Abstract and subjects
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–Väisälä frequency to the Coriolis frequency. The parameter ranges
$0<N<f$
, domain aspect ratio
$1\leqslant \unicode[STIX]{x1D6FF}_{d}\leqslant 32$
and Burger number
$Bu=\unicode[STIX]{x1D6FF}_{d}N/f\leqslant 1$
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
$n$
th-order spectral moments in both horizontal and vertical directions, for integer
$n\leqslant 3$
. In flows with linear potential vorticity, the horizontal vortical length scale
$L_{0}$
, characterizing a typical width of columnar structures, grows as
${\sim}(N/f)^{1/2}$
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
$\unicode[STIX]{x1D6FF}_{0}$
asymptotes to a scaling of
${\sim}(N/f)^{-1}$
, in agreement with quasi-geostrophic estimates. In contrast, the
$\unicode[STIX]{x1D6FF}_{0}$
in tall-aspect-ratio domain flows yields a decay rate of at most
${\sim}(N/f)^{-1/2}$
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.