Which Internal Waves are Excited by Turbulent Flows?

Many geophysical and astrophysical fluids, including planetary atmospheres, stars and oceans, have turbulent flows adjacent to stably-stratified fluid layers. Because internal waves in stably-stratified fluids can drive large-scale flows, increase scalar mixing and are sometimes easier to observe than turbulent motions, two important questions for these fluids are: How much energy goes from the turbulence into internal waves in the stable layer? What kind of waves are generated most efficiently (i.e. what wavenumbers and frequencies)?

In this talk we will answer these two questions by presenting a theoretical prediction for the energy flux spectrum of internal waves generated by adjacent turbulent convection and comparing it with results from 3D direct numerical simulations (DNS) of a generic convective--stably-stratified fluid model. We will show that DNS and theory agree well for the range of strong turbulence-strong stratification parameters tested, giving some confidence in the analytical expression for the energy flux spectrum of the waves. Our results should help estimate the effects that internal waves have on the dynamics and evolution of geophysical and astrophysical fluids.