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Spectra and distribution functions of stably stratified turbulence

Presented by: 
J Herring [N.C.A.R.]
Thursday 11th December 2008 -
14:00 to 14:30
INI Seminar Room 1
We consider homogeneous stably stratified turbulence both decaying and randomly forced cases. Our tools include direct numerical simulations (DNS) and elements of statistical theory as expressed by two-point closures. Our DNS--at $1024^3$--permits a large scales Taylor micro scale $R_{\lambda}\sim 300$ The size distribution of such large scales is closely related to conservation principles, such as angular momentum, energy, and scalar variance; and we relate these principles to our DNS results. Stratified turbulence decays more slowly than isotropic turbulence with the same initial conditions. We offer a simple explanation in terms of the diminution of energy transfer to small scales resulting from phase-mixing of gravity waves (Kaneda 1998). Enstrophy structures in stratified flows (scattered pancakes) are distinctly different from those found from isotropic turbulence (vortex tubes), and we show examples of the transition from isotropic turbulence enstrophy structures to those of strongly stratified turbulence. We discuss briefly changes in the probability distribution functions for velocity and vorticity for stratified turbulence concluding that stratification induces a return towards Gaussianity for these quantities. For the forced case, we examine the modification of the inertial range induced by strong stratification ($k_{\perp}^{-5/3}\rightarrow \sim k_{\perp}^{-2}$) for the wave component, and ($k_{\perp}^{-5/3}\rightarrow\sim k_{\perp}^{-3}$) for the vortical component. Here, $k_{\perp}$ is the horizontal wave number. These DNS findings are discussed from the perspective of two-point closure.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons