Turbulence-mean field interactions and layer formation in a stratified fluid

✍ Scribed by Martin Galmiche; J.C.R Hunt; O Thual; P Bonneton

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 100 KB
• Volume: 20
• Category: Article
• ISSN: 0997-7546
• DOI: 10.1016/s0997-7546(01)01127-x

✦ Synopsis

We briefly review some recent numerical and theoretical results on turbulence-mean field interactions in stratified turbulent flows. Results from direct numerical simulations are presented. In these simulations, turbulence decay in a stably-stratified fluid is investigated with a pseudo-spectral numerical code solving the fully non-linear Navier-Stokes equations under the Boussinesq approximation with periodic boundary conditions. The flow is decomposed into a turbulent field and a horizontal mean flow u(z, t) defined as the average of the horizontal velocity component in a horizontal plane at height z and time t. Similarly, the density field is decomposed into a turbulent field and a (stable) mean density profile ρ(z, t) defined as the average of the density field in a horizontal plane at height z and time t. Attention is paid to the effect of the turbulent velocity field on an initial z-periodic horizontal mean flow or an initial z-periodic perturbation of the mean density profile. The results show that the turbulence-mean field interactions are strongly affected by the buoyancy forces: when a strong stratification is applied, the perurbations in the mean profiles tend to grow, which accounts for the tendency of stratified turbulence to form horizontal layers.

The linear processes involved in these turbulence-mean field interactions are briefly discussed using a slightly non-homogeneous version of the Rapid Distortion Theory. The results of the linear model show that in the first stage of decay of turbulence, the eddy viscosity and diffusivity take negative values when the flow is subject to a strong stable stratifcation. These conclusions are in good agreement with the results from direct numerical simulation for short time.

We conclude that the linear processes play a significant role in these turbulence-mean field interactions and are widely involved in the formation of horizontal layers in stratified geofluids such as oceans and atmospheres.  2001 Éditions scientifiques et médicales Elsevier SAS * Correspondence and reprints.