Governing Equations for Free Surface Flows

Abstract

The best working definition of free surface flow is the following:

Free surface flow occurs in a deformable solution region whereby the shape and size of the region is part of the solution.

Free surface flow can be either steady or unsteady. In the unsteady mode the shape and size of the solution region is known at the initial time but it changes continually as the solution progresses. In the steady mode the boundaries of the solution region are not known and must be found by some technique. The steady problem — and to some extent the unsteady problem — forms a mathematical enigma: To find a solution, the differential equation must have well defined boundary conditions applied to the boundary of the solution region, but how can the conditions be applied if the location of the boundary is not known?

Part of the material of this chapter is taken from Liggett, J. A., Fluid Mechanics, McGraw-Hill, 1994, with permission.