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On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence. (English) Zbl 0794.76044
The incompressible Navier-Stokes equations are transformed (homogeneous case) to the restricted Euler system, which can be solved in a closed form. Such an oversimplified model still shows a close correspondence to direct numerical simulations of the full Navier-Stokes equations, when the homogeneity assumption is slightly relaxed. The velocity gradient tensor in three-dimensional flow tends to evolve toward an attractor in the space of tensor invariants. This conclusion comes from numerical simulations, which give an insight into the topography of the attractor. Consequently one has an evidence that the restricted Euler system solution plays a significant role in the dynamics of kinetic energy dissipation.
Reviewer: P.Garbaczewski

76F99 Turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Full Text: DOI
[1] DOI: 10.1063/1.858295 · Zbl 0754.76004
[2] DOI: 10.1016/0378-4371(84)90008-6 · Zbl 0599.76040
[3] DOI: 10.1017/S0022112056000317 · Zbl 0071.40603
[4] DOI: 10.1063/1.866513
[5] DOI: 10.1017/S0022112093000473 · Zbl 0825.76685
[6] DOI: 10.1063/1.857730
[7] DOI: 10.1063/1.857824 · Zbl 0696.76070
[8] DOI: 10.1016/0167-2789(89)90151-6
[9] DOI: 10.1146/annurev.fl.13.010181.002325
[10] DOI: 10.1063/1.858282
[11] DOI: 10.1063/1.863957 · Zbl 0536.76034
[12] DOI: 10.1063/1.858798 · Zbl 0793.76046
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