This article is cited in 3 papers

Features of the linear stage of the development of three-dimensional perturbations in the plane Poiseuille–Couette flow

I. V. Savenkov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia

Abstract: Within the framework of the triple-deck theory, the linear stage of the development of three-dimensional disturbances in the Poiseuille–Couette flow was investigated. Numerical computations revealed “ripples” developing in the side direction in the initial phase of the linear stage. As in the case of two-dimensional disturbances, an increase in the relative velocity of the walls leads to the splitting of disturbances into two wave packets, of which the first grows faster and moves at a higher velocity. The disturbances propagate within a certain angle range.

Key words: plane Poiseuille–Couette flow, Tollmien–Schlichting waves, three-dimensional disturbances, wave packets, asymptotic expansions, triple-deck theory, Navier–Stokes equations.

UDC: 519.634

Received: 13.10.2009

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:8, 1399–1408

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