A streamtube model of rotating turbidity currents

A rotating turbidity current is modeled as a steady tube of sediment-laden water traversing along and down a uniform slope representing the continental shelf. The model includes parameterizations of erosion of sediment from the seabed into the plume, deposition onto the seafloor, bottom friction, and turbulent entrainment of the overlying ambient seawater. The purpose of the work is to study how these parameterizations affect the path the current takes on the slope and to determine criteria which affect the qualitative behavior of the model solutions. It is found that there are three possible final states to the model. The first is near-geostrophic flow along the slope which is similar to the uniform state found in streamtube models. The second is the catastrophic state which describes an erosive current entraining and depositing a large amount of sediment and traveling downslope much like an avalanche. In the third state the current decelerates and flows along slope whilst depositing its load. The current is extinguished on a length scale 2(aQ*/nu(s)K(f)r(0))(1/2) from the source where a is the aspect ratio, Q* is the initial volume flux, nu(s) is the settling velocity, K-f is a frictional coefficient and r(0) is the deposition rate. The state the current adopts depends on the initial conditions and model parameters. A linear stability analysis finds that the geostrophic state is always unstable while the catastrophic state is always stable. Thus the model predicts either catastrophic flow down slope or depositional flow along-slope. Given a sufficiently large initial disturbance the current will always ignite. This behavior is illustrated with parameters appropriate to the Kveitehola outflow. However the catastrophic state is unrealistic in that the turbulent energy required to maintain the sediment in suspension can be greater than that available to the current. Consequently a five-equation model is introduced which contains a turbulent kinetic energy equation and a parameterization of interfacial shear stress based on turbulence. With this model the Coriolis force has a much greater impact on the plume's path and the sediment erosion is not so unreasonably large.