Streamtube models of gravity currents in the ocean

A streamtube model of an outflow is developed that accounts for changes in hydrostatic pressure owing to variations in the height of the plume. The resulting one-dimensional equations are similar in form to the St. Venant equations, but additionally specify the path of the outflow down the slope. For no entrainment, uniform steady solutions exist with the flow nearly geostrophic and gradually descending the slope. However, these solutions are unstable if the uniform Froude number is subcritical. Instead, the model predicts a flow straight down the slope with increasing spreading and decreasing fluid flow. ational data for three outflows indicate that the flow is subcritical and flows predominantly along the slope. Consequently, a two-dimensional steady model is introduced that uses the stream function as the transverse coordinate. Subcritical flow is stable when the transverse pressure gradient (caused by changes in height) supports the fluid along the slope. A numerical simulation suggests that an outflow might be considered as a sheet of fluid in which the fluid velocity varies considerably from the downslope to upslope boundary. The bulk of the fluid flows along the slope but is drained by an Ekman-like layer at the base of the outflow. This picture and the stability calculations cast doubt on whether an outflow should be modelled as a steady tube of fluid with properties uniform across the tube.