  The mass-transport induced by crossed surface waves consists of the 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 it 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 both contributions have different time
scales 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 evolves faster, feeling the additional 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 presented on the fluid surface with the compression modulus being the only
non-zero rheological parameter of the film. Then the Euler contribution into
the mass-transport becomes parametrically larger and the evolution of the
Stokes contribution becomes parametrically faster. The parameter is the same in
both cases and it is equal to the quality factor of surfaces waves, which is
modified by the presence of a surface film. 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.
