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

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

Topical Section: Mathematical Analysis in Fluid Dynamics

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.
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Keywords 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. AIMS Mathematics, 2018, 3(4): 554-564. doi: 10.3934/Math.2018.4.554

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