Efficiency of mixing in thin stratified layers

An important source of ocean turbulence is the inflectional instability of a stratified shear layer, commonly called Kelvin-Helmholtz (KH) instability. This instability concentrates the vorticity of the layer into a periodic train of billows. At large amplitude, the billows may break, become turbulent and drive rapid mixing.

KH instability exists only in shear layers where the stratification is sufficiently weak. In the stronger stratification that characterizes much of the ocean, an alternative mode of instability is possible. Holmboe instability generates a pair of billow trains, displaced from one another in the vertical and propagating at different velocities in the horizontal. The two trains interact to form a complex, oscillatory wave field. In its simplest form, Holmboe instability requires an initial flow in which stratification is confined to a thin layer at the center of the shear layer. A more general class of oscillatory instabilities requires only that mean density vary on smaller vertical scales than does mean velocity, a common circumstance due to low diffusivities of heat and salt in water.

Although the Holmboe instability grows more slowly than does the KH instability, recent results indicate that its potential for mixing is actually greater. This result could have important implications, not just for stratified shear flows, but for the interpretation of linear stability analysis in general, as it suggests that the fastest-growing instability is not necessarily the most important.

I will describe a sequence of direct numerical simulation experiments on stratified shear flows. Turbulence evolution is simulated in a variety of initial flows in which density changes in thin layers and oscillatory instability results. Analysis focuses on mixing efficiency and other turbulence statistics.