Anisotropic constraints on energy distribution in rotating and stratified turbulence

¹  Theoretical Division, Los Alamos National Laboratory - Los Alamos, NM 87545, USA
²  Computer and Computational Sciences Division, Los Alamos National Laboratory - Los Alamos, NM 87545, USA
³  Exploratory Simulations Technologies, Sandia National Laboratories - Albuquerque, NM 87185, USA

Corresponding author: skurien@lanl.gov

Received: 27 March 2008
Accepted: 8 September 2008

Abstract

It is shown that for Boussinesq flows in which rotation and stratification are equally strong, the forward cascade of potential enstrophy constrains the spectral distribution of horizontal kinetic energy and potential energy. Horizontal kinetic energy is suppressed in the smallaspect-ratio wave modes, and potential energy in suppressed in the largeaspect-ratio wave modes. Scaling estimates based on phenomenological arguments yield scaling of k_h^{- 3} and k_z^{- 3}, respectively, of the two spectra. High-resolution numerical simulations of the Boussinesq equations in the relevant parameter regimes show spectral scaling exponent closer to - 4, and hence even stronger suppression than is predicted by dimensional estimates.