Frictional influence on internal Kelvin waves

Frictional influence on free internal Kelvin waves is studied theoretically. For continuous stratification the friction enters as an eddy viscosity, and the solutions are written in terms of normal modes. This approach implies a stress-free bottom. To obtain an analytical solution, we have assumed that the vertical variation of the eddy viscosity is inversely proportional to the square of the Brunt- frequency. Coastal as well as equatorial Kelvin waves are considered. The effects of bottom friction and frictional drag at an interface are studied explicitly in a vertically integrated two-layer model, taking the shear stress at a boundary to be proportional to the velocity difference across it. Formally, the continuously stratified case and the two-layer model result in the same set of equations. Explicit formulae for the frictional damping in time, the Rossby radius of deformation, the frequency, the phase difference between velocity and elevation, and the tilting of the internal co-phase lines backwards from the coast are given. In particular, the latter effect is shown to be much stronger for baroclinic waves than for the barotropic mode of the same wavelength.