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We study the stability of coherent structures in plane Couette flow againstlong-wavelength perturbations in wide domains that cover several pairs ofcoherent structures. For one and two pairs of vortices, the states retain thestability properties of the small domains, but for three pairs new unstablemodes are found. They are shown to be connected to bifurcations that break thetranslational symmetry and drive the coherent structures from the spanwiseextended state to a modulated one that is a precursor to spanwise localizedstates. Tracking the stability of the orbits as functions of the spanwise wavelength reveals a rich variety of additional bifurcations.

Long wavelength instability of coherent structures in plane Couette flow