Coexistence of Eckhaus instability in forced zigzag Turing patterns

Abstract

Wavelength selection is an important feature in pattern forming systems. There are two distinct instabilities that arise when a mismatching wavelength is imposed on a pattern forming system, the Eckhaus instability (when the imposed wavelength is smaller than the preferred wavelength) and the zigzag instability (when the imposed wavelength is larger than the preferred wavelength). These two perhaps contradicting instabilities coexist in an experiment in which Turing patterns are forced with slowly moving stripes with a wavelength that is about 1.5 the wavelength of the Turing patterns. We also show that these two instabilities coupled together can lead to the reorientation of patterns under traveling stripe forcing.