Extended states of nonlinear traveling-wave convection. I. The Eckhaus instability.

Abstract

I describe experiments on one-dimensional states of nonlinear traveling-wave convection in a narrow annular cell. Spatially uniform states are found to be stable within a band of wave numbers whose width grows approximately as the square root of the distance above a saddle-node Rayleigh number. Inside the band, I have measured the static properties of the traveling waves, including their response to spatial inhomogeneities in the Rayleigh number. Outside the stability band, traveling-wave states become unstable to temporally growing modulations of the spatial wave-number profile that propagate through the system at the group velocity of the underlying traveling waves. If allowed to grow, this Eckhaus instability leads, via a subcritical bifurcation, to spatiotemporal defects in which pairs of rolls are created or annihilated. In contrast with the action of the Eckhaus instability in stationary pattern-forming systems, the recurrent appearance and propagation of defects leads to long, erratic transients in which the system may or may not be driven back into the stable wave-number band.