Scaling of high-wavenumber energy spectra in the unit aspect-ratio rotating Boussinesq system

TL;DR

This paper investigates the small-scale energy spectra in high-Reynolds-number rotating Boussinesq flows, revealing how potential enstrophy influences spectral scaling and energy transfer anisotropy through numerical simulations.

Contribution

It introduces a non-dimensional parameter Gamma to analyze the suppression of energy transfer modes and validates the spectral scaling laws using high-resolution numerical simulations.

Findings

Potential enstrophy suppresses certain energy transfer modes depending on Gamma.

Spectral scaling of energy follows a -5 power law under specific conditions.

Empirical evidence supports joint energy and potential enstrophy transfer with constrained spectral scaling.

Abstract

Phenomenological and numerical studies of the small scale spectra of energy are presented for high Reynolds number rotating Boussinesq flows in unit aspect-ratio domains. We introduce a non-dimensional parameter Gamma such that when the potential vorticity is nearly linear in the dynamical variables, we deduce that for Gamma much less than 1, the potential enstrophy suppresses the transfer of horizontal kinetic energy into wavemodes with large horizontal component k_h while forcing it to become independent of vertical wavevector component k_z, scaling as k_h^{-5}. When Gamma much greater than 1, the potential enstrophy suppresses the transfer of potential energy into the wavemodes with large vertical component k_z while forcing it to become independent of k_h, scaling as k_z^{-5) power. Spectra computed from high-resolution simulations of the Boussinesq equations with isotropic low-wavenumber forcing are used to explore such anisotropic constraints on the energy and provide a posteriori justification for the joint flux ansatz used to obtain the (-5) scaling exponent. In all cases the empirical evidence points to both energy and potential enstrophy being jointly transferred downscale with the spectral scaling of the the former constrained by the latter.