D.N. Straub, K. Ngan & P. Bartello
Growth and saturation of 3d perturbations to decaying 2d turbulence in a homogeneous fluid is considered as a function of domain (vertical-to-horizontal) aspect ratio. Scaling arguments and numerical simulations are used to suggest that the horizontal pressure gradient plays a relatively minor role in growth of the 3d perturbations. The growth mechanism is analogous to that for material line elements embedded in a turbulent 2d flow and can be thought of as similar to hyperbolic instability, with the caveat that the 2d base state is time dependent. Consistent with a simple scaling argument, perturbations are found to saturate at a level proportional to the aspect ratio. Similarly, feedback of the 3d modes on the 2d base state is also proportional to the domain aspect ratio. Possible implications of these ideas to energy transfers between geostrophic turbulence and near-inertial oscillations is also discussed.