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Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking

Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking
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Year:    2016

Author:    Magnar Bjørkavåg, Henrik Kalisch, Zahra Khorsand, Dimitrios Mitsotakis

Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 221–237

Abstract

In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary conditions with spectral accuracy.
The algorithm is applied to the study of undular bores, and in particular to the onset of wave breaking connected with undular bores. As proposed in [2], an improved version of the breaking criterion recently introduced in [5] is used. This tightened breaking criterion together with a careful choice of the relaxation parameter yields rather accurate predictions of the onset of breaking in the leading wave of an undular bore.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v49n3.16.02

Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 221–237

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Boussinesq system Legendre projection undular bore wave breaking boundary conditions spectral accuracy.

Author Details

Magnar Bjørkavåg

Henrik Kalisch

Zahra Khorsand

Dimitrios Mitsotakis

  1. Wave breaking in the KdV equation on a flow with constant vorticity

    Senthilkumar, Amutha | Kalisch, Henrik

    European Journal of Mechanics - B/Fluids, Vol. 73 (2019), Iss. P.48

    https://doi.org/10.1016/j.euromechflu.2017.12.006 [Citations: 5]

  2. Spectral Jacobi approximations for Boussinesq systems

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    Studies in Applied Mathematics, Vol. 153 (2024), Iss. 1

    https://doi.org/10.1111/sapm.12680 [Citations: 0]

  3. Wave Breaking in Undular Bores with Shear Flows

    Bjørnestad, Maria | Kalisch, Henrik | Abid, Malek | Kharif, Christian | Brun, Mats

    Water Waves, Vol. 3 (2021), Iss. 3 P.473

    https://doi.org/10.1007/s42286-020-00046-6 [Citations: 4]