Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1727613 | Ocean Engineering | 2012 | 13 Pages |
Abstract
A remarkably accurate approximation to the profile of a limiting progressive gravity wave in water of infinite depth is given by the expression(0.1)y/L=Acosh(x/L),where L is the wavelength, x and y are horizontal and vertical coordinates and A is a constant given by(0.2)A=1/(3sinh12)=1.1080.This determines the wave steepness (H/L) as 0.14140 a proportional error of less than 0.3% (about 10 times closer than previous approximations) and the phase speed c/(gL)1/2 as 0.43511, which is accurate to within 0.2%. The entire surface profile is accurate to less than 0.7%. The corresponding particle velocities are found by a straightforward numerical integration. It is shown that this type of approximation cannot be made exact by the introduction of further parameters.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Ocean Engineering
Authors
R.C.T. Rainey, Michael S. Longuet-Higgins,