CONPORMAL MAPPING SOLUTION OP A WAVE FIELD ON THE ARBITRARILY SHAPED SEA BOTTOM

Kazuo Nadaoka, Mikio Hino

Abstract


A new wave equation has been derived for the full nonlinear dispersive waves propagating over an arbitrarily shaped sea bed. The method of the derivation of the equation uses a conformal mapping technique by which the original domain can be transformed onto a domain with a uniform depth to make the basic equation easily integrable vertically. By taking an inverse Fourier transform, the velocity potential obtained by the integration can be expressed in the form which can construct the exact wave equation from the water surface boundary conditions. An algorithm for the numerical integration of the equation is presented with some examples of the solution.

Keywords


mapping solution; wave field; sea bottom

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