Pattern selection in a slowly varying environment

Abstract

Usually, in supercritical conditions, steady cellular structures (as rolls in Taylor-Couette experiments) may have any wavenumber in a finite band for an unbounded pattern. If the external conditions change slowly, the wavelength becomes a function of the local control parameter. If a subcritical region is smoothly connected to a supercritical one, the wavelength of steady rolls in the supercritical region is uniquely defined, up to exponentially small terms