A practical alternative to the “mild-slope” wave equation |
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| Authors: | Graham JM Copeland |
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| Institution: | Department of Civil Engineering, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, U.K. |
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| Abstract: | The “mild-slope” equation which describes wave propagation in shoaling water is normally expressed in an elliptic form. The resulting computational effort involved in the solution of the boundary value problem renders the method suitable only for small sea areas. The parabolic approximation to this equation considerably reduces the computation involved but must omit the reflected wave. Hence this method is not suited to the modelling of harbour systems or areas near to sea walls where reflections are considerable. This paper expresses the “mild-slope” equation in the form of a pair of first-order equations, which constitute a hyperbolic system, without the loss of the reflected wave. A finite-difference numerical scheme is described for the efficient solution of the equations which includes boundaries of arbitrary reflecting power. |
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