Analytical solutions for forced long waves on a sloping beach

Philip L.F. Liu; Patrick Lynett; Costas E. Synolakis

doi:10.1017/S0022112002003385

Analytical solutions for forced long waves on a sloping beach

Philip L.F. Liu, Patrick Lynett, Costas E. Synolakis

Department of Hydraulic and Ocean Engineering

Research output: Contribution to journal › Article › peer-review

92 Citations (Scopus)

Abstract

We derive analytic solutions for the forced linear shallow water equation of the following form: ∂²Y/∂t²Y ∂/∂x (x∂Y/∂x) = ∂²f/∂t² 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 described 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.

Original language	English
Pages (from-to)	101-109
Number of pages	9
Journal	Journal of Fluid Mechanics
Volume	478
DOIs	https://doi.org/10.1017/S0022112002003385
Publication status	Published - 2003 Mar 10

All Science Journal Classification (ASJC) codes

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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title = "Analytical solutions for forced long waves on a sloping beach",

abstract = "We derive analytic solutions for the forced linear shallow water equation of the following form: ∂2Y/∂t2Y ∂/∂x (x∂Y/∂x) = ∂2f/∂t2 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 described 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.",

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T1 - Analytical solutions for forced long waves on a sloping beach

AU - Liu, Philip L.F.

AU - Lynett, Patrick

AU - Synolakis, Costas E.

PY - 2003/3/10

Y1 - 2003/3/10

N2 - We derive analytic solutions for the forced linear shallow water equation of the following form: ∂2Y/∂t2Y ∂/∂x (x∂Y/∂x) = ∂2f/∂t2 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 described 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.

AB - We derive analytic solutions for the forced linear shallow water equation of the following form: ∂2Y/∂t2Y ∂/∂x (x∂Y/∂x) = ∂2f/∂t2 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 described 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.

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JO - Journal of Fluid Mechanics

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Analytical solutions for forced long waves on a sloping beach

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