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

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.

Locality of triad interaction and Kolmogorov constant in inertial wave turbulence

“…Next, neglecting the parallel energy flux, we provide an estimate of the Kolmogorov constant that could be verified by direct numerical simulation or experimentally. Our study completes that carried out by Galtier (2003) and provides theoretical support for recent numerical and experimental studies where energy spectra consistent with the prediction of inertial wave turbulence theory have been reported (Le Reun et al 2020;Monsalve et al 2020;Yokoyama & Takaoka 2021).…”

Three-dimensionality of the triadic resonance instability of a plane inertial wave

“…An important consequence of our results concerns flows in the wave turbulence regime (at larger Reynolds number than the ones considered here) [28,30]. One of the key assumptions made when deriving the scaling laws for the spatial energy spectrum from the kinetic equations in weak inertial-wave turbulence theory [33] is the statistical axisymmetry of the flow around the rotation axis.…”

“…In this context, wave turbulence theory (WTT), which addresses the statistical properties of weakly nonlinear ensembles of waves in large domains [24][25][26], stands as an interesting direction for improving turbulence parametrizations in coarse atmospheric and oceanic models [27]. This is particularly the case since several recent studies have given credence to the WTT framework for inertial waves in experiments [28] and in numerical simulations [29,30] as well as for internal gravity waves in experiments [31,32].…”

Three-dimensionality of the triadic resonance instability of a plane inertial wave

“…In this context, Wave Turbulence Theory (WTT), which addresses the statistical properties of weakly nonlinear ensembles of waves in large domains [24][25][26], stands as an interesting direction for improving turbulence parametrizations in coarse atmospheric and oceanic models [27]. This is particularly the case since several recent studies have given credence to the WTT framework for inertial waves in experiments [28] and in numerical simulations [29,30] as well as for internal gravity waves in experiments [31,32].…”