Long wave instability development in the laminar boundary layer near porous wall. Asymptotic analysis

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.As a result of laminar flows analysis for large Reynolds number asymptotic theory was developed to describe variety of flows with relatively large longitudinal gradients where classical Prandtl’s boundary layer theory should be replaced by another theory. The most familiar example was associated with the theory of free interaction which allows to describe flows with small separated regions. This theory is applicable as well for many other flows including abrupt change in the boundary conditions, flows with reattachment etc. Unsteady free interaction theory allowed to describe long wave instability processes in the laminar boundary layers. In fact linearized variant of this theory may be deduced from original OrrSommerfeld equation. At the same time asymptotic theory may be useful to describe nonlinear instability processes as well. It is important that boundary condition on the wall describing relation between pressure change and vertical velocity is linear and doesn’t change uniformity of the problem. So it is possible to investigate as well linear stability problems incorporating early obtained results. Presented are results of stability analysis describing long wave disturbances development. These results may be useful to provide passive boundary layer flow control along with the buffet onset control.