?
Formation and decay of eddy currents generated by crossed surface waves
The mass transport induced by crossed surface waves consists of Stokes and Euler contributions, which are very different in nature. The first contribution is a generalization of Stokes drift for a plane wave in ideal fluid and the second contribution arises due to the fluid viscosity and is excited by a force applied in the viscous sublayer near the fluid surface. We study the formation and decay of the induced mass transport theoretically and experimentally and demonstrate that the two contributions have different timescales for typical experimental conditions. The evolution of the Euler contribution is described by a diffusion equation, where the fluid kinematic viscosity plays the role of the diffusion coefficient, while the Stokes contribution instantly tracks the wave pattern and therefore it evolves faster due to the additional wave damping near the system boundaries. The difference becomes more pronounced if the fluid surface is contaminated. We model the effect of contamination by a thin insoluble liquid film present on the fluid surface, with the compression modulus being the only nonzero rheological parameter of the film. Then the Euler contribution to the mass transport becomes larger and the evolution of the Stokes contribution becomes faster than in the free surface case. We infer the value of the compression modulus of the film by fitting the results of transient measurements of eddy currents and demonstrate that the obtained value leads to the correct ratio of amplitudes of
horizontal and vertical velocities of the wave motion and is in reasonable agreement with the measured dissipation rate of surface waves.