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

Pages: 794 - 802, Issue Special, September 2011

 Abstract        Full Text (444.2K)              

Oleg V. Kaptsov - Institute of Computational Modeling SB RAS, Akademgorodok, 66036, Krasnoyarsk, Russian Federation (email)
Alexey V. Schmidt - Institute of Computational Modeling SB RAS, Akademgorodok, 66036, Krasnoyarsk, Russian Federation (email)

Abstract: Semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a self-propelled body in a passively strati ed 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 di erential equations satisfying natural boundary conditions was solved numerically. The obtained solutions agree with experimental data.

Keywords:  Turbulence, far turbulent wake, $k-\epsilon$ models of turbulence, B-determining equations method.
Mathematics Subject Classification:  Primary: 76F60, 35Q35.

Received: July 2010;      Revised: March 2011;      Published: October 2011.