Mixing in Symmetric Holmboe Waves

Direct simulations are used to study turbulence and mixing in Holmboe waves. Previous results showing that mixing in Holmboe waves is comparable to that found in the better-known Kelvin–Helmholtz (KH) billows are extended to cover a range of stratification levels. Mixing efficiency is discussed in detail, as are effective diffusivities of buoyancy and momentum. Entrainment rates are compared with results from laboratory experiments. The results suggest that the ratio of the thicknesses of the shear layer and the stratified layer is a key parameter controlling mixing. With that ratio held constant, KH billows mix more rapidly than do Holmboe waves. Among Holmboe waves, mixing increases with increasing density difference, despite the fact that the transition to turbulence is delayed or prevented entirely by the stratification. Results are summarized in parameterizations of the effective viscosity and diffusivity of Holmboe waves.