Nonequilibrium Continuous Transition in a Fast Rotating Turbulence

TL;DR

This paper investigates a critical transition in fast rotating turbulence from coherent two-dimensional states to three-dimensional states, revealing a non-mean-field critical exponent and on-off intermittency through DNS and stability analysis.

Contribution

It identifies a nonequilibrium continuous transition in rotating turbulence and characterizes its critical behavior using direct numerical simulations and a reduced linear stability model.

Findings

Transition exhibits critical scaling with a non-mean-field exponent.

Critical rotation rate scales linearly with forcing wave number.

Reduced linear stability model agrees with DNS results.

Abstract

We study the saturation of three-dimensional unstable perturbations on a fast rotating turbulent flow using direct numerical simulations (DNSs). Under the effect of Kolmogorov forcing, a transition between states dominated by coherent two-dimensional modes to states with three-dimensional variations (quasi-two-dimensional) is observed as we change the global rotation rate. We find this akin to a critical phenomenon, wherein the order parameter scales with the distance to the critical point raised to an exponent. The exponent itself deviates from the predicted mean field value. Also, the nature of the fluctuations of the order parameter near the critical point indicate the presence of on-off intermittency. The critical rotation rate at which the transition occurs exhibits a linear scaling behaviour with the forcing wave number. A reduced model based on linear stability analysis is used to find the linear threshold estimates; we find these to be in good agreement with the 3D nonlinear DNS results.