Sequential Bifurcations in Sheared Annular Electroconvection

Abstract

A sequence of bifurcations is studied in a one-dimensional pattern forming system subject to the variation of two experimental control parameters: a dimensionless electrical forcing number $\mathcal{R}$ and a shear Reynolds number $\mathrm{Re}$. The pattern is an azimuthally periodic array of traveling vortices with integer mode number $m$. Varying $\mathcal{R}$ and $\mathrm{Re}$ permits the passage through several codimension-two points. We find that the coefficients of the nonlinear terms in a generic Landau equation for the primary bifurcation are discontinuous at the codimension-two points. Further, we map the stability boundaries in the space of the two parameters by studying the subcritical secondary bifurcations in which $m\to m+1$ when $\mathcal{R}$ is increased at constant $\mathrm{Re}$.

4 pages, 4 figures, see also http://mobydick.physics.utoronto.ca

References in corpus (5)

• Annular electroconvection with shear
• Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film
• Electrically driven convection in a thin annular film undergoing circular Couette flow
• Bifurcations in annular electroconvection with an imposed shear
• Pattern formation in annular convection

Cited by in corpus (5)

• Aspect ratio dependence of charge transport in turbulent electroconvection
• Charge Transport Scalings in Turbulent Electroconvection
• Localized states in sheared electroconvection
• Codimension-two points in annular electroconvection as a function of aspect ratio
• Electroconvection of Thin Liquid Crystals: Model Reduction and Numerical Simulations