One-dimensional pattern formation with galilean invariance near a stationary bifurcation
One-dimensional pattern formation with Galilean symmetry is not governed by the Ginzburg-Landau equation near onset; an additional equation describing a large-scale mean flow is required. We derive these amplitude equations and predict the solution amplitude. All steady patterns are unstable, with the growth of the instability taking place on a faster time scale than the formation of the pattern itself. Numerical simulations show that chaotic solutions are obtained, whose amplitude is consistent with our theory.
Matthews
PC
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
Cox
SM