Short- and Resonant-Range Interactions Between Scales in Turbulence and Their Applications

GAO Zhi

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GAO Zhi. Short- and Resonant-Range Interactions Between Scales in Turbulence and Their Applications[J]. Applied Mathematics and Mechanics, 2004, 25(8): 837-846.

Citation:

GAO Zhi. Short- and Resonant-Range Interactions Between Scales in Turbulence and Their Applications[J]. Applied Mathematics and Mechanics, 2004, 25(8): 837-846.

Citation:

GAO Zhi. Short- and Resonant-Range Interactions Between Scales in Turbulence and Their Applications[J]. Applied Mathematics and Mechanics, 2004, 25(8): 837-846.

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Short- and Resonant-Range Interactions Between Scales in Turbulence and Their Applications

GAO Zhi

Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China

Received Date: 2002-02-24
Rev Recd Date: 2004-01-09
Publish Date: 2004-08-15

Abstract

Abstract

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the short-range viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation (LES) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.
- turbulence,
- interacting scale,
- eddy viscosity,
- short-range viscous stress,
- resonant-range viscous stress,
- multiscale equation

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References(11)

References

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