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Paper   IPM / Physic / 6649
School of Physics
  Title:   Exact Two-Point Correlation Functions of Turbulence without Pressure in Three Dimensions
  Author(s): 
1.  A.R. Rastegar
2.  M.R. Rahimi Tabar
3.  A.H. Hawaii
  Status:   Published
  Journal: Phys. Lett. A
  No.:  52
  Vol.:  245
  Year:  1998
  Pages:   425-429
  Supported by:  IPM
  Abstract:
We investigate exact results of isotropic turbulence in three-dimensions when the pressure gradient is negligible. We derive exact two-point correlation functions of density in three-dimensions and show that the density-density correlator behaves as
|x1x2|−α3, where α3=2+[(√{33})/6]. It is shown that, in three-dimensions, the energy spectrum E(k) is the inertial range scales with exponent 2−[(√{33})/12] ≅ 1.5212. We also discuss the time scale for which our exact results are valid for strong 3D-turbulence in the presence of the pressure. We confirm our predictions by using the recent results of numerical calculations and experiment.

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