Boundary layer receptivity and control

Receptivity processes initiate natural instabilities in a boundary layer. The instabilities grow and eventually break down to turbulence. Consequently, receptivity questions are a critical element of the analysis of the transition process. Success in modeling the physics of receptivity processes thus has a direct bearing on technological issues of drag reduction. The means by which transitional flows can be controlled is also a major concern: questions of control are tied inevitably to those of receptivity. Adjoint systems provide a highly effective mathematical method for approaching many of the questions associated with both receptivity and control. The long term objective is to develop adjoint methods to handle increasingly complex receptivity questions, and to find systematic procedures for deducing effective control strategies. The most elementary receptivity problem is that in which a parallel boundary layer is forced by time-harmonic sources of various types. The characteristics of the response to such forcing form the building blocks for more complex receptivity mechanisms. The first objective of this year's research effort was to investigate how a parallel Blasius boundary layer responds to general direct forcing. Acoustic disturbances in the freestream can be scattered by flow non-uniformities to produce Tollmien-Schlichting waves. For example, scattering by surface roughness is known to provide an efficient receptivity path. The present effort is directed towards finding a solution by a simple adjoint analysis, because adjoint methods can be extended to more complex problems. In practice, flows are non-parallel and often three-dimensional. Compressibility may also be significant in some cases. Recent developments in the use of Parabolized Stability Equations (PSE) offer a promising possibility. By formulating and solving a set of adjoint parabolized equations, a method for mapping the efficiency with which external forcing excites the three-dimensional motions of a non-parallel boundary layer was developed. The method makes use of the same computationally efficient formulation that makes the PSE currently so appealing. In the area of flow control, adjoint systems offer a powerful insight into the effect of control forces. One of the simplest control strategies for boundary layers involves the application of localized mean wall suction.