The Johnson-Segalman model is an example of a model that exhibits a nonmonotone curve for the shear stress in terms of shear rate. There are many works based on such models for an explanation of the spurt phenomenon but they have concerned the one-dimensional problem. This paper concerns a model problem, taking a one-dimensionally stable ‘spurted solution,” viewed in two dimensions. A two-layer arrangement between walls in parallel shear, with a thin layer in the higher shear rate and the bulk of the fluid in the lower shear rate, is examined for linear stability in two dimensions. The spectrum is computed numerically for normal mode solutions. Instabilities with dominant growth rates for short waves are found. Thus, the one-dimensionally stable solutions of this model are actually two-dimensionally unsta
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