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The Boundary Value Problem for the Nonlinear Shallow Water Equations

21 Pages Posted: 11 Dec 2007  

Matteo Antuono

affiliation not provided to SSRN

Maurizio Brocchini

affiliation not provided to SSRN

Abstract

We propose an approximate analytical solution of the boundary value problem (BVP) for the nonlinear shallow waters equations. Our work, based on the Carrier and Greenspan [1] hodograph transformation, focuses on the propagation of nonlinear non-breaking waves over a uniformly plane beach. Available results are briefly discussed with specific emphasis on the comparison between the Initial Value Problem and the BVP' the latter more completely representing the physical phenomenon of wave propagation on a beach. The solution of the BVP is achieved through a perturbation approach solely using the assumption of small waves incoming at the seaward boundary of the domain. The most significant results, i.e., the shoreline position estimation, the actual wave height and velocity at the seaward boundary, the reflected wave height and velocity at the seaward boundary are given for three specific input waves and compared with available solutions.

Suggested Citation

Antuono, Matteo and Brocchini, Maurizio, The Boundary Value Problem for the Nonlinear Shallow Water Equations. Studies in Applied Mathematics, Vol. 119, Issue 1, pp. 73-93, July 2007. Available at SSRN: https://ssrn.com/abstract=1067218 or http://dx.doi.org/10.1111/j.1365-2966.2007.00378.x

Matteo Antuono (Contact Author)

affiliation not provided to SSRN

No Address Available

Maurizio Brocchini

affiliation not provided to SSRN

No Address Available

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