NON-EQUILIBRIUM,NONLINEAR CRITICAL LAYERS IN LAMINAR-TURBULENT TRANSITION

We describe some recent developments of high-Reynolds-number asymptotic theory forthe nonlinear stage of laminar-turbulent transition in nearly parallel flows.The classic weakly nonlineartheory of Landau and Stuart is briefly revisited with the dual purposes of highlighting its fundamentalideas,which continue to underlie much of current theoretical thinking,as well as its difficulty in dealingwith unbounded flows.We show that resolving such a difficulty requires an asymptotic approach basedon the high-Reynolds-number assumption,which leads to a nonlinear critical-layer theory.Major recentresults are reviewed with emphasis on the non-equilibrium effect.Future directions of investigation areindicated.