Turbulent mixing has an important influence on many physical processes in the ocean. For example, the upwelling of water through the stably stratified ocean interior, needed to close the global circulation, is only possible through the enhanced vertical mixing resulting from turbulence. The transport of heat, carbon and nutrients is also affected by this mixing. Understanding its spatial and temporal intermittency is therefore vital for determining the regional distribution of these important tracers. Away from boundaries, turbulence in the ocean is commonly attributed to the breaking of internal waves. When an internal wave grows to a large amplitude, it can break due to convective instabilities or shear instabilities. A fundamental understanding of the turbulent transition arising from these instabilities is useful for both interpreting observations and predicting 'hotspots' of turbulence in the field. Focusing solely on canonical instabilities however neglects the wide range of complex flows occurring at small scales in the ocean. Interactions with mean flows or with the background internal wave field can alter the properties of turbulence and the ensuing mixing. In this thesis, we use numerical simulations to investigate three problems aimed at enhancing our understanding of mixing in such stratified flows.

We first investigate the development of Kelvin-Helmholtz instability in a stratified shear layer. We quantify the maximum energy extracted from the mean flow by the instability as a function of the Richardson number Ri. By applying forcing to the governing equations, we are able to extend our simulations up to the marginal stability threshold of Ri=1/4, and show that the maximum energy decreases to a small but non-zero value as this threshold is approached. Our next study focuses on mixing in stratified turbulence that is kept in a statistically steady state through large-scale forcing. We compare flows forced by vortical modes with those forced by internal gravity waves. A higher mixing efficiency in the wave-forced simulations is attributed to a more convective-driven mixing process. Intermittency in the flows allows us to verify that the mixing efficiency is constant throughout each domain. This is despite wavelet analysis showing that regions of high and low energy dissipation have distinct scalings in their energy spectra. Finally, we consider the interaction of a large-amplitude internal gravity wave with a sinusoidal shear flow. We find both convective and shear processes to be important in the transition to turbulence. Through extending the concept of available potential energy to triply periodic domains, we show that the scalar variance dissipation rate χ is a good approximation to the 'true' rate of mixing Μ, even when sizeable regions of static instability are present.