JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. A2, PAGES 1763-1778, FEBRUARY 1, 1995 A model for the three-dimensional magnetic field correlation spectra of low-frequency solar wind fluctuations during Alfvnic periods Vincenzo Carbone, Francesco Malara, and Pierluigi Veltri Dipartimento di Fisica, Universitk della Calabria, Cosenza, Italy Abstract. Using statistical homogeneity, magnetic field fluctuations in the solar wind during Alfv6nic periods are analyzed in terms of the two independent polarizationsallowedfor each wave vector k. It is shownthat the energy spectra of the two polarizations can be related both to the correlation tensor and to the variance matrix, which is generally used to characterize the anisotropy of the turbulence.Assuming simple anisotropic power law models, the parameters defining the spectra of the two polarizationsare determinedby fitting the eigenvalues of the variance matrix on the corresponding eigenva.lues evaluated by Bavassanoet al. (1982) for Helios2 data. Then the corresponding form of the correla. tion tensoris obtained.In particular,we foundthat the spectrum of polarization [1] fluctuations (corresponding, in a weakturbulence theoryapproach, to the Alfv6n mode)is steeper tha•n the polariza, tion [2] spectrum (corresponding to the ma,gnetosonic modes). While the former spectrum is dominated by wave vectors parallel to B0, the latter is strongly flattened on the plane containingthe radial and the mean magnetic field B0 directions. A discussion of these results in connectionwith other observational and theoretical issues is outlined. Introduction The study of the nature and of the propertiesof solar wind low-frequency fluctuations in the frequency range 10 -7 Hz < f < I Hz notonly isimportant in itself, since it represents a way to understand the behavior of the magnetohydrodynamic (MHD) turbulence in a param- eter region which is not accessible in terrestrial labora- tories, but it also furnishesinformation that is useful in many differentastrophysical problems.In the last years a considerable amount of work has been done concern- ing both the analysis of the solar wind data and the theoretical understandingof the physical mechanisms which determine the features observed in the solar wind turbulence. It is now well established that, at least in the inner hellosphere and for the range of frequencies 10 -4 Hz < f < 10 -• Hz, interplanetary fluctuations in the trailing edgesof solar wind high-speed streams (Alfv•nic periods)displaythe following main proper- ties [Coleman, 1968;Belcher and Davis, 1971;Barnes, 1979]: 1. A power law range is presentin the energy spec- trum; i.e., the energy spectrum is proportional to fful•• where c• is often close to the values typical of a developed turbulence. 2. The fluctuations are essentially noncompressive: During long periodsthe density fluctuations 5p are ex- Copyright 1995 by the American Geophysical Union. Paper number 94JA02500. O148-022 7/95/94 JA-02500805.00 tremely reduced, and the magnetic field intensity re- mains almost constant. In particular, 5pip < 0.1 and IBI/IBI- 0.0½, where B is the magnetic nld, the normalized fluctuations •IBI/IBI o• the B compo- nents are of the order of unity. The fluctuations and IBI/IBI smaller for large-scale structures and slightly increasewith increasing frequency. 3. A strong correlation between velocity 5v and magnetic field 5B fluctuations is present in the form 5v •_q-SB/(4•rp) •/2. Thesign is thatcorresponding to fluctuations which propagate away from the Sun. These fluctuations are also strongly anisotropicover all the power law range. The anisotropy has been re- vealed through a minimum varianceanalysis [Bavas- sanoet al., 1978, 1982; Chang and Nishida, 1973]. This method givesinformation about the energydistribution among the different components of the magnetic fluc- tuations. It is based on the determination of the eigen- values and the eigenvectors of the variance matrix Sij of the magnetic fluctuations, Sij = {SBiSBj) (1) where the angle brackets indicate a time average.This analysis hasbeen carried out by Bavassano et al. [1982] for the solarwind magnetic fluctuations during Alfvdnic periods; theseauthors found that oneof the eigenvalues of S/j is typically much smaller than the other two, say, A3<< A2< A1(for example, typicalvalues for the ratios of the eigenvalues of Sij are A1 : A2: A3 = 10: 3: 1). The minimum variance direction turns out to be ahnost parallel to the average magneticfield B0, so the lnag- netic field fluctuations 5B lie in a plane approximately 1763