Open AccessCONPORMAL MAPPING SOLUTION OP A WAVE FIELD ON THE ARBITRARILY SHAPED SEA BOTTOM
Author(s) -
Kazuo Nadaoka,
Mikio Hino
Publication year - 1984
Publication title -
proceedings of conference on coastal engineering/proceedings of ... conference on coastal engineering
Language(s) - English
Resource type - Journals
eISSN - 2156-1028
pISSN - 0589-087X
DOI - 10.9753/icce.v19.81
Subject(s) - conformal map , integrable system , mathematical analysis , wave equation , fourier transform , mathematics , field (mathematics) , domain (mathematical analysis) , boundary value problem , inverse problem , pure mathematics
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.