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  Estonian Journal of Engineering

ISSN 1736-7522 (electronic)  ISSN 1736-6038  (print)

 An international scientific journal
Formerly: Proceedings of the Estonian Academy of Sciences Engineering
(ISSN 1406-0175)
Published since 1995

Estonian Journal of Engineering

ISSN 1736-7522 (electronic)  ISSN 1736-6038  (print)

 An international scientific journal
Formerly: Proceedings of the Estonian Academy of Sciences Engineering
(ISSN 1406-0175)
Published since 1995

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Nonlinear interaction of large-amplitude unidirectional waves in shallow water; pp. 289–300

(Full article in PDF format) doi: 10.3176/eng.2011.4.02


Authors

Ira Didenkulova, Efim Pelinovsky, Artem Rodin

Abstract

Nonlinear interaction of long unidirectional waves is studied numerically in the frame­work of nonlinear shallow water theory in a basin of constant depth. The interaction of two initially separated unidirectional waves occurs only when the waves (transformed into the shock waves) overtake each other. It is demonstrated that the interaction of two large-amplitude wave crests results in the formation of one shock wave of triangular shape, which is qualitatively similar to the outcome of the nonlinear interaction of two weak-amplitude waves. The formation of shock waves from initially negative disturbances (wave troughs) is accompanied by the generation of reflected waves of negative polarity. These waves additionally influence the process of interaction. The interaction of waves of opposite polarities is possible only when the leading wave is negative.

Keywords

nonlinear wave interaction, shallow water theory, unidirectional waves, Riemann waves, shock waves.

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