We have investigated the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the cross flow Reynolds number, Ri and the dimensionless wall velocity, k. Corresponding to each k ∈ [0,1], we have observed two ranges of Ri for which the flow is unconditionally linearly stable. In the lower range, we have a stabilisation of long wavelengths leading to a cut-off Ri. In this range, cross-flow stabilisation and Couette stabilisation appear to act via very similar mechanisms in this range, leading to the potential for robust compensatory design of flow stabilisation using either mechanism. As Ri is increased, we see first destabilisation and then stabilisation at very large Ri. The instability is again a long wavelength mechanism. A linear energy analysis reveals that in this range the Reynolds stress becomes amplified, the critical layer is irrelevant and viscous dissipation is completely dominated by the energy production/negation, which approximately balances at criticality.

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