INTERNAL TIME, IRREVERSIBILITY AND INTERMITTENCY IN THE QUASI-SELF-SIMILARITY OF TURBULENCE

We have presented the description of a dynamical regime inherent in a hierarchical velocity-correlation function defined for the time series of turbulent velocities. The regime is described with an average time scale termed the "internal time", which measures the rates of local energy transfers flowing through the hierarchy and of dissipation accompanying the energy flow. Viscosity of the fluid elongates the internal time in very small length scales in the neighborhood of the smallest scale, enhancing its own effect on nonlinear action. The elongation yields a time arrow resulting from the irreversibility of the dissipative nature. We put a new interpretation on intermittency (i.e. multifractal), and also give an explanation that the multifractal structure of turbulence makes our hierarchical description possible. Our model demonstrates the experimental results of Batchelor and Townsend for the decay of turbulent flows.