Journal article

Numerical and analytical study of undular bores governed by the full water wave equations and bidirectional Whitham-Boussinesq equations

Rosa Maria Vargas-Magana, TR Marchant, Noel F Smyth



Undular bores, also termed dispersive shock waves, generated by an initial discontinuity in height as governed by two forms of the Boussinesq system of weakly nonlinear shallow water wave theory, the standard formulation and a Hamiltonian formulation, two related Whitham-Boussinesq equations, and the full water wave equations for gravity surface waves are studied and compared. It is found that the Whitham-Boussinesq systems give solutions in excellent agreement with numerical solutions of the full water wave equations for the positions of the leading and trailing edges of the bore up until the onset on modulational instability. The Whitham-Boussinesq systems, which are far simpler than the f..

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Funding Acknowledgements

R.M.V.-M. was funded by Consejo Nacional de Ciencia y Tecnologia (CONACyT), calls, EPE2018(1) and EPE2019(2), Estancias Posdoctorales en el Extranjero Vinculadas a la Consolidacion de Grupos de Investigacion y Fortalecimiento del Posgrado Nacional Ano 2018 y Continuidad en 2019 (Postdoctoral stay abroad granted by the Mexican National Council of Science and Technology to develop a submitted research project, year 2018 and extension in 2019). R.M.V.-M. would also like to thank CONACyT and the collective "Cientificaes Mexicanaes en el Extranjero" for funding her postdoctoral position at the University of Edinburgh.