Hydromechanics of Tidal Jets

A unified theoretical investigation of the fully-developed region of a tidal jet is presented. The jet is treated as a vertically-averaged flow and the effects of lateral mixing, bottom friction, and variable bathymetry are included. It is shown, without assuming any specific form of the similarity function, that the cross-stream length scale and the centerline velocity of the jet must satisfy certain differential equations in order for the jet to be self-similar. Solutions of these equations are obtained for some simple forms of bottom topography. For a flat, frictional bottom, the jet exhibits exponential growth and decay of the centerline velocity which is in agreement with earlier investigations. An exact analytical solution for the similarity function is obtained upon introduction of Prandtl's eddy viscosity hypothesis. The theory contains two free constants which must be determined in future experimental investigations.