  Recently the generation of eddy currents by interacting surface waves was
observed experimentally. The phenomenon provides the possibility for
manipulation of particles which are immersed in the fluid. The analysis shows
that the amplitude of the established eddy currents produced by stationary
surface waves does not depend on the fluid viscosity in the free surface case.
The currents become parametrically larger being inversely proportional to the
square root of the fluid viscosity in the case when the fluid surface is
covered by an almost incompressible thin liquid (i.e. shear elasticity is zero)
film formed by an insoluble agent with negligible internal viscous losses as
compared to the dissipation in the fluid bulk. Here we extend the theory for a
thin insoluble film with zero shear elasticity and small shear and dilational
viscosities on the case of an arbitrary elastic compression modulus. We find
both contributions into the Lagrangian motion of passive tracers, which are the
advection by the Eulerian vertical vorticity and the Stokes drift. Whereas the
Stokes drift contribution preserves its value for the free surface case outside
a thin viscous sublayer, the Eulerian vertical vorticity strongly depends on
the fluid viscosity at high values of the film compression modulus. The Stokes
drift acquires a strong dependence on the fluid viscosity inside the viscous
sublayer, however, the change is compensated by an opposite change in the
Eulerian vertical vorticity. As a result, the vertical dependence of the
intensity of eddy currents is given by a sum of two decaying exponents with
both decrements being of the order of the wave number. The decrements are
numerically different, so the Eulerian contribution becomes dominant at some
depth for the surface film with any compression modulus.
