Self-similar decay of localized perturbations in the integral boundary layer equation

[摘要] The integral boundary layer equation (IBLe) arises as a long wave approximation for the flow of a viscous incompressible fluid down an inclined plane. The trivial solution of the IBLe is linearly at best marginally stable, i.e., it has essential spectrum at least up to the imaginary axis. Here, we show that in the stable case this trivial solution is in fact nonlinearly stable, with a Burgers like self-similar decay of localized perturbations. The proof uses renormalization theory and the fact that in the stable case Burgers equation is the amplitude equation for long small amplitude waves in the IBLe. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15

[关键词] inclined film flow;integral boundary layer equation;Nusselt solution;nonlinear stability;Burgers equation;renormalization