Titre/Title : Vertical spectra of stratified turbulence at large horizontal scales
Contact : Pierre Augier (Equipe MEIGE)
Résumé/Abstract : In recent years, a consistent theory of strongly stratified turbulence, mainly based on scaling analysis, has emerged. This theory allows us to predict the vertical length scale of the characteristic layers of stratified turbulence and the energy spectra in the horizontal and vertical direction. In this work, I look at the reasons why vertical energy spectra measured in direct numerical simulations (DNS) are actually in disagreement with the prediction from this theory. To do this, I use a scale decomposition of the vertical spectrum into a large-scale vertical spectrum E_large(k_v) and a small-scale vertical spectrum E_small(k_v), based on a spectral cut-off filter at a certain horizontal wavenumber. A similar method allows the velocity field to be decomposed in a large-scale part u_large(x,y,z) and a small-scale part u_small(x,y,z) (see Figure). The decomposition was applied to DNS of stratified turbulence with forcing and it was found that E_large(k_v) is in very good agreement with the theoretical prediction. The reason for the discrepancy of the full vertical spectrum E(k_v) = E_large(k_v) + E_small(k_v) with this prediction is that the small scales are aliased onto the full spectrum at moderate wavenumbers, which should correspond to large scales. By filtering out the small scales we therefore recover the theoretical form and we find results that are also in good agreement with ocean measurements. This work reconciles theory and numerical simulations of strongly stratified turbulence and may provide a way to interpret observations of ocean turbulence.
