Standing Gravity Wave Regimes in a Shallow-Water Resonator

Alexey Slunyaev (1) , Alexander Ezersky (2) , Dominique Mouazé (2) , Wuttersack Chokchai (2)

1 RAS - the Russian Academy of Sciences [Moscow, Russia]
2 M2C - Morphodynamique Continentale et Côtière

Arising modulations of surface gravity waves in a shallow-water resonator under harmonic forcing is discovered in laboratory experiments. Different types of modulations are found. When certain conditions are satisfied (appropriate frequency and sufficient force of excitation), the standing waves become modulated, and the envelopes of standing waves propagate in the channel. Strongly nonlinear numerical simulations of the Euler equations are performed reproducing the modulational regimes observed in the laboratory experiments. The physical mechanism responsible for the occurrence of modulated waves is determined on the basis of the simulations; quantitative estimates are made with the help of a simplified weakly nonlinear theory. This work was initiated by and performed under the guidance of Prof. A. Ezersky. We dedicate this text to the memory of him.

Mots clés: Gravity waves; Standing waves; Resonator; Modulations; Three-wave interaction; Shallow water

Domaines: Océanographie; Mécanique des fluides [physics.class-ph]

Alexey Slunyaev, Alexander Ezersky, Dominique Mouazé, Wuttersack Chokchai. Standing Gravity Wave Regimes in a Shallow-Water Resonator. Abcha, N.; Pelinovsky, E.; Mutabazi, I. Nonlinear Waves and Pattern Dynamics, Springer International Publishing, pp.63-75, 2018, 978-3-319-78193-8. ⟨10.1007/978-3-319-78193-8_3⟩. ⟨hal-03348795⟩