Parametrization of dispersion in the depth-averaged transport equation (Q1344671)

The presence of a vertical shear in the flow in an estuary means that the depth averaging of the Navier-Stokes equations gives rise to an extra dispersion-like term acting along the direction of flow. Here a method is developed that more realistically represents the physics involved, by defining two new coefficients: a general background dispersion coefficient and one expressing the dispersion due to the vertical shear. This scheme is applied first to a simple test problem and is then used in a model of the tidal flow within the Severn estuary, using in each case a previously developed finite-element formulation of the shallow water equations.