FORCED NONLINEAR DISTURBANCES IN INCOMPRESSIBLE BOUNDARY-LAYERS

In this paper we explore essentially nonlinear disturbances produced i n an incompressible boundary layer by a roughness on the wall. The sca le of the stationary roughness is supposed to be large enough so that generated waves are governed by the forced Benjamin-Davis-Acrivos (fBD A) equation. The disturbance patterns for a wide range of roughness si zes are analyzed revealing the remarkable phenomenon of bifurcations. A very specific oscillation motion over the obstacle is found. It appe ars to be the basic mechanism causing the periodic generation of solit ary waves upstream and downstream. The general structure of disturbanc es in space at different values of time is discussed. The asymptotic a nalysis of the solution, when the intensity of the external agency Q b ecomes a small parameter, is given. The quadratic term of an expansion based on this parameter is responsible for the redistribution of solu tion mass between regions located ahead and behind the obstacle, inevi tably leading to the gradual growth of nonlinear effects. According to the asymptotic consideration the time T(c) determining the onset of the nonlinear stage of disturbance development is O(Q(-3)), this estim ation correlates well with numerical results. (C) 1996 American Instit ute of Physics.