### PERIODIC GRAVITY WAVES OVER A GENTLE SLOPE AT A THIRD ORDER OF APPROXIMATION

#### Abstract

The concepts of energy flux and group velocity for nonlinear periodic gravity waves are discussed The average energy flux, average energy per wavelength and "group velocity" are calculated for irrotational periodic gravity waves at a third order of approximation. Then the principle of conservation of transmitted energy between wave orthogonals is applied to the same order of approximation for determining the variation of wave height m decreasing depth. The results are presented as nomographs. It is seen that the "shoaling coefficient" needs to be expressed at least at a third order of approximation to account for experimental results.

#### Keywords

gravity waves; gentle slope; third order; energy flux; group velocity

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