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| Paper IPM / Physic / 6649 |
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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
|x1−x2|−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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