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  • Journal of Fluid Mechanics, Volume 710
  • November 2012, pp. 379-418

On the steady-state fully resonant progressive waves in water of finite depth

  • Dali Xu (a1), Zhiliang Lin (a1), Shijun Liao (a2) (a1) and Michael Stiassnie (a3)
  • DOI:
  • Published online: 07 September 2012

The steady-state fully resonant wave system, consisting of two progressive primary waves in finite water depth and all components due to nonlinear interaction, is investigated in detail by means of analytically solving the fully nonlinear wave equations as a nonlinear boundary-value problem. It is found that multiple steady-state fully resonant waves exist in some cases which have no exchange of wave energy at all, so that the energy spectrum is time-independent. Further, the steady-state resonant wave component may contain only a small proportion of the wave energy. However, even in these cases, there usually exist time-dependent periodic exchanges of wave energy around the time-independent energy spectrum corresponding to such a steady-state fully resonant wave, since it is hard to be exactly in such a balanced state in practice. This view serves to deepen and enrich our understanding of the resonance of gravity waves.

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24.V. E. Zakharov 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9 (2), 190194.

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