Reduction of three-dimensional model of the far turbulent wake to one-dimensional problem

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2011, 2011(Special): 794-802. doi: 10.3934/proc.2011.2011.794

Reduction of three-dimensional model of the far turbulent wake to one-dimensional problem

Oleg V. Kaptsov ^1, and Alexey V. Schmidt ^1,

1.	Institute of Computational Modeling SB RAS, Akademgorodok, 66036, Krasnoyarsk, Russian Federation, Russian Federation

Received July 2010 Revised March 2011 Published October 2011

Abstract
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Semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a self-propelled body in a passively stratied medium is considered. The sought quantities are the kinetic turbulent energy, kinetic energy dissipation rate, averaged density defect and density uctuation variance. The full group of transformations admitted by this model is found. The governing equations are reduced into ordinary differential equations by similarity reduction and method of the B-determining equations (BDEs). This system of ordinary dierential equations satisfying natural boundary conditions was solved numerically. The obtained solutions agree with experimental data.

Keywords: B-determining equations method., far turbulent wake, $k-\epsilon$ models of turbulence, Turbulence.

Mathematics Subject Classification: Primary: 76F60, 35Q3.

Citation: Oleg V. Kaptsov, Alexey V. Schmidt. Reduction of three-dimensional model of the far turbulent wake to one-dimensional problem. Conference Publications, 2011, 2011 (Special) : 794-802. doi: 10.3934/proc.2011.2011.794

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