# Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves

## TL;DR

This paper extends the theory of eddy currents generated by surface waves to include the effects of a thin, compressible insoluble liquid film, revealing how the film's properties influence fluid motion and particle advection.

## Contribution

It introduces a generalized model accounting for arbitrary elastic compression modulus of the film, analyzing its impact on eddy currents and passive tracer motion.

## Key findings

- Eddy current amplitude is unaffected by viscosity in free surface case.
- Surface films with negligible shear elasticity significantly alter eddy current behavior.
- Vertical vorticity and Stokes drift contributions depend differently on fluid viscosity and film properties.

## Abstract

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.