Large-scale vertical vorticity generated by two crossing surface waves

We demonstrate that two surface waves propagating at a small angle 2 θ 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 /(4 ν k²sin²θ ) , 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.