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

Oleg V. Kaptsov; Alexey V. Schmidt

doi:10.3934/proc.2011.2011.794

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2011, Volume 2011: 794-802. Doi: 10.3934/proc.2011.2011.794 open access

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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

Received: June 30, 2010

Revised: February 28, 2011

Published: August 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 76F60, 35Q35.

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