Numerical simulations of freely evolving turbulence in stably stratified fluids

Abstract

Results of direct numerical simulations of stably stratified, freely evolving, homogeneous turbulence are presented. An examination of initial data designed to give insight into laboratory flows suggests that the numerical simulations have a satisfactory degree of realism, insofar as statistical parameters such as total energy and length scales are concerned. The motion is decomposed into a stratified turbulence (vortical) component and a wave component. For initial-value problems similar to laboratory studies of stratified flows, the vortical component decays at a rate virtually identical to that of the non-buoyant case up to t = 6N−1 (N is the Brunt-Väisälä frequency). The decay rate decreases after this time, suggesting a kind of turbulence ‘collapse’. The temperature structure that emerges clearly shows the development of the collapse stage of the flow, which is also diagnosed by the behaviour of parameters such as the Thorpe scale.We next examine the very small-Froude-number regime in order to understand possible universal aspects of the flow. An examination of various initial conditions with different proportions of stratified and wave components indicates a lack of universality. For initial data containing only vortical motion (motions derived from the vertical vorticity field), the vortical field tends to dominate, in subsequent evolution, at strong stratification. However, contrary to two-dimensional turbulence, the flow is more strongly dissipative than two-dimensional flows due to the frictional effect associated with layering. Other quantities examined are frequency spectra, and the probability distribution for vertical shear. The frequency spectra exhibit some features in common with spectra extracted from oceanographic data.