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Many fundamental processes in oceanic transport and limnology occur in geophysical flows that are both local in space and transient in time, and that require equally space and time-resolved methods of analysis. The importance of providing physics-based, quantitative modeling of such flows has driven the development of numerical methods for geophysical fluid dynamics for over three decades. Here, we use direct numerical simulations to investigate a range of stratified, particle-laden flows that are accurately described by the three-dimensional Navier-Stokes equations for an incompressible flow in the Boussinesq limit. We firstly investigate the propagation, transport and mixing dynamics of density-driven gravity currents moving in stratified environments. We propose new models for the intrusion of a turbidity current into a linearly stratified ambient based on three-dimensional simulations. We then describe the interaction between a gravity-current and an internal wave and characterize a phenomenological change in the long-term effect of the interaction at a critical wave height. We then quantify the role of double-diffusive processes in the Dead Sea in Summer and their role in the seasonality of salt crystallization and deposition. We also describe large-scale double-diffusive instabilities that arise in high-Prandtl sedimentary double-diffusive systems such as linearly stratified particle-laden salt water. Finally, we quantify mixing induced by a swarm of small-scale self-propelled organisms migrating in a stratified ambient fluid. We compare the relative contribution to mixing by individual swimmers within the swarm to that of the large-scale motion produced by the collective motion of the swarm.

Many fundamental processes in oceanic transport and limnology occur in geophysical flows that are both local in space and transient in time, and that require equally space and time-resolved methods of analysis. The importance of providing physics-based, quantitative modeling of such flows has driven the development of numerical methods for geophysical fluid dynamics for over three decades. Here, we use direct numerical simulations to investigate a range of stratified, particle-laden flows that are accurately described by the three-dimensional Navier-Stokes equations for an incompressible flow in the Boussinesq limit. We firstly investigate the propagation, transport and mixing dynamics of density-driven gravity currents moving in stratified environments. We propose new models for the intrusion of a turbidity current into a linearly stratified ambient based on three-dimensional simulations. We then describe the interaction between a gravity-current and an internal wave and characterize a phenomenological change in the long-term effect of the interaction at a critical wave height. We then quantify the role of double-diffusive processes in the Dead Sea in Summer and their role in the seasonality of salt crystallization and deposition. We also describe large-scale double-diffusive instabilities that arise in high-Prandtl sedimentary double-diffusive systems such as linearly stratified particle-laden salt water. Finally, we quantify mixing induced by a swarm of small-scale self-propelled organisms migrating in a stratified ambient fluid. We compare the relative contribution to mixing by individual swimmers within the swarm to that of the large-scale motion produced by the collective motion of the swarm.