at a crossroads of faith and decided to organize a new church. Four years later, West View Park Methodist Episcopal Church South opened its doors.Comments
Valerie Elliott Shepard is the only daughter of Elisabeth and Jim Elliot, missionaries to the Quichua Indians of the Amazon jungle in Ecuador.Comments
A meditation on Psalm 146:3-4Comments
A meditation on John 9:25Comments
All camp operations were suspended in 2013, following flooding that destroyed accommodations and trails where many children from Kingsport and surrounding areas had spent their summers exploring and hiking.Comments
The video, recorded on an iPhone, lasts less than eight minutes. The message from Pope Francis to Pentecostals is simple: We're brothers despite our differences.Comments
A meditation on John 1:7.Comments


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A request for information ("RFI") by the U.S. Department of Labor ("DOL") was published on August 21, 2014 regarding the use of so-called "brokerage windows" under retirement plans, such as many Section 401(k) plans, that...more
We are a nation of over abundance and we should be grateful for that. The problem is that over abundance can lead to a life of excess. We are often told that more is more and the problem is that there are many times where...more
What makes a good retirement plan financial advisor? Well it takes an attention to detail, an understanding of what the role to entails, and a dedication to the client. In addition, what I find is the way a good financial...more
Any type of item that keeps you in health is a good thing as long as you use it. So the floss I bought after my last checkup and the exercise equipment that I bought my wife a few years ago that is collecting dust are...more
Now that some of the dust has settled on the U.S. Supreme Court's decision in U.S. v. Windsor, employers who haven't done so already should take immediate steps to review their retirement plan documents and administrative...more
The Fifth Circuit Court of Appeals held that a deferred compensation plan through which key employees received annual bonuses and were able to defer both bonuses and other income was an "employee pension benefit plan"...more
Employers that sponsor defined benefit qualified retirement plans benefiting only Puerto Rico employees should be aware that Pension Benefit Guaranty Corporation (PBGC) coverage may no longer apply. Last year, the PBGC...more
For the ESOP fiduciary of a publicly traded employer, the Supreme Court has made clear that non-public insider information is not required to be used in reaching a decision to buy, hold or sell employer securities....more
Now that the 2014-2015 Ontario budget has been passed by the Ontario legislature, Ontario employers should think about how the new Ontario Retirement Pension Plan (ORPP) could affect them.
The ORPP is part of the...more
Plan Sponsor Should Avoid These Retirement Plan Provider "Con Games".
Scams you should watch out for.
The George Clooney-Brad Pitt trilogy of heist films known as Ocean's Eleven, Ocean's Twelve, and Ocean's...more
A recurring scenario in ERISA litigation involves claims against fiduciaries of 401(k) retirement plans who are alleged to have breached their fiduciary duty by failing to discontinue investment in employer stock following a...more
Amending Retirement Plans to Recognize Same-Sex Marriages Plan sponsors need to review retirement plan documents and operations to determine whether changes are needed in response to last year's Supreme Court decision in U.S....more
A major reason that employee benefits, such as employer- provided healthcare and retirement plans, exist is that they provide a tax-advantaged way for an employer to provide additional compensation to an employee, her spouse,...more
We live in politically charged times. Congress seems unable to reach a consensus on anything, including where to have the annual congressional Christmas ball! Years of political crossfire over the Affordable Care Act have...more
HMRC's policy on reclaiming VAT on investment management and other costs remains under review in the light of two recent decisions from the Court of Justice of the European Union.
