Large-scale vertical vorticity generated by two crossing surface waves

Physical Review Fluids. 2020. Vol. 5. No. 9. P. 094702.

Parfenyev V., Vergeles S. S.

We demonstrate that two surface waves propagating at a small angle 2θ to each other generate large-scale (compared to the wavelength) vertical vorticity owing to hydrodynamic nonlinearity in a viscous fluid. The horizontal geometric structure of the induced flow coincides with the structure of the Stokes drift in an ideal fluid, but its steady-state amplitude is larger and it penetrates deeper into the fluid volume as compared to the Stokes drift. In an unbounded fluid, the steady-state amplitude and penetration depth are increased by the factor of 1/sinθ and the evolution time of the induced flow can be estimated as 1/(4νk^2 sin^2 θ), where ν is the fluid kinematic viscosity and k is the wave number. Also, we study how the finite depth of the fluid and a thin insoluble liquid film that possibly covers the fluid surface due to contamination effect the generation of large-scale vorticity and discuss the physical consequences of this phenomenon in the context of recent experiments.

Keywords: surface waves (fluid), тонкие пленки, thin films, vortex, поверхностные волны, завихренность