Stably-Stratified and Unstably-Stratified Quasigeostrophic Flows
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.