The first of these cases, PPG...more
To me, there is no greater television show than Seinfeld because it's timeless and there is something about each episode that reminds you of normal day life. In the reverse chronology episode set in India called "The...more
In 2006, the SEC adopted rules which created the Pension Benefits Table and Nonqualified Deferred Compensation Table to supplement the Summary Compensation Table. The tables mandate certain specific disclosures with respect...more
The Maine Supreme Judicial Court (Law Court) recently handed down an important ruling limiting the administrative authority of the Maine Public Employees Retirement System (MPERS). In Kennebec County v. Maine Public...more
The Issue: When an employer fails to take into consideration all forms of compensation (e.g., commissions, bonuses, etc.) for purposes of employee deferrals to its 401(k) Plan, is that a problem?...more
In This Presentation:
- Affordable Care Act
- Affordable Care Act: Fees and Taxes 2015 – Employer Shared Responsibility Fee
- Forms for Reporting Fees
- Retirement Plan Errors - Overview
- Retirement Plan...more
In This Presentation:
- Eligibility Errors
- Vesting Errors
- Compensation Errors
- Distribution Errors
- Loan Errors
- Testing Errors
- Other Errors and Things to Consider
Excerpt from...more
The Treasury Department and Internal Revenue Service ("IRS") have issued Notice 2014-9 (the "Notice") and related Frequently Asked Questions ("FAQs") providing much anticipated guidance on the application of the Supreme...more
''I would like to start receiving my retirement benefits now, but I would also like to keep working for a bit. Can I do this?'' Baby boomers pose this question to their employers on a routine basis. Unfortunately, there is no...more
The 2014 session of the Connecticut General Assembly has just concluded. The following is a cursory description of bills that were passed by the General Assembly that may be of interest. A more detailed summary of these...more
Retirement plan administrators routinely receive requests from employees to accept rollover contributions of amounts held in a prior employer's qualified plan or, in some cases, an IRA. When processing these requests, plan...more
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The Morning Ledger: Accounting, Governance Standards Improve in Africa
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Businesses in African nations are making strides in keeping better books and becoming more transparent to investors, with more recently adopting International Financial Reporting Standards, CFO Journal's Kimberly S. Johnson reports.
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Ask almost any of the CFOs who court investors in Europe, and they will tell you they have to tailor their company's story around their environmental, social and governance strategies.
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The Securities and Exchange Commission is embarking on a project to review corporate disclosures and may "rethink" the type of information companies release to investors, the agency's head said on Monday.
"I believe we should rethink not only the type of information we ask companies to disclose, but also how that information is presented, where and how that information is disclosed, and how we can take advantage of technology to facilitate investors' access to information and make it more meaningful to them," SEC Chair Mary Jo White said in comments to Securities Regulation Institute in California.
Corporate boards and institutional investors have very different views about how well the U.S. executive pay model is working, but neither group thinks a pay-ratio disclosure rule for chief executives will help.
The clock is ticking on the R&D tax credit, and businesses have no way of knowing if it will be renewed. The perpetual uncertainty around the credit is pushing some companies to shift research overseas and making it harder for smaller firms to compete with larger rivals, writes Emily Chasan in today's Marketplace section. Lawmakers "play chicken with it," says Dell CFO Brian Gladden. "What companies do is they make decisions based on an assumption that it's not going to happen."
Activist hedge fund Starboard Value LP said in a federal filing that it on Wednesday filed a complaint in Delaware Court of Chancery that seeks to force Office Depot Inc. to hold an annual meeting, at which it hopes to replace some of the Office Depot board of directors with its own candidates.
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Corporate governance advocates have taken more strides to eliminate staggered elections of directors at large companies this year.
Through August, at least 27 companies in the Standard & Poor's 500-stock index have declassified their boards following shareholder approval of management proposals, according to Shareholder Rights Project, a clinical program being conducted at Harvard Law School that advocates on behalf of six institutional investors, including state pension funds. The management proposals were secured through negotiated agreements between the companies and investors aided by SRP, the group said.
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Kevin Harvick, Kyle Busch punished
Updated: May 11, 2011, 8:06 PM ETBy David Newton | ESPN.com
CONCORD, N.C. -- Kevin Harvick and Kyle Busch were placed on four weeks' probation and fined $25,000 Tuesday for their pit road confrontation following Saturday night's Sprint Cup race at Darlington Raceway.
Harvick tweeted about his penalty, and officials from Kevin Harvick Inc., confirmed the punishment Tuesday.
Both drivers are on probation in all three of NASCAR's series -- Sprint Cup, Nationwide and Camping World Truck -- until June 15.
"We have to maintain ...
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