HR: 0800h
AN: SH51C-0282    [Abstracts]
TI: Turbulence and the Third Moment of Fluctuations: Kolmogorov's 4/5 law and its MHD Analogues in the Solar Wind
AU: * Forman, M A
EM: miriam.forman@sunysb.edu
AF: Stony Brook University, Nicholls Road, Stony Brook, NY 11794-3800
AU: Smith, C W
EM: Charles.Smith@unh.edu
AF: Institute for Earth, Atmospheres and Oceans, University of New Hampshire, Durham, NH 03824
AU: MacBride, B
EM: Benjamin.MacBride@unh.edu
AF: Institute for Earth, Atmospheres and Oceans, University of New Hampshire, Durham, NH 03824
AB: The assertion that the third moment of fluctuations at lag L, is proportional to L in the inertial range is fundamental to Kolmogorov's early and late theories of inertial-range turbulence, and all models of intermittent hydrodynamic turbulence obey it. Kolmogorov's "4/5 law" more specifically states that the third moment of longitudinal fluctuations is equal to minus 4/5 times the length scale times the energy dissipation rate per unit mass, E. Longitudinal fluctuations are the component of velocity parallel to the lag direction, e.g. fluctuations in radial velocity parallel to the solar wind. For solar wind measured by a single spacecraft using the Taylor hypothesis, the longitudinal fluctuation is [-Vr(t+L)+ Vr(t)]. The 4/5 law then states that $<$[Vr(t+L/V)- Vr(t)]3$>$ = + 4/5 EL.. The pdf of the fluctuations cannot be symmetric in an energy-conserving cascade, i.e., in an inertial range. We are not aware of a theory of the shape of the pdf that would characterize the sign and scaling of the third moment. MHD equivalents of the 4/5 law using the Elsasser variables, have been proposed by Politano and Pouquet and others and discussed in Biskamp's book on MHD turbulence. Since the third moment has such a crucial role in turbulence theory, we thought we ought to find out how it actually behaves in the solar wind, and if it is related to the energy dissipation rate as theories imply. We used ACE solar wind data to calculate signed third moments at lags from 64 seconds to days. They are indeed proportional to lag and positive in sign. Dissipation rates inferred from these moments compare well with the energy dissipation rates computed with other measures of the heating of the solar wind as inferred from Helios and Voyager and from the observed power spectrum of IMF fluctuations.
DE: 2149 MHD waves and turbulence
SC: SPA-Solar and Heliospheric Physics [SH]
MN: 2004 AGU Fall Meeting