Estimates of Mass and Momentum Transport by Eddy Turbulence in the Plasma Sheet Using Satellite Observations and a Mixing-Length Theory

Large-amplitude turbulent fluctuations are observed by satellites in the plasma sheet. ISEE-2 measurements found that the flow-velocity fluctuations have an rms velocity of about 75 km/sec and a correlation time of about 140 sec. From these Eulerian flow measurements, an estimate of the correlation length of the turbulence is obtained with the use of a mixing-length theory [Tennekes and Lumley, A First Course in Turbulence, secs. 2.3 and 7.1, MIT Press, 1974]. This estimate is 10,000 km for the correlation length of the turbulent flow. In a similar fashion, the Eulerian flow measurements can be combined with a mixing-length theory to predict the eddy-diffusion coefficient that governs the turbulent transport of mass and the coefficient of eddy viscosity that governs the turbulent transport of momentum. For the Earth's magnetotail, the calculated eddy-diffusion coefficient is used to predict mass-transport timescales and the calculated coefficient of eddy viscosity is used to construct a flow Reynolds number for the magnetotail. The amounts of turbulent diffusivity and viscosity in the magnetotail are compared with the amounts of numerical diffusivity and viscosity in global MHD codes.