An empirical investigation of compressibility in magnetohydrodynamic turbulence

The density fluctuations which occur in magnetohydrodynamic (MHD) turbulence are an important diagnostic of the turbulent dynamics, and serve as the basis of astrophysical remote sensing measurements. This paper is concerned with the relation between density fluctuations and fluctuations of the magnetic field and velocity. The approach is empirical, utilizing spacecraft observations of slow solar wind turbulence. Sixty-six data intervals of 1 h duration were chosen, in which the solar wind speed was less than 450 km/s, and in which the fluctuations in density and vector magnetic field appeared to be approximately stationary. The parameters of interest were the root-mean-square fluctuations of density and magnetic field, normalized by the respective mean values, epsilon(N)equivalent to<(deltan)(2)>(0.5)/n(0) and epsilon(B)equivalent to<(deltab)(2)>(0.5)/B-0, respectively, where n(0) and B-0 are the mean plasma number density and magnetic field strength. The conclusions of this study are as follows: (1) Consistent with previous investigations, the dependence of the normalized density fluctuation on the normalized magnetic field fluctuation is found to be between linear (epsilon(N)=epsilon(B)) and quadratic (epsilon(N)=epsilon(B)(2)). (2) The value of Requivalent toepsilon(N)/epsilon(B) shows a wide range from <0.1 to >4; the median value is 0.46 and the mean is 0.72. (3) Typical normalized fluctuation amplitudes (epsilon(N) and epsilon(B)) for records of one hour length (maximum scale size of similar or equal to1.6x10(6) km) are 0.03-0.08 for the density, and 0.04-0.21 for the magnetic field. (4) For most intervals, the magnitude of the perpendicular (to the large scale magnetic field) magnetic field fluctuations exceeds that of the parallel fluctuations by a factor of 3-4. This indicates that the turbulent magnetic field fluctuations are primarily transverse fluctuations. The implications of these results for theories of MHD turbulence, and for the remote sensing of turbulent plasmas such as the corona, the near-Sun solar wind, and the interstellar medium, are discussed. (C) 2004 American Institute of Physics.