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Optimal transient growth in compressible turbulent boundary layers

Type
Articles dans des revues avec comité de lecture
Author
ALIZARD, Frédéric
134975 Laboratoire de Dynamique des Fluides [DynFluid]
PIROZZOLI, Sergio
51482 Dipartimento di Energetica, Universita di Roma - La Sapienza-
BERNARDINI, Matteo
453696 Sapienza University [Rome]
GRASSO, Francesco
134975 Laboratoire de Dynamique des Fluides [DynFluid]

URI
http://hdl.handle.net/10985/18612
DOI
10.1017/jfm.2015.142
Date
2015
Journal
Journal of Fluid Mechanics

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.

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