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Interaction of Shallow Water Waves
Author(s) -
Sekhar T. Raja,
Sharma V. D.
Publication year - 2008
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2008.00402.x
Subject(s) - waves and shallow water , geology , physics , acoustics , geophysics , oceanography
In this paper, we consider the Riemann problem and interaction of elementary waves for a nonlinear hyperbolic system of conservation laws that arises in shallow water theory. This class of equations includes as a special case the equations of classical shallow water equations. We study the bore and dilatation waves and their properties, and show the existence and uniqueness of the solution to the Riemann problem. Towards the end, we discuss numerical results for different initial data along with all possible interactions of elementary waves. It is noticed that in contrast to the p ‐system, the Riemann problem is solvable for arbitrary initial data, and its solution does not contain vacuum state.