HRT

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 $k_{\perp}^{-5/3}$. Meanwhile the wave spectra shows $k_{\perp}^{-2}$ for the large scales, and $k_{\perp}^{-5/3}$ 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, $E(k) =\alpha N^2k^{-3}$, and the Kolmogorov spectrum, $E(k)=C_K\epsilon^{2/3} k^{-5/3}$. By equating these spectra, $k_b \sim (\alpha/C_K)^{3/4}\sqrt {N^3/ \epsilon}$ 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. {\bf 427} 205--239.