The Turbulence Cascade in Physical Space

Abstract

Some recent developments on the physical mechanism of turbulence cascades are summarised. It is first shown that the energy cascade in statistically steady isotropic turbulence is local in scale, at least on average, and that temporal variations of the large-scale forcing are transferred to smaller scales as a ‘wave’ consistent with the classical Kolmogorov model. It is further shown that, when energy-containing structure are individually tracked in band-pass filtered velocity fields, they also behave classically. The correlation of their physical position with larger (or smaller) structures is highest towards the beginning (or end) of their lifetimes. The analysis is then extended to the structures of momentum flux in the logarithmic layer of turbulent channels. Small structures grow and shrink smoothly along their lifetimes, but larger ones change size mostly by splits and mergers involving structures of similar size. For the largest structures, splits predominate, although not overwhelmingly.