Kelvin-Helmholtz instabilities are the most commonly studied type of instability in sheared density stratified flows. Turbulence caused by these instabilities is an important mechanism for mixing in geophysical flows. The primary objectives of this study are the evolution of these instabilities and quantifying the mixing they generate using direct numerical simulations. The results are presented in three chapters.

First, the evolution of primary Kelvin-Helmhlotz instabilities in two dimesnions is studied for a wide range of Reynolds and Prandtl numbers, representing real oceanic and atmospheric flows. The results suggest that some properties of KH billows are predictable by a semi-analytical model. It is shown that a new Corcos-Sherman scale is a useful guide when simulating turbulent KH flow fields.

The details of the mixing process generated by the evolution of Kelvin-Helmholtz instabilities as it goes through different stages, is analyzed. As the Reynolds number increases a transition in the overall amount of mixing is found, which is in agreement with previous experimental studies. This transition is explained quantitatively by the entrainment and mixing caused by three-dimensional motions, in addition to those resulted from the two-dimensional growth of the instability.

The effect of Prandtl number on mixing is studied to understand the characteristics of high Prandtl number mixing events in the ocean;​ these cases have usually been approximated by low Prandtl number simulations. The increase in the Pradtl number has some significant implications for the evolution of the billow, the time variation of mixing properties, and the overall mixing.