Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2001-11-02
Nonlinear Sciences
Pattern Formation and Solitons
4 pages, 4 figures, see also http://mobydick.physics.utoronto.ca
Scientific paper
10.1103/PhysRevE.66.015201
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 ${\rm Re}$.
Daya Zahir A.
Deyirmenjian Vatche B.
Morris Stephen W.
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