Annular Electroconvection with Shear

Abstract

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio η ∼ 0.8. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.Typeset using REVT E X 1

Bifurcations in annular electroconvection with an imposed shear

“…The Reynolds number Re is a measure of the strength of the applied shear, which is regarded as a second control parameter. It has been established [3,6] that the instability leads to a one-dimensional pattern of m vortex pairs where m is the azimuthal mode number. Linear stability predicts the value of the critical control parameter R c and the critical mode number m c at which the film becomes marginally unstable.…”

“…The small parameter ǫ is a reduced control parameter given by 6) and is a measure of the distance from threshold. The amplitude equation is accurate for small ǫ and describes a bifurcation from the A m ≡ 0 state (ǫ < 0) to the A m = 0 state with 2m vortices (ǫ > 0).…”

“…When driven, the pattern once again breaks the azimuthal symmetry, but since the reflection symmetry is absent due to shear, the pattern is free to travel azimuthally in the direction of the mean flow. [6] In addition, as we show in detail below, the shear flow alters the primary bifurcation, making it hysteretic.…”

“…The electroconvective state is then stationary and appears with the spontaneous breaking of the azimuthal invariance. [6] When sheared, the reflection symmetry of the base state is not present. When driven, the pattern once again breaks the azimuthal symmetry, but since the reflection symmetry is absent due to shear, the pattern is free to travel azimuthally in the direction of the mean flow.…”

“…It was previously described in Refs. [3] and [6]. The film was suspended between concentric circular electrodes and was driven by a voltage difference between the electrodes.…”