On the energy spectrum of rapidly rotating forced turbulence

TL;DR

This paper uses numerical simulations to analyze the energy spectrum of rapidly rotating turbulence, revealing exponential decay at small scales and anisotropic power-law behavior at larger scales, consistent with wave turbulence theory.

Contribution

It models the energy spectrum of rotating turbulence, demonstrating exponential decay at small scales and anisotropic power-law scaling at larger scales, aligning with weak inertial-wave turbulence predictions.

Findings

Energy spectrum follows exponential decay for high wavenumbers.

Anisotropic power-law scaling observed at large scales.

Results agree with weak inertial-wave turbulence theory.

Abstract

In this paper, we investigate the statistical features of the fully developed, forced, rapidly rotating, {turbulent} system using numerical simulations, and model {the} energy {spectrum} that {fits} well with the numerical data. Among the wavenumbers ($k$) larger than the Kolmogorov dissipation wavenumber, the energy is distributed such that the suitably non-dimensionized energy spectrum is ${\bar E}({\bar k})\approx \exp(-0.05{\bar k})$, where overbar denotes appropriate non-dimensionalization. {For the wavenumbers smaller than that of forcing, the energy in a horizontal plane is much more than that along the vertical rotation-axis.} {For} such wavenumbers, we find that the anisotropic energy spectrum, $E(k_\perp,k_\parallel)$ follows the power law scaling, $k_\perp^{-5/2}k_\parallel^{-1/2}$, where `$\perp$' and `$\parallel$' respectively refer to the directions perpendicular and parallel to the rotation axis; this result is in line with the Kuznetsov--Zakharov--Kolmgorov spectrum predicted by the weak inertial-wave turbulence theory for the rotating fluids.