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Analytical solutions for forced long waves on a sloping beach

Published online by Cambridge University Press:  19 March 2003

PHILIP L.-F. LIU ,
PATRICK LYNETT  and
COSTAS E. SYNOLAKIS
PHILIP L.-F. LIU
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
PATRICK LYNETT
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA Present address: Department of Civil Engineering, Texas A&M University, College Station, TX 77843-3136, USA
COSTAS E. SYNOLAKIS
Affiliation:
School of Engineering, University of Southern California, Los Angeles, CA 90089-2531, USA
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Abstract

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We derive analytic solutions for the forced linear shallow water equation of the following form:

<?TeX \partial^2 Y \over \partial t^2}-b{\partial \over \partial x}\left(x {\partial Y \over \partial x}\right)={\partial^2 f\over \partial t^2 ?>

for x>0, in which Y(x,t) denotes an unknown variable, f(x,t) a prescribed forcing function and b a positive constant. This equation has been used to describe landslide-generated tsunamis and also long waves induced by moving atmospheric pressure distributions. We discuss particular and general solutions. We then compare our results with numerical solutions of the same equation and with the corresponding solutions of the nonlinear depth-integrated equations and discuss them in terms of landslide-generated tsunamis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 478 , 10 March 2003 , pp. 101 - 109
Copyright
© 2003 Cambridge University Press