Nonlinear generation of vorticity in thin smectic films

TL;DR

This paper investigates how nonlinear hydrodynamic effects in thin smectic films lead to the generation of in-plane vortices due to transverse oscillations, emphasizing the role of surrounding air in this process.

Contribution

It provides an analytical demonstration of vortex generation from transverse oscillations in smectic films, highlighting the influence of air on the film's hydrodynamics.

Findings

Transverse oscillations induce in-plane vortices via nonlinear hydrodynamics.

Air surrounding the film significantly affects the oscillation dispersion relation.

Explicit relation between film displacement and generated vorticity is derived.

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.