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arXiv · hep-th/9707173

Exact Two-Point Correlation Functions of Turbulence Without Pressure in Three-Dimensions

A. R. Rastegar·M. R. Rahimi Tabar·P. Hawaii
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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 $ |{x_1 - x_2}|^{-α_3}$, where $α_3 = 2 + \frac{\sqrt{33}}{6}$. It is shown that, in three-dimensions, the energy spectrum $E(k)$ in the inertial range scales with exponent $ 2 - \frac {\sqrt{33}}{12} \simeq 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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A. R. Rastegar, M. R. Rahimi Tabar, P. Hawaii. 1998-01-06. Exact Two-Point Correlation Functions of Turbulence Without Pressure in Three-Dimensions. https://doi.org/10.1016/s0375-9601(98)00445-9

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