×

zbMATH — the first resource for mathematics

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

MSC:
76F99 Turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.