NDLI: Small amplitude wave in shallow water over linear and quadratic sloping beds

Content Provider	Springer Nature Link
Author	Bhatta, Dambaru D. Debnath, Lokenath
Copyright Year	2003
Abstract	Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.
Starting Page	53
Ending Page	65
Page Count	13
File Format	PDF
ISSN	15985865
Journal	Journal of Applied Mathematics and Computing
Volume Number	13
Issue Number	1-2
e-ISSN	18652085
Language	English
Publisher	Springer-Verlag
Publisher Date	2003-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Water wave linear nonlinear bottom boundary condition free surface condition linear form of bed quadratic form of bed Water waves, gravity waves; dispersion and scattering, nonlinear interaction PDEs in connection with fluid mechanics Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theory of Computation Mathematics of Computing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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