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Sequential Bifurcations in Sheared Annular Electroconvection

Zahir A. Daya·V. B. Deyirmenjian·Stephen W. Morris
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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 ${\cal R}$ and a shear Reynolds number ${\rm Re}$. The pattern is an azimuthally periodic array of traveling vortices with integer mode number $m$. Varying ${\cal R}$ and ${\rm Re}$ 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 ${\cal R}$ is increased at constant ${\rm Re}$.

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Zahir A. Daya, V. B. Deyirmenjian, Stephen W. Morris. 2001-11-02. Sequential Bifurcations in Sheared Annular Electroconvection. https://doi.org/10.1103/physreve.66.015201

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