n the Nature of Boundary Con s for Flows with Moving Free ~~rfa~~~

We consider smali perturbations of plane parallel flow be&veer. a wail and a moving free surface. The problem is posed on a rectangle with inflow and out!low bout?dariss. The ~sua! boundary conditions are posed at the wall and the free surface, and the fluid satisfies the Navier-Stokes equations. We examine the nature of boundary conditions which car. be imposed at the inflow and outflow boundaries in order to yield a well-posed problem. This question tilrns out to be more delicate than is generally appreciated. Depending on the precise situation and on the regularity required of the solution, boundary conditions aijust one or both endpoints of the free surface need to be imposed. For example, v.e shobi that if :he velocities at the inflow and outflow boundaries are prescribe+ then the position of the free surface at the inflow boundary can be prescribed, but not at the out!Iow if an HI-soiuticz is desired. Numerical simulations with the FIDAP package are used to illxtrate our analytical resulrs. !Z 1991 Academic Press. Inc