Depth decay rate for surface gravity wave pressure and velocity

Abstract

Linear governing equations are formulated for the depth decay of the pressure and velocity variations associated with propagating surface gravity waves. These governing equations come from combining Bernoulli’s equation for steady frictionless flow along a streamline and the cross stream force balance involving gravity, the centrifugal force and a pressure gradient. Quali tative solutions show that the pressure decreases down ward faster than the velocity does and at a rate that is probably not the normal exponential decrease, which does not agree with the clas sical result. The radius of curvature of the stream lines is a non-constant coefficient in these equations and it needs to be supplied, either from measurements or another theory, in order to complete the solution of the derived governing equations. There is no sensitivity of the solution to the exact path the radius of curvature takes between its minimum value at the surface of a crest and trough and infinity at great depth. In the future measurements, perhaps streak photographs, will be needed to distinguish between the new and old theories.