We consider the budget of turbulent kinetic energy (TKE) in stably stratified flows. TKE is generated by velocity shear, then partially converted to potential energy, but basically cascades towards very small eddies and dissipates into heat. The TKE dissipation rate is vital for comprehending and modelling turbulent flows in geophysics, astrophysics, and engineering. Until now its dependence on static stability remained unclear. We define it theoretically and validate against experimental data.

The objective of this paper is to study the dynamics of turbulence near a pycnocline, both in the free regime and under the action of an internal wave (IW) propagating along a pycnocline by direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer above the pycnocline. The DNS results show that turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW, and most of the TKE is localized in the vicinity of the pycnocline.