Turbulence: mechanics and structure of anomalous scaling

Abstract

As the finite correlation time of a force driving turbulence is taken into account, a new, dimensionless parameter occurs in the theory of turbulence. This new parameter is responsible for two different mechanisms of formation of anomalous spectra. The first mechanism is related to the change of a governing parameter, which defines the spectrum of turbulent fluctuation. The second mechanism is associated with spontaneous formation of characteristic scales that differ parametrically from the scale of the external force. The last mechanism can explain the intermittent structure of turbulent flows. The appropriate discrete set of the possible characteristic scales and anomalous spectra has been calculated. The results give a new insight into the concept of universality: there is a set of universal power laws, although occurrence in the spectrum segments described by one or another power law from this set depends on the dimensionless parameter mentioned above. It is noted that for the broad class of geophysical flows, the new dimensionless parameter is connected with the so-called degree of turbulence, which guarantees that the smallness of this parameter, as the degree of turbulence is usually small enough. That explains the important role of the Kolmogorov spectrum in geophysical applications.