THE SELF-MODULATION OF STRONGLY NONLINEAR WATER WAVES. INCOMPLETE RECURRENCE

  • A. V. Slunyaev Institute of Applied Physics RAS
  • A. S. Dosaev Institute of Applied Physics RAS
DOI 10.29006/1564-2291.JOR-2019.47(1).36
Keywords modulational instability, numerical simulatio, Cherenkov radiation, recurrence

Abstract

The processes of spontaneous self-modulation of steep gravity waves on the water surface with the formation of very short groups are investigated by means of the numerical simulation of the primitive Euler equations. It is shown that the subsequent demodulation is incomplete as a result of the generation of new waves with other lengths propagating both along the way and towards the main wave. Thus, in the framework of the full hydrodynamic equations an approximate analogue corresponds to the breather solution of the nonlinear Schrödinger equation.
The parts of the research was supported by the RSF grant No 16-17-00041 and by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».

References


  1. Slunyaev A.V. Group-wave resonances in nonlinear dispersive media: The case of gravity water waves. Phys. Rev. E., 2018, Vol. 97, pp. 010202.

  2. Slunyaev A.V. and Dosaev A.S. On the incomplete recurrence of modulationally unstable deepwater surface gravity waves. Communications in Nonlinear Science and Numerical Simulation 66, 2019, Vol. 66, pp. 167–182.
Published
2019-05-29
Issue
Vol 47 No 1 (2019): Journal of Oceanological Research
Section
The XXII workshop of the Council of nonlinear dynamics of the Russian Academy of

Transfer of copyrights occurs on the basis of a license agreement between the Author and Shirshov Institute of Oceanology, RAS