ABSTRACT
ABSTRACT: Depth-averaged modelling of shallow flows is widely used with greater computational efficiency than 3-D modelling. Limitations for recirculating flows are reviewed here and some new analysis is presented. The shallow wakes of a conical island of small slope have been predicted by a 3-D, hydrostatic-pressure, boundary-layer model using a 3-D, two-mixing-length, eddy-viscosity, turbulence model. Wakes may be stable or vortex shedding. With the horizontal mixing length about six times the vertical Prandtl values good predictions were obtained. A 2-D, depth-averaged model may have the same form of horizontal mixing but the bed shear stress can only be given by an empirical formula based on parallel flow conditions. Depth-averaged wakes show a much greater tendency to be unstable because in 3-D the horizontal and vertical strain rates modify eddy viscosity and as a consequence increase bed shear stress above that given by a formula based on parallel flow.
