Dispersive stabilization of the inverse cascade for the Kolmogorov flow

TL;DR

This paper demonstrates that Rossby wave dispersion stabilizes the inverse cascade in Kolmogorov flow, challenging traditional theories and showing the largest scale depends logarithmically on beta.

Contribution

It reveals how dispersive Rossby waves halt the inverse cascade in Kolmogorov flow, providing new insights into flow stabilization mechanisms.

Findings

Inverse cascade is halted by Rossby wave dispersion.

Largest excited scale scales with logarithm of 1/beta.

Standard phenomenology does not predict this scale behavior.

Abstract

It is shown by perturbation techniques and numerical simulations that the inverse cascade of kink-antikink annihilations, characteristic of the Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted by the dispersive action of Rossby waves in the beta-plane approximation. For beta tending to zero, the largest excited scale is proportional to the logarithm of one over beta and differs strongly from what is predicted by standard dimensional phenomenology which ignores depletion of nonlinearity.