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A scalar form of the complementary mild-slope equation

Published online by Cambridge University Press:  01 July 2010

YARON TOLEDO  and
YEHUDA AGNON
YARON TOLEDO*
Affiliation:
Department of Civil and Environmental Engineering, Technion, Haifa 32000, Israel
YEHUDA AGNON
Affiliation:
Department of Civil and Environmental Engineering, Technion, Haifa 32000, Israel
*
†Email address for correspondence: yaron.toledo@gmail.com
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Abstract

Mild-slope (MS) type equations are depth-integrated models, which predict under appropriate conditions refraction and diffraction of linear time-harmonic water waves. Among these equations, the complementary mild-slope equation (CMSE) was shown to give better agreement with exact two-dimensional linear theory compared to other MS-type equations. Nevertheless, it has a disadvantage of being a vector equation, i.e. it requires solving a system of two coupled partial differential equations. In addition, for three-dimensional problems, there is a difficulty in constructing the additional boundary condition needed for the solution. In the present work, it is shown how the vector CMSE can be transformed into an equivalent scalar equation using a pseudo-potential formulation. The pseudo-potential mild-slope equation (PMSE) preserves the accuracy of the CMSE while avoiding the need of an additional boundary condition. Furthermore, the PMSE significantly reduces the computational effort relative to the CMSE, since it is a scalar equation. The accuracy of the new model was tested numerically by comparing it to laboratory data and analytical solutions.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 656 , 10 August 2010 , pp. 407 - 416
Copyright
Copyright © Cambridge University Press 2010

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