Characteristic length scales of strongly rotating Boussinesq flow in variable-aspect-ratio domains

摘要

We quantify the variability of the characteristic length scales of isotropically forced Boussinesq flows with stratification and frame rotation, as functions of the ratio N / f of the Brunt-Vaisala frequency to the Coriolis frequency. The parameter ranges 0 N f, domain aspect ratio 1 = delta(d) = 32 and Burger number Bu = delta N-d / f = 1 are explored for two values of f, one resulting in linear potential vorticity and the other in nonlinear potential vorticity. Characteristic length scales of the wave and vortical linear eigenmodes are separately quantified using nth-order spectral moments in both horizontal and vertical directions, for integer n = 3. In flows with linear potential vorticity, the horizontal vortical length scale L-0, characterizing a typical width of columnar structures, grows as similar to (N / f)(1/2) at all orders of n, regardless of domain aspect ratio. In unit-aspect-ratio domains, when intermediate scales are measured by filtering out the largest scales and using higher-order moments n 1, the vortical-mode aspect ratio delta(0) asymptotes to a scaling of similar to N /f)(-1), in agreement with quasi-geostrophic estimates. In contrast, the delta(0) in tall-aspect-ratio domain flows yields a decay rate of at most similar to(N /f )(-1/2) after large-scale filtering. Flows with nonlinear potential vorticity display consistently weaker dependence of the characteristic scales on N / f than the corresponding ones with linear potential vorticity. The wave-mode aspect ratios for all flows are essentially independent of N / f. We highlight the differences of these flow structure scalings relative to those expected for quasi-geostrophic flows, and those observed in strongly stratified, non-quasi-geostrophic flows.