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

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 $|x_1-x_2{|}^{-{\alpha }_3}$, where ${\alpha }_3=2+\frac{\sqrt{33}}{6}$. 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.

9 pages, latex, no figures, we have corrected the our basic equations. We predict the inertial-range exponent for the energy spectrum for 3D-turbulence without pressure. We will present the detail of calculation and the results for 2D-turbulence elsewhere. Also some references are added

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• Turbulence without pressure
• Instantons in Burgers Equation
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Cited by in corpus (1)

• Theoretical Model for the Kramers-Moyal Description of Turbulence Cascades