Nonlinear generation of vorticity in thin smectic films


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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.

About the authors

V. M. Parfenyev

Landau Institute for Theoretical Physics

Author for correspondence.
Email: parfenius@gmail.com
Russian Federation, Chernogolovka, Moscow region, 142432

S. S. Vergeles

Landau Institute for Theoretical Physics

Email: parfenius@gmail.com
Russian Federation, Chernogolovka, Moscow region, 142432

V. V. Lebedev

Landau Institute for Theoretical Physics

Email: parfenius@gmail.com
Russian Federation, Chernogolovka, Moscow region, 142432

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