Abstract
A new (topological or loop-) type of intermittency is studied in three-dimensional turbulence. The spectral (or fracton) dimension D s = 7 (4 − 7 ) ≃ 1.95 for this turbulence (i.e. all states are localized). This intermittency is different both from Kolmogorov type (unlocalized, since D S > 2) and from Alexander-Orbach type (strong localized helical fractons with D S ≃ 4 3 ). The corresponding energy spectral exponent is obtained to be equal to (1 − 7 ) ≃ -1.65 . These results are in good agreement with recent numerical (spectral dimension) and laboratory (turbulent energy spectrum) data. The anomaly in the experimentally observed fractal dimension of clouds surface D σ ≃ 2.35 can be also explained in the framework of this intermittency phenomenon. The results have been obtained by a renormalization of the noise-like ( 1 k ) energy spectrum in isotropic incompressible turbulence with taking into account of spontaneous parity breaking (by virtual pairs of helical excitations).
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