Blackaby, Nicholas Derick; (1991) On viscous, inviscid and centrifugal instability mechanisms in compressible boundary layers, including non-linear vortex/wave interaction and the effects of large Mach number on transition. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The stability and transition of a compressible boundary layer, on a flat or curved surface, is considered using rational asymptotic theories based on the large size of the Reynolds numbers of concern. The Mach number is also treated as a large parameter with regard to hypersonic flow. The resulting equations are simpler than, but consistent with, the full Navier Stokes equations, but numerical computations are still required. This approach also has the advantage that particular possible mechanisms for instability and/or transition can be studied, in isolation or in combination, allowing understanding of the underlying physics responsible for the breakdown of a laminar boundary layer. The nonlinear interaction of Tollmien-Schlichting waves and longitudinal vortices is considered for the entire range of the Mach number; it is found that compressibility has significant effects on the solution properties. The arguments breakdown when the Mach number reaches a certain, large, size due to the 'collapse' of the multi-layered boundary layer present and thus we are naturally led on to investigate this new regime where 'non-parallelism' must be incorporated in the theory. Also, the effects of compressibility are then more significant, analytically, causing the governing equations to be more comphcated, and further analytic progress relies on shorter scales being employed for any perturbations to the basic flow. The numerical solution is discussed along with a non-linear asymptotic solution capturing a 'finite-time break-up' of the interactive boundary layer. This work suggests that for larger Mach numbers the crucial non-linear interaction is between inviscid modes and Gortler vortices and these are discussed in the remaining chapters. The inviscid modes are studied initially with no shock present, before the theory is modified for the inclusion of shock-wave/boundary layer interaction. In the last chapter the Gortler-vortex mechanism for large Mach numbers is considered.

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