STRUCTURE OF POLYSPECTRA OF SCALE-INVARIANT FIELDS APPLIED TO TURBULENCE

The global probabilistic structure of fully developed turbulence is predicted on the ground of the hypothesis of scale-invariance. It is shown that the spatial high-order spectra (spectral cumulants) of a velocity field and a pressure field of homo-geneous isotropic turbulence depend on the combined wavenumber according to a power law. The formula derived for the one-dimensional spatial third-order spectrum (bispectrum) of a velocity field of a turbulent flow is in excellent agreement with previously obtained experimental data. This fact adds considerable supports for the Kolmogorov’s hypothesis of scale-invariance of a velocity field at small scales with the scaling exponent 1/3. PACS: 47.27.Gs; 05.40.+j 1