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The effect of heating/cooling on the upper-branch stability of boundary layer flows over a compliant boundary. (English) Zbl 1016.76023

Summary: We investigate the evolution of Tollmien-Schlichting waves in boundary layers in the presence of moderate buoyancy arising from the heating or cooling of a compliant wall. We exploit the multi-deck structure of the flow in the limit of large Reynolds numbers to make an asymptotic analysis of the perturbed flow along the upper branch of neutral stability curve, and to derive linear neutral results. These results are discussed and compared to rigid wall results. Also, a brief parametric study, based on linear neutral results, is presented, and the results are discussed.

MSC:

76E05 Parallel shear flows in hydrodynamic stability
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
80A20 Heat and mass transfer, heat flow (MSC2010)
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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