List Of Figures

View Image Figure 1:
Turbulence as observed in a river. Here we can see different turbulent wakes due to different obstacles (simple stones) emerging naturally above the water level. The photo has been taken by the authors below the dramatically famous Crooked Bridge in Mostar (Bosnia-Hercegovina), which was destroyed during the last Balