Stably-Stratified
and Unstably-Stratified Quasigeostrophic Flows
Keith Julien
University of Colorado
It is well known the numerical
simulations of rotationally constrained fluids are unable to reach the
parameter values, both in terms of Rossby number and Reynolds number, characteristic
of geophysical flows. Indeed, the
former compounds the prohibitive temporal and spatial restrictions placed on
high-Re simulations through the presence of high frequency inertial waves and
the development of (Ekman) boundary layers. This has motivated the development
of reduced pde's that filter fast waves and relax the need to resolve boundary
layers.
Recently we have derived such pde's for the case of thermal
convection in the presence of upright rotation. However, this formulation
cloaks a true comparison with the reduced description for stably stratified dynamics
(namely, the stably-stratified quasi- geostrophic equations). It is shown that
the key parameter that distinguishes these limits is aspect ratio defining the
degree of spatial anisotropy between characteristic and vertical scales.
Varying this parameter naturally leads to a hierarchy of reduced pde's for slow
rotational constrained dynamics valid on the f-plane. Solutions in this regime
are discussed, as well as the possibility of coupling of the extreme limits of
stably-stratified and unstably-stratified regimes.