A general theory for stratified wakes
Résumé
The stratification of the ocean and the atmosphere plays a major role in geophysicalflows (wakes of mountains, islands or sea-mounts) and in nautical applications(wakes of submarines) since it largely modifies the late stages of the wake. Althoughseveral experiments1,2 and numerical simulations3,4,5 described in detail the evolutionof the wake and found empirical scalings for the decaying laws, there has beenno theory predicting the characteristics of a stratified wake.Here, we extend the model of a self-preserved non-stratified wake to the case of astratified fluid, by assuming that the wake expands in the horizontal direction due toan eddy diffusivity (which was derived from experimental results) and in the verticaldirection due to viscous diffusion. The mean characteristics of the wake (wake heightand width, velocity defect) are derived analytically, and show a good agreement withthe previous empirical results (see figure1). The three regimes from the literature arerecovered and two new regimes are discovered. These results are valid for any bluffbody once its momentum thickness is known, and can thus be directly applied togeophysical and nautical applications.