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Modal description of internal optimal streaks

Published online by Cambridge University Press:  10 May 2009

MARÍA HIGUERA  and
JOSÉ M. VEGA
MARÍA HIGUERA*
Affiliation:
E. T. S. Ingenieros Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, 28040 Madrid, Spain
JOSÉ M. VEGA
Affiliation:
E. T. S. Ingenieros Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros, 3, 28040 Madrid, Spain
*
†Email address for correspondence: maria.higuera@upm.es
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Abstract

This paper deals with the definition and description of optimal streaky (S) perturbations in a Blasius boundary layer. First, the asymptotic behaviours of S-perturbations near the free stream and the leading edge are studied to conclude that the former is slaved to the solution inside the boundary layer. Based on these results, a quite precise numerical scheme is constructed that allows concluding that S-perturbations produced inside the boundary layer, near the leading edge, can be defined in terms of just one streamwise-evolving solution of the linearized equations, associated with the first eigenmode of an eigenvalue problem first formulated by Luchini (J. Fluid Mech., vol. 327, 1996, p. 101). Such solution may be seen as an internal unstable streaky mode of the boundary layer, similar to eigenmodes of linearized stability problems. The remaining modes decay streamwise. Thus, the definition of streaks in terms of an optimization problem that is used nowadays is not necessary.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 626 , 10 May 2009 , pp. 21 - 31
Copyright
Copyright © Cambridge University Press 2009

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