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A New Hypothesis on the Anisotropic Reynolds Stress Tensor for Turbulent FlowsThree-Dimensional Anisotropic Similarity Theory of Turbulent Velocity Fluctuations

A New Hypothesis on the Anisotropic Reynolds Stress Tensor for Turbulent Flows: Three-Dimensional... [This chapter focuses on the three-dimensional anisotropic similarity theory of turbulent oscillatory motions or Galilean invariant turbulent velocity fluctuations as a necessary theoretical background to understand the new hypothesis on the anisotropic Reynolds stress tensor in Chap. 5. The anisotropic similarity theory of three-dimensional turbulent velocity fluctuations was developed by Czibere [2, 3] in conjunction with a stochastic turbulence model (STM) to describe the Reynolds-averaged velocity fluctuations in the anisotropic Reynolds stress tensor (1.54). The three-dimensional theory of Czibere [2, 3] introduces an anisotropic similarity tensor—which is related to the dimensionless vector potential of the mechanically similar local velocity fluctuations—to distribute anisotropically the principal (dominant) turbulent shear stress in the fluid flow field. It is important to note that certain components of the anisotropic similarity theory presented in this chapter—e.g. the definition of the unit base vectors of the fluctuating natural coordinate system—are discussed in a slightly different way compared to the original theory of Czibere [2, 3]. The reason for minor modifications to the original theory is to introduce a fully Galilean invariant formulation of the anisotropic Reynolds stress tensor (1.54). The objective is to put the anisotropic similarity theory of velocity fluctuations into practice and make it available to those researchers who are intended to develop the next generation of anisotropic turbulence models.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A New Hypothesis on the Anisotropic Reynolds Stress Tensor for Turbulent FlowsThree-Dimensional Anisotropic Similarity Theory of Turbulent Velocity Fluctuations

Part of the Fluid Mechanics and Its Applications Book Series (volume 120)
Könözsy, László
Springer Journals — Feb 27, 2019
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36 pages

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-13542-3
Pages
67 –103
DOI
10.1007/978-3-030-13543-0_4
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter focuses on the three-dimensional anisotropic similarity theory of turbulent oscillatory motions or Galilean invariant turbulent velocity fluctuations as a necessary theoretical background to understand the new hypothesis on the anisotropic Reynolds stress tensor in Chap. 5. The anisotropic similarity theory of three-dimensional turbulent velocity fluctuations was developed by Czibere [2, 3] in conjunction with a stochastic turbulence model (STM) to describe the Reynolds-averaged velocity fluctuations in the anisotropic Reynolds stress tensor (1.54). The three-dimensional theory of Czibere [2, 3] introduces an anisotropic similarity tensor—which is related to the dimensionless vector potential of the mechanically similar local velocity fluctuations—to distribute anisotropically the principal (dominant) turbulent shear stress in the fluid flow field. It is important to note that certain components of the anisotropic similarity theory presented in this chapter—e.g. the definition of the unit base vectors of the fluctuating natural coordinate system—are discussed in a slightly different way compared to the original theory of Czibere [2, 3]. The reason for minor modifications to the original theory is to introduce a fully Galilean invariant formulation of the anisotropic Reynolds stress tensor (1.54). The objective is to put the anisotropic similarity theory of velocity fluctuations into practice and make it available to those researchers who are intended to develop the next generation of anisotropic turbulence models.]

Published: Feb 27, 2019

Keywords: Anisotropic similarity theory of turbulent velocity fluctuations; Three-dimensional similarity hypothesis; Map space of turbulence; Dimensionless vector potential; Anisotropic similarity tensor; Stochastic turbulence model (STM); Coordinate transformations

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