Manchester Applied Mathematics and Numerical Analysis Seminars

Winter 1999/2000

December 15, 1999, 4.00 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

Generation of Tollmien-Schlichting waves by free-stream disturbances

Dr. Xuesong Wu, Dept. of Mathematics, Imperial College

The talk will address one of the fundamental problems in laminar-turbulent transition, the receptivity, which is concerned with the physical processes by which the external disturbances excite instability waves. Previous theories will be reviewed first; these include leading-edge receptivity, and the receptivity due to the acoustic and vortical disturbances interacting with a local wall roughness. I will then present a new receptivity mechanism, which involves a direct interaction between the acoustic and vortical disturbances in the free stream. This mechanism has several distinct features: (a) the scale conversion is achieved without resorting to local inhomogeneity and thus it operates even in a flat boundary layer, and (b) the instability waves are excited at the lower branch of the neutral curve and hence they do not undergo immediate decay. The efficiency of this mechanism is assessed by a parametric study.

The second part of my talk is concerned with the calculation of the initial amplitude of the instability waves generated by more conventional mechanisms, namely, the waves due to the acoustic and vortical disturbances interacting with a wavy wall. A second-order asymptotic theory is developed and the theoretical results are compared with the latest experimental data. A good quantitative agreement has been found. The results clarify a few issues regarding the role of free-stream turbulence in boundary-layer transition.

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For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).

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