We will present high-resolution, Navier-Stokes based simulations and linear stability investigations of turbidity currents, and their two- way interaction with the seafloor. The turbidity currents we consider are driven by particles with negligible inertia that are much smaller than the smallest length scales of the buoyancy-induced fluid motion. For the mathematical description of the particulate phase an Eulerian approach is employed, with a transport equation for the particle-number density.

We will discuss some effects due to complex topography. Furthermore, we will analyze the linear stability problem of channel and sediment wave generation by turbidity currents. A novel linear instability mechanism is identified that can potentially create both of these topographical features. Its relation vis-a-vis the classical lee wave mechanism is discussed. In addition, results will be shown regarding the unsteady interaction of a gravity current with a submarine structure, such as a pipeline.