Theoretical model for k−3 spectra in dispersed multiphase flows

The spectrum of a signal consisting of a sum of localized random bursts can exhibit, under certain conditions, an intermediate subrange evolving as the power −3 of the wavenumber k. These bursts should have a smooth and regular pattern, their strength and size should be statistically independent, and their size should be uniformly distributed between two finite wavelengths. This is probably the explanation for the k−3 subrange that is commonly observed in the velocity spectra of bubble-induced turbulence, which results from the interaction of the localized velocity disturbances caused by the bubbles.