Mass transport in internal coastal Kelvin waves

We investigate theoretically the mass transport in internal coastal Kelvin waves by integrating the horizontal momentum equations in the vertical. Applying a perturbation method, the time-averaged Lagrangian horizontal fluxes are determined to second order in wave steepness. The linear wave field is expanded in the vertical using orthogonal functions. Due to the orthogonality property of these functions, formulae for the non-linear Stokes drift and the mean vertically-averaged Eulerian transport driven by the radiation stress can be derived for arbitrary vertical variation of the Brunt-Väisälä frequency N. For values of N typical of the thermocline in the Caspian Sea, the calculation of the non-linear transports yields a jet-like mean flow along the coast, limited in the off-shore direction by the internal Rossby radius. It is suggested that this wave-induced mean drift may contribute to the mean circulation in the Caspian Sea.