The buoyancy flux from internal gravity wave breaking

Abstract

The role of vertical buoyancy flux, i.e., the cross-spectrum between vertical velocity and buoyancy fluctuations, plays a highly controversial role in different theories concerning the breakdown from internal gravity waves to smaller-scale turbulence. One line of thought is that the buoyancy flux is primarily responsible for suppressing turbulence by converting kinetic energy to gravitational potential energy. An opposite line of thought is that the buoyancy flux plays no significant role in the energetics of the internal wave breakdown. Theoretical calculations following these two views yield almost the same predictions for spectra of velocity and buoyancy variance. Therefore observations of spectra are unable to distinguish between these nearly antithetical theories. Numerical simulation experiments, both in a 2-D (vertical planar) geometry and in 3-D, help to clarify some issues. It is shown that buoyancy flux is systematically down-gradient on length scales larger than local overturning but that internal wave breaking tends to induce counter-gradient (restratifying) flux on shorter scales. This character of the buoyancy flux is due (arguably!) to differences in the efficiency with which nonlinear processes transfer buoyancy and velocity variances across scales. Only for sufficiently intense turbulence is the buoyancy flux down-gradient at all scales. A very practical consequence of the differences between theories is that methods to estimate vertical transport from observed spectra (or from dissipation rates as moments of spectra) depend upon grossly uncertain premises. Direct observations of buoyancy flux cross-spectra are the essential key to resolving the wide disparities between theoretical approaches.