Three-dimensional periodic flows of an inhomogeneous fluid in the case of oscillations of part of an inclined plane

The linearized problem of the generation of flows of a continuously stratified fluid by means of the moving part of a stationary infinite inclined plane is solved, taking account of the effects of diffusion, by the methods of the theory of singular perturbations. The moving part of the plane executes longitudinal periodic oscillations. The results obtained contain components that are regularly perturbed with respect to dissipative factors, that is, internal waves and a family of singularly perturbed components, two of which are due to the action of viscosity and a further one due to the effect of diffusion. The solutions of the problems in two-dimensional and one-dimensional formulations correspond to limit cases and the Stokes solution when buoyancy effects are neglected. The internal wave calculations are in satisfactory agreement with aboratory data.