Evidence of the Zakharov-Kolmogorov spectrum in numerical simulations of inertial wave turbulence

TL;DR

This study uses direct numerical simulations to demonstrate that inertial wave turbulence in rotating flows follows the Zakharov-Kolmogorov spectrum, confirming wave turbulence theory's applicability in three-dimensional anisotropic turbulence.

Contribution

It provides numerical evidence that inertial wave turbulence in rotating flows adheres to the Zakharov-Kolmogorov spectrum, highlighting bi-stability depending on initial conditions.

Findings

Inertial wave turbulence follows the Zakharov-Kolmogorov spectrum.

Flow can exhibit either geostrophic or wave turbulence based on initial conditions.

Numerical simulations confirm wave turbulence theory for 3D anisotropic flows.

Abstract

Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a downscale energy cascade. In this letter, we investigate the statistical properties of three-dimensional rotating turbulence by the means of direct numerical simulations in a triply periodic box where geostrophic vortices are specifically damped. The resulting turbulent flow is an inertial wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived analytically by Galtier (Phys. Rev. E, 68, 2003), thus offering numerical proof of the relevance of wave turbulence theory for three-dimensional, anisotropic waves. Lastly, we show that the same forcing leads to either geostrophic or wave turbulence depending on the initial condition. Our results thus bring further evidence for bi-stability in rotating turbulent flows.