Incorporating a tensor in the effective viscosity model of turbulence and the Reynolds stress

Koichi Takahashi; Koichi Takahashi

doi:10.3934/Math.2018.4.554

AIMS Mathematics

2018, Volume 3, Issue 4: 554-564. doi: 10.3934/Math.2018.4.554

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Research article Topical Sections

Incorporating a tensor in the effective viscosity model of turbulence and the Reynolds stress

Koichi Takahashi ^,

Institute for Research in Human Informatics, Tohoku Gakuin University, 2-1-1, Tenjinzawa, Izumi-ku, Sendai 981-3193, Japan

Received: 30 August 2018 Accepted: 04 November 2018 Published: 15 November 2018

The mean field model of turbulence proposed by the author describes interaction among mean velocity and effective viscosity. In this paper, the model is extended to incorporate a tensor field by keeping invariance under Galilei transformation and rotation. It is found that, when the form and the strengths of interactions among fields are appropriately chosen, the symmetric components of the tensor for steady channel turbulence exhibit fair correspondence with the observed Reynolds stress.
- Navier-Stokes equation,
- turbulence,
- variational principle,
- eddy viscosity,
- Reynolds stress
Citation: Koichi Takahashi. Incorporating a tensor in the effective viscosity model of turbulence and the Reynolds stress[J]. AIMS Mathematics, 2018, 3(4): 554-564. doi: 10.3934/Math.2018.4.554

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Abstract

The mean field model of turbulence proposed by the author describes interaction among mean velocity and effective viscosity. In this paper, the model is extended to incorporate a tensor field by keeping invariance under Galilei transformation and rotation. It is found that, when the form and the strengths of interactions among fields are appropriately chosen, the symmetric components of the tensor for steady channel turbulence exhibit fair correspondence with the observed Reynolds stress.

References

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