Finite amplitude neutrally stable two‐dimensional disturbances in parallel flows are determined for large Reynolds numbers when both nonlinearity and viscosity are important in the critical layer. The phase shift across the critical layer depends on the local vertical Reynolds number in the critical layer, and it varies monotonically between the value zero of the nonlinear theory and —πof the viscous theory. AnO(ɛ½) distortion of both the mean and fundamental harmonic is shown to be necessary. The eigenvalue problem is solved for long waves yielding neutral modes which link the two previous theories. In particular certain difficulties of the nonlinear theory are re
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