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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3530438]