Wind-induced perturbations of the surface of a viscous fluid (Q794839)

The author considers time-dependent interacting perturbations of a heavy incompressible fluid (ocean water) by a steady motion of a light incompressible fluid (air flow) in two dimensions. The linearized Navier- Stokes equations are simplified by first-order perturbation methods using various perturbation parameters. Two major examples are investigated in detail. In the first case, both fluids occupy each a half space. Surface waves of the lower heavy fluid are generated by a steady wind velocity prescribed at some assumed height above the interacting surface. In the second case, the lower heavy fluid layer is assumed of constant depth. The surface waves are generated by a prescribed constant surface stress acting on the perturbed fluid layer. The corresponding simplified equations are solved by appropriate integral transform techniques. A comparison with actual wind-induced water waves would have been helpful.