Locality of triad interaction and Kolmogorov constant in inertial wave turbulence

TL;DR

This paper investigates the locality of triad interactions and estimates the Kolmogorov constant in inertial wave turbulence, confirming the validity of the anisotropic KZ spectrum and analyzing energy flux contributions.

Contribution

It establishes the locality conditions for the kinetic equation solutions and confirms the anisotropic KZ spectrum's validity in rotating fluid turbulence.

Findings

The anisotropic KZ spectrum satisfies locality conditions.

Parallel energy flux interactions can be negative, transverse interactions are positive.

Estimated Kolmogorov constant is approximately 0.749.

Abstract

Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (2003), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic Kolmogorov-Zakharov (KZ) spectrum satisfies these conditions, which justifies the existence of this constant (positive) energy flux solution. Although a direct cascade is predicted in the transverse ($\perp$) and parallel ($\parallel$) directions to the rotation axis, we show numerically that in the latter case some triadic interactions can have a negative contribution to the energy flux, while in the former case all interactions contribute to a positive flux. Neglecting the parallel energy flux, we estimate the Kolmogorov constant at $C_K \simeq 0.749$. These results provide theoretical support for recent numerical and experimental studies.