ANALYTICAL SOLUTION FOR THE VELOCITY POTENTIAL OF LINEAR WAVES OVER SLOPING BEACHES

An analytical solution for the velocity potential of linear waves traveling over sloping beaches is obtained in the present paper, the restriction to the solution, i.e.the cube of bottom slope α being negligible.When the terms of order of α² are neglected, the solution is the same as that presented by Biesel in 1951^[1].When the terms of order of α² are retained, the wave dispersion relation is corrected.Forthermore, the solution corrected to any higher order of α can be obtained without difficulty by means of the disturbation method given by this paper¹⁾.