On the Landau constant in mixing layers

The nonlinear evolution of weakly amplified waves in a hyperbolic tangent-free shear layer is described when the Reynolds number is large and the critical layer is dominated by viscosity. The Stuart-Landau equation governing the finite-amplitude development of disturbances is obtained by asymptotic matching. If R denotes the Reynolds number, the Landau constant multiplying the cubic onlinearity is determined to be O (R⅓) and is stabilizing. A stable finite-amplitude equilibrium state is therefore reached by linearly amplified waves. The earlier result in Huerre (Phil. Trans. R. Soc. Lond. A 293, 643-675 (1980)) is shown to be incorrect.