Kinetic and related models with applications in the natural sciences

Evolving turbulence spectra en route to the Kolmogorov spectrum

Sergey Nazarenko

University of Warwick

I will describe the evolution stages of turbulence which is initially excited in a finite wavenumber range. Most interesting picture arises for the finite-capacity systems, when the corresponding Kolmogorov (or Kolmogorov-Zakharov) spectrum has a negligible amount of energy (or another cascading invariant) at the inertial range end close to the dissipation scale. The evolving turbulence spectrum in such systems undergoes through three self-similar stages. At stage one, the spectrum spreads from the initial wavenumber range toward the dissipation scales, leaving a power law behind the propagating front whose exponent is different from Kolmogorov. After that, the Kolmogorov spectrum forms as a reflection wave propagating from the dissipation range toward the initial scales. This evolution is characterized by self-similarity of a new kind. When the initial scales are reached, the Kolmogorov spectrum decays as a whole in a shrinking inertial range.