The amplitude method is used for predictions of the roughness-induced transition on a parabolic arc-shaped swept wing in Mach=3.5 free stream. As contrasted to the e~N method, the amplitude method incorporates the excitation of stationary CF-vortices by local and/or distributed roughness, downstream amplification of these vortices and the amplitude criterion associated with their nonlinear breakdown. With these ingredients it is feasible to evaluate the transition onset in a rational physics-based manner as well as estimate roughness parameters at which the CF-dominated transition onset occurs at a certain distance from the wing leading edge. It is shown that randomly distributed roughness is much more effective than isolated imperfections. The critical size of distributed roughness is so small that it is very difficult to maintain the wing surface aerodynamically smooth as soon as CF-vortices have appreciable amplification factors. It is also shown that the interplay between receptivity and downstream growth of CF-disturbances may lead to unexpected dependencies of the CF-transition onset on the basic parameters. E.g. the wing surface cooling may increase the initial amplitude of CF vortices and decrease their growth rates so that the transition onset moves downstream as the wall temperature ratio decreases.
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