## Generalized Quasi-geostrophy for Spatially Anisotropic Rotationally Constrained Flows: Non-Hydrostatic Flows

#### Keith JulienUniversity of Colorado, Boulder

By Ketih Julien, Edgar Knobloch, Ralph Milliff and Joseph Werne.

Large-scale geophysical flows often exhibit balanced motions that reflect an
underlying reduced dynamic contained within the primitive equations. The
identification of reduced equations that accurately capture these balanced
motions can offer dramatic theoretical and computational advantages over the
primitive equations and a greater understanding in probing large-scale flows.
A classic example is provided by the quasigeostrophic equations for
rotationally constrained flows where high-frequency, spatio-temporal,
inertial-gravity waves are filtered.

In this talk closed reduced equations analogous to the QGE are derived in the
extratropics for small Rossby numbers and vertical scales comparable to or much
larger than horizontal scales. On these scales significant vertical motions are
permitted an found to couple to balanced geostrophic dynamics. These equations
are located by a systematic exploration of different aspect ratio, Froude
numbers and bouyancy numbers. Results from numerical simulations will also be
presented.

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