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

¹ Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE UMR 7342 - Marseille, France
² DAMTP, University of Cambridge - Wilberforce Road, Cambridge CB3 0WA UK

Received: 21 September 2020
Accepted: 16 November 2020

Abstract

Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo an 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 (Galtier S., Phys. Rev. E, 68 (2003) 015301), 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 conditions. Our results thus bring further evidence for bi-stability in rotating turbulent flows at low Rossby numbers.