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Instability wave–streak interactions in a supersonic boundary layer

Published online by Cambridge University Press:  13 October 2017

Pedro Paredes Open the ORCID record for Pedro Paredes [Opens in a new window] ,
Meelan M. Choudhari  and
Fei Li
Pedro Paredes*
Affiliation:
Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Meelan M. Choudhari
Affiliation:
Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Fei Li
Affiliation:
Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA
*
†Email address for correspondence: pedro.paredes@nasa.gov
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Abstract

The interaction of stationary streaks undergoing non-modal growth with modally unstable instability waves in a supersonic flat-plate boundary-layer flow is studied using numerical computations. For incompressible flows, previous studies have shown that boundary-layer modulation due to streaks below a threshold amplitude level can stabilize the Tollmien–Schlichting instability waves, resulting in a delay in the onset of laminar–turbulent transition. In the supersonic regime, the most-amplified linear waves become three-dimensional, corresponding to oblique, first-mode waves. This change in the character of dominant instabilities leads to an important change in the transition process, which is now dominated by oblique breakdown via nonlinear interactions between pairs of first-mode waves that propagate at equal but opposite angles with respect to the free stream. Because the oblique breakdown process is characterized by a strong amplification of stationary streamwise streaks, artificial excitation of such streaks may be expected to promote transition in a supersonic boundary layer. Indeed, suppression of those streaks has been shown to delay the onset of transition in prior literature. This paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite-amplitude streaks in a two-dimensional, Mach 3 adiabatic flat-plate boundary-layer flow, followed by the modal instability characteristics of the perturbed, streaky boundary-layer flow. Both parts of the investigation are performed with the plane-marching parabolized stability equations. Consistent with previous findings, the present study shows that optimally growing stationary streaks can destabilize the first-mode waves, but only when the spanwise wavelength of the instability waves is equal to or smaller than twice the streak spacing. Transition in a benign disturbance environment typically involves first-mode waves with significantly longer spanwise wavelengths, and hence, these waves are stabilized by the optimal growth streaks. Thus, as long as the amplification factors for the destabilized, short wavelength instability waves remain below the threshold level for transition, a significant net stabilization is achieved, yielding a potential transition delay that may be comparable to the length of the laminar region in the uncontrolled case.

JFM classification

Boundary Layers: Boundary layer stability Flow Control: Instability control Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 831 , 25 November 2017 , pp. 524 - 553
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Copyright
© Cambridge University Press 2017. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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