Turbulence, Viscosity, and Dissipation in the Solar-Wind Plasma

Abstract

Estimates of the power spectra of the solar-wind magnetic field B and the radial component of the solar- wind plasma velocity V have been computed for the frequency range from one cycle per solar rotation to 1.35 X 10-1 Hz. The measurements used in the calculations were obtained in 1962 with instruments on board the spacecraft Mariner 2. From the spectral properties of the plasma fluctuations, it is tentatively concluded that the solar-wind flow is often turbulent in the region near 1.0 a.u. A heuristic model of the turbulent flow that is consistent with the observations is one in which the energy for the turbulence is derived from the differential motion of the streams in the solar-wind plasma. Instabilities associated with the differential streaming produce long-wavelength A1fv~n waves. The energy extracted from the dif- ferential motion cascades through a hierarchy of Alfvén waves until it reaches waves short enough for dissipation by proton cyclotron damping. As a result of this turbulent process the differential motion of the plasma streams is eliminated. During the Mariner 2 flight the mean variation in the streaming velocity over one period of solar rotation was 86 km sec', so that the energy available in the plasma at 1 0 au. due to this differential motion was about 3.8 X 1O'~ ergs gm'. The inertial-range spectrum of the turbu- lence evidently extended from about 10 cycles per day to somewhere above the magnetometer Nyquist frequency, 1.35 X 10-2 Hz. At these frequencies, the fluctuations in B were primarily transverse to the spiral-field direction. The fluctuations in the radial components of V and B exhibited equipartition of kinetic and magnetic energy, and the frequency dependences of both variables were roughly f' 2 The difference between the observed f1 2 dependence and thef' 6 dependence for such turbulence predicted by Kraichnan is tentatively attributed to fluctuations at the higher frequencies, described by Scarf, Wolfe, and Silva, that result from the operation of the garden-hose instability. Evidence for dissipation in the rangef> 0.2 Hz, probably due to proton cyclotron damping, is cited. The power density in the inertial range indicates that the approximate mean rate of dissipation due to turbulence near 1.0 a u. was 2.4 X 106 ergs gm' sec'. The lower limit for turbulent heating of the solar-wind protons between the Sun and 1.0 a.u. is estimated to have been 3.6 X 1O~ ° K. The integral of the spectrum of the plasma fluctuations over the entire frequency range shows that energy remaining in the differential streaming and turbulence at 1.0 a.u. was sufficient to heat the protons by another 8 X 1O~ ° K