TITLE:
Depth decay rate for surface gravity wave pressure and velocity
AUTHORS:
Kern E. Kenyon
KEYWORDS:
Surface Gravity Waves; Depth Decay Rate
JOURNAL NAME:
Natural Science,
Vol.5 No.1,
January
15,
2013
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
crossstream force balance involving
gravity, the centrifugal force and a
pressure gradient. Qualitative solutions
show that the pressure decreases downward faster than the velocity does
and at a rate that is probably not the normal exponential decrease, which does
not agree with the classical result. The
radius of curvature of the streamlines
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.