Cazalbou, JeanBernard and Chassaing, Patrick New results on the model problem of the diffusion of turbulence from a plane source. (2001) Physics of Fluids, 1 (2). ISSN 10706631

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Official URL: http://dx.doi.org/10.1063/1.1336155
Abstract
The problem of the diffusion of turbulence from a plane source is addressed in the context of twoequation eddyviscosity models and Reynoldsstresstransport models. In the steady state, full analytic solutions are given. At second order, they provide the equilibrium value of the anisotropy level obtained with different combinations of returntoisotropy and turbulentdiffusion schemes and confirm the results obtained by Straatman et al. [AIAA J. 36, 929 (1998)] in an approximate analysis. In addition, all the characteristics of the turbulence decrease can be determined and it is shown that a special constraint on the value of the modeling constants should hold if turbulence fills the whole surrounding space. In a second step, precise results can be given for the unsteady model problem at the firstorderclosure level. The evolution cannot be described with a single set of characteristic scales and one has to distinguish the cases of short and large times. In the shorttime regime, the flow is governed by the characteristic scales of turbulence at the source and contamination of the flow proceeds as t^1/2. At large times, the flow is governed by timedependent characteristic scales that correspond to the solution of the steady problem at the instantaneous location of the front. Contamination of the flow proceeds as a power of time that can be related to the value of the modeling constants. The role of a combination of these constants is emphasized whose value can be specified to produce a solution that matches simultaneously the experimental data for the decrease of turbulent kinetic energy in the steady state and the exponent of the propagation velocity in the transient regime.
Item Type:  Article 

HAL Id:  hal03609996 
Audience (journal):  International peerreviewed journal 
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Institution:  Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace  ISAESUPAERO (FRANCE) Université de Toulouse > Institut National Polytechnique de Toulouse  Toulouse INP (FRANCE) Université de Toulouse > Université Toulouse III  Paul Sabatier  UT3 (FRANCE) French research institutions > Centre National de la Recherche Scientifique  CNRS (FRANCE) 
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Deposited On:  16 Apr 2008 10:55 
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