SPECTRAL LAWS FOR THE ENSTROPHY CASCADE IN A 2-DIMENSIONAL TURBULENCE

The author uses a generalised Von Karman-Heisenberg-von-Weizsacker-type model for the inertial transfer to give a generalised spectral law for the enstrophy cascade in a two-dimensional turbulence that exhibits a steeper energy spectrum for large wavenumbers and reduces to the well known k-3 spectrum at the other end of the spectrum. For very high wavenumbers, this spectrum is, in fact, an arbitrarily steep power law. Nonetheless, it is possible to give an even more rapidly decaying spectrum for this range, using a continuous spectral cascading model. He then discusses the intermittency aspects of the departures from the Batchelor-Kraichnan scaling law and shows that while the intermittency corrections within the framework of the beta model of Frisch et al. (1984) are in qualitative agreement with the predictions made by the generalised spectral law given in this paper, intermittency by itself is unable to account fully for the steeper spectra at large wavenumbers observed in the numerical experiments. The author discusses further fractal aspects of the enstrophy cascade, and shows that for the enstrophy cascade, the fractal dimension rules not only the manner in which the cascading proceeds but also the point where it stops.