Nonlinear generation of vorticity in thin smectic films
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.
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- 4.M. Airiau, DEA Report (ENS, Paris, 1986).Google Scholar
- 10.E. I. Kats and V. V. Lebedev, Fluctuational Effects in the Dynamics of Liquid Crystals (Springer, Berlin, 1993).Google Scholar
- 11.wwwjetplettersacru.Google Scholar
- 13.L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, 2nd ed. (Pergamon, Oxford, UK, 1987).Google Scholar