Title: Revisiting the quest for a universal log-law and the role of pressure gradient in "canonical" wall-bounded turbulent flows,
Abstract: The trinity of so-called "canonical" wall-bounded turbulent flows, comprising
the zero pressure gradient turbulent boundary layer, abbreviated ZPG TBL,
turbulent pipe flow and channel/duct flows has continued to receive intense
attention as new and more reliable experimental data have become available.
Nevertheless, the debate on whether the logarithmic part of the mean velocity
profile, in particular the Kármán constant $\kappa$, is identical for these
three canonical flows or flow-dependent is still ongoing. In this paper, which
expands upon Monkewitz and Nagib (24th ICTAM Conf., Montreal, 2016), the
asymptotic matching requirement of equal $\kappa$ in the log-law and in the
expression for the centerline/free-stream velocity is reiterated and shown to
preclude a single universal log-law in the three canonical flows or at least
make it very unlikely. The current re-analysis of high quality mean velocity
profiles in ZPG TBL's, the Princeton "Superpipe" and in channels and ducts
leads to a coherent description of (almost) all seemingly contradictory data
interpretations in terms of TWO logarithmic regions in pipes and channels: A
universal interior, near-wall logarithmic region with the same parameters as in
the ZPG TBL, in particular $\kappa_{\mathrm{wall}} \cong 0.384$, but only
extending from around $150$ to around $10^3$ wall units, and shrinking with
increasing pressure gradient, followed by an exterior logarithmic region with a
flow specific $\kappa$ matching the logarithmic slope of the respective
free-stream or centerline velocity. The log-law parameters of the exterior
logarithmic region in channels and pipes are shown to depend monotonically on
the pressure gradient.