Numerical investigation of turbulence generation in non-breaking potential waves

Theoretically, potential waves cannot generate the vortex motion, but the scale considerations (Babanin, 2006) indicate that if the steepness of waves is not too small, the Reynolds number can exceed the critical values. This means that in presence of initial non-potential disturbances the orbital velocities can generate the vortex motion and turbulence. This problem was investigated by means of linear-instability theory (Benilov et al, 1993). It was shown that pure two-dimensional motion always remains potential because one-dimensional vortex (in vertical plane) does not interact with the orbital motion. The waves can generate the vortex in horizontal plane, and further development of vorticity occurs due exchange of energy between the components of vorticity. Then, due to non-linearity, motion at smaller scales and more or less developed turbulent regime arises.