One-third spectrum in large scale Hall-magnetohydrodynamic turbulence

Abstract

In a recent study [H. Branover, A. Eidelman, and E. Golbraikh, ``On the universality of large-scale turbulence,'' Phys. Fluids 16, 845 (2004)] the properties of the large scale turbulence have been investigated theoretically and experimentally concluding that the kinetic energy spectrum goes as k1/3 at large spatial scales and citing a few examples for the existence of such a spectrum in natural systems [J. C. Kaimal, R. A. Eversole, D. H. Lenschow, B. B. Stankov, P. H. Kahn, and J. A. Businger, ``Spectral characteristics of the convective boundary layer over uneven terrain,'' J. Atmos. Sci. 39, 1098 (1982); I. Gultepe and D. O'C. Starr, ``Dynamical structure and turbulence in cirrus clouds: Aircraft observations during FIRE,'' ibid. 52, 4159 (1995)]. In this paper we show that the 1/3 spectrum for the kinetic energy is a direct consequence of the magnetic helicity invariant of the Hall-magnetohydrodynamic turbulence. We present the simultaneous kinetic and magnetic energy spectra and propose the verification of the latter in the laboratory and natural systems.