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Center for Nonlinear Studies |
Synoptic scale ocean and atmospheric motion is often considered to be approximately balanced, with quasigeostrophy being the simplest balance approximation. Balanced flows have the property that they do not cascade energy forward to small scales and as such, 2d flow can be thought of as similar to balanced flow. This motivates us to consider three-dimensionalization of 2d turbulence. In a thin aspect ratio homogeneous fluid, we find 3d perturbations grow exponentially by a "pressureless" mechanism. The perturbations saturate at a level determined by the (vertical-to-horizontal) aspect ratio, with thinner flows corresponding to lower saturation levels. The net effect is a slow drain of energy from the 2d flow. In rotating-stratified flow, clearly identifying a "balanced" and "unbalanced" part of the flow is more problematic. We choose to decompose the field into its linear vortical and gravity wave modes since vortical modes would correspond to balanced (QG) motion in the small Rossby and Froude number limits. In turbulent simulations, we find a transfer of energy from the vortical modes high vertical wavenumber gravity wave modes. This is associated with a forward energy cascade and damping of the large scale vortical motion and we speculate that such transfers may be important in global energy balances.
Host: Balu Nagida