On the time-evolution of resonant triads in rotational capillary-gravity water waves

Abstract

We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume a constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero we recover the well known integrable three-wave system.

arXiv comment20 pages, 1 figure

References in corpus (8)

• Transition to turbulence in a shear flow
• Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
• Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity
• Transition to turbulence in shear flows
• Effect of the dynamical phases on the nonlinear amplitudes' evolution
• Dynamics of nonlinear resonances in Hamiltonian systems
• Externally forced triads of resonantly interacting waves: boundedness and integrability properties
• Nonlinear resonances of water waves

Cited by in corpus (4)

• An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields
• On the modelling of short and intermediate water waves
• The Lagrangian formulation for wave motion with a shear current and surface tension
• Modelling surface waves on shear current with quadratic depth-dependence