Triple-deck theory in transonic flows and boundary layer stability

A. N. Bogdanov   ; V. N. Diesperov   ; V. I. Zhuk   ; A. V. Chernyshev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 12, pp. 2208-2222

Résumé

An analysis of the lower branch of the neutral curve for the Blasius boundary layer leads to a perturbed velocity field with a triple-deck structure, which is a rather unexpected result. It is the asymptotic treatment of the stability problem that has a rational basis, since it is in the limit of high Reynolds numbers that the basic flow has the form of a boundary layer. The principles for constructing a boundary layer stability theory based on the triple-deck theory are proposed. Although most attention is focused on transonic outer flows, a comparative analysis with the asymptotic theory of boundary layer stability in subsonic flows is given. The parameters of internal waves near the lower branch of the neutral curve are associated with a certain perturbation field pattern. These parameters satisfy dispersion relations derived by solving eigenvalue problems. The dispersion relations are investigated in complex planes.

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