Abstract
The stability of a plane parallel flow which varies randomly across a channel is investigated. The mean velocity profile corresponds to plane Couette flow which is stable in the absence of fluctuations. The mean component of an infinitesimal disturbance in the flow is governed by an equation which is analogous to the Rayleigh equation arising in the classical stability analysis of an inviscid flow. The flow is found to be unstable when the correlation scale of the fluctuations in the basic flow is small compared with the channel width.
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