Nonlinear generation of vorticity in thin smectic films

Abstract

We analyze a solenoidal motion in a vertically vibrated freely suspended thin smectic film. We demonstrate analytically that transverse oscillations of the film generate two-dimensional vortices in the plane of the film owing to hydrodynamic nonlinearity. An explicit expression for the vorticity of the in-plane film motion in terms of the film displacement is obtained. The air around the film is proven to play a crucial role, since it changes the dispersion relation of transverse oscillations and transmits viscous stresses to the film, modifying its bending motion. We propose possible experimental observations enabling to check our predictions.

References in corpus (2)

• Growing condensate in two-dimensional turbulence
• Universal profile of the vortex condensate in two-dimensional turbulence

Cited by in corpus (4)

• Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves
• Effect of thin film on the generation of vorticity by surface waves
• Acoustic streaming in 2D freely suspended smectic liquid crystal film
• Profile of a Two-Dimensional Vortex Condensate Beyond the Universal Limit