Abstract
We perform numerical experiments on natural and controlled transition in two types of shear flows: a periodic ulated flat plate. In the mixing-layincompressible mixing layer, and a supersonic (Mach 5) boundary layer developing on an inser case, a direct-numerical simulation is developed, starting with a hyperbolic-tangent velocity profile. When the flow is forced initially by a small 3D isotropic residual turbulence (natural transition), it develops a vortex-lattice structure of the Kelvin-Helmholtz billows: this subharmonic secondary instability, corresponding to the helical-pairing instability studied by Pierrehumbert and Widnall (J. Fluid Mech., 114, pp 59-82, 1982), is in our calculation more amplified than the two-dimensional pairing. This is at variance with the predictions of the secondary instability theory, and yields a highly three- dimensional structure of the flow. A quasi two-dimensional perturbation (controlled transition), on the contrary, leads to longitudinal hairpin vortices strained between quasi two-dimensional billows, as found in the laboratory experiments of Bernal and Roshko (J. Fluid Mech., 170, pp 499-525, 1986). The compressible turbulent boundary layer at Mach 5 is numerically out of reach if one restricts to direct-numerical simulations. We have developed a large-eddy simulation using eddy-coefficients based on the second-order structure function of the velocity. This allows us to have a controlled-transition experiment, where the flow is forced upstream by a set of two-dimensional waves (second mode), to which a small 3D. Unitè Mixte de recherché CNRS, Institut National Polytechnique de Grenoble, Universitè Joseph Fourier. This work was supported by D.R.E.T. under contract 88/150, by CNES/Avions Marcel Dassault (HERMES European Space Programme), and by GDR-CNRSMécanique des Fluides Numérique. Part of the calculations were done on a grant of the Centre de Calcul Vectoriel pour la Recherche.
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Lesieur, M., Comte, P., Normand, X. (1992). The Vortex-Lattice Structure of Turbulent-Shear Flows. In: Gatski, T.B., Speziale, C.G., Sarkar, S. (eds) Studies in Turbulence. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2792-2_32
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DOI: https://doi.org/10.1007/978-1-4612-2792-2_32
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