Auteurs : A. Burlot, B.-J. Gréa, F. S. Godeferd, C. Cambon
We model a turbulent mixing zone between two fluids of different densities. The Boussinesq turbulent mixing zones is induced by a Rayleigh-Taylor instability [1, 2], and its properties are mostly determined by the fluctuating turbulent quantities at the centerline of the flow, in a region which can be considered nearly homogeneous if the mixing zone is large enough. We therefore focus on the anisotropic and unsteady aspects of turbulence, responsible for the self-similar regime. Unstably Stratified Homogeneous (USH) turbulence is used as a model for the mixing zone in an idealized theoretical and practical approach, assuming that the mean density profile inside the mixing zone is frozen. It is based on the concept of homogeneous isotropic turbulence proposed by Taylor [3], but here extended to the study of incompressible Boussinesq turbulence.
Our study of USH turbulence is carried out using an EDQNM (Eddy Damping Quasi-Normal Markovianization) model initially developped for isotropic turbulence [4], and later improved to deal with stable stratification [5, 6]. We propose in this work to extend the model to unstable stratification. This two-point statistical model allows to investigate axisymmetric turbulence through a set of velocity-density correlation function spectra that depend on the wave-number and on the angle between the wave-vector and the vertical direction that bears gravity.
Two major applications of our EDQNM model for USH turbulence will be presented: (a) the inquiry of turbulent quantities evolution at very large Reynolds number [7] ; (b) the study of large-scale turbulence that control the mixing zone dynamics [8, 9].
We shall also compare the results of the model with those of direct numerical simulations.
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[3] G. I. Taylor. Statistical theory of turbulence. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 151(873):pp. 421-444, 1935.
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[8] O. Poujade and M. Peybernes. Growth rate of rayleigh-taylor turbulent mixing layers with the foliation approach. Physical Review E, 81:016316, Jan 2010.
[9] O. Soulard, J. Griffond, and B.-J. Grea. Large-scale analysis of self-similar unstably stratified homogeneous (USH) turbulence. Physics of Fluids, NC:NC, Submitted.