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Optimal transient growth in compressible turbulent boundary layers

Published online by Cambridge University Press:  30 March 2015

F. Alizard ,
S. Pirozzoli ,
M. Bernardini  and
F. Grasso
F. Alizard*
Affiliation:
Laboratoire DynFluid, Arts & Métiers ParisTech et CNAM, 151 Boulevard de l’Hôpital, 75013 Paris, France
S. Pirozzoli
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Rome, Italy
M. Bernardini
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Rome, Italy
F. Grasso
Affiliation:
Laboratoire DynFluid, Arts & Métiers ParisTech et CNAM, 151 Boulevard de l’Hôpital, 75013 Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

The structure of zero-pressure-gradient compressible turbulent boundary layers is analysed using the tools of optimal transient growth theory. The approach relies on the extension to compressible flows of the theoretical framework originally developed by Reynolds & Hussain (J. Fluid Mech., vol. 52, 1972, pp. 263–288) for incompressible flows. The model is based on a density-weighted triple decomposition of the instantaneous field into the contributions of the mean flow, the organized (coherent) motions and the disorganized background turbulent fluctuations. The mean field and the eddy viscosity characterizing the incoherent fluctuations are here obtained from a direct numerical simulation database. Most temporally amplified modes (optimal modes) are found to be consistent with scaling laws of turbulent boundary layers for both inner and outer layers, as well as in the logarithmic region, where they exhibit a self-similar spreading. Four free-stream Mach numbers are considered: $\mathit{Ma}_{\infty }=0.2$, 2, 3 and 4. Weak effects of compressibility on the characteristics length and the orientation angles are observed for both the inner- and the outer-layer modes. Furthermore, taking into account the effects of mean density variations, a universal behaviour is suggested for the optimal modes that populate the log layer, regardless of the Mach number. The relevance of the optimal modes in describing the near-wall layer dynamics and the eddies that populate the outer region is discussed.

JFM classification

Compressible Flows: Compressible Flows Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 770 , 10 May 2015 , pp. 124 - 155
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© 2015 Cambridge University Press 

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