摘要：

The linear and nonlinear evolution of unstable disturbances in high-Reynolds-number flows is reviewed from the perspective of asymptotic theory. For non-parallel and/or unsteady flows, quasi-parallel and quasi-steady approximations can only be strictly justified by asymptotic expansions based on the smallness of the inverse Reynolds number. Further, such an asymptotic approach allows the inclusion of nonlinear effects in a self-consistent manner. Attention is focussed primarily on three asymptotic regions: the lower-branch Tollmien-Schlichting (TS) scaling for boundary layers, the upper-branch TS scaling for boundary layers, and the Rayleigh scaling for (decelerating) boundary layers, free shear layers, jets and wakes. For fixed frequency disturbances in a decelerating boundary layer, these asymptotic regions occur at increasing distances from the leading edge. A disturbance propagating downstream from the leading edge will pass through each region in turn. The larger the initial disturbance, the further upstream nonlinear effects must be taken into account. Weakly nonlinear theory is possible when the relative growth-rate of disturbances is small, e.g. near a neutral curve. Close to the lower branch, it is possible to take into account non-parallelism, wavetrain modulation (i.e. wavepackets), and three dimensional effects such as those that lead to TS-wave/vortex interactions. A number of different models are described and critically assessed. Similar possibilities are examined on the upper-branch scaling, where an additional feature is the effect of nonlinear critical layers. Critical layers play a preeminent role on the Rayleigh scaling. Physical effects explained include the nonlinear saturation of two-dimensional disturbances in free shear layers and decelerating boundary layers, the explosive growth in amplitude of three dimensional disturbances, and the generation of surprisingly large longitudinal vortices and spanwise-dependent mean flows.

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