Abstract

Energy spectrum for forced stably stratified turbulence is investigated numerically by solving the 3D Navier-Stokes equations under the Boussinesq approximation with stochastic forcing applied to the largest velocity scales. Using pseudo-spectral simulations with 1024^{3 grid points, we could verify the transition in the vortex (horizontal) spectrum (as a function of horizontal wave number) from $k_{perp}}{-3}$ to $k_{perp}^{$. Meanwhile the wave spectra shows $k_{perp}}{-2}$ for the large scales, and $k_{perp}^{$ for the small scales. According to Carnevale {it et._{al.}, the transition wave number is understood as the Ozmidov scale with a correction by the coefficients of the buoyancy spectrum, $E(k) =lpha N}}2k^{$, and the Kolmogorov spectrum, $E(k)=C_Kpsilon}{2/3} k^{$. By equating these spectra, $k_b im (lpha/C_K)}{3/4} qrt {N^{3/ psilon}$ is obtained for the transition wavenumber. Our calculation shows, however, that the vortex spectra at large scales seem to have the same slope irrespective of stratification, which implies a possibility of a different mechanism for producing the $k_{perp}}{-3}$ spectrum. We will discuss possibility that the spectrum corresponds to two-dimensional turbulence.

Referece: Carnevale,G.F. {it et.al}: 2001 J.~Fluid Mech. {f 427} 205—239.