Largescale vertical vorticity generated by two crossing surface waves
Abstract
We demonstrate that two surface waves propagating at a small angle 2 θ to each other generate largescale (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 steadystate amplitude is larger and it penetrates deeper into the fluid volume as compared to the Stokes drift. In an unbounded fluid, the steadystate 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 k^{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 largescale vorticity and discuss the physical consequences of this phenomenon in the context of recent experiments.
 Publication:

Physical Review Fluids
 Pub Date:
 September 2020
 DOI:
 10.1103/PhysRevFluids.5.094702
 Bibcode:
 2020PhRvF...5i4702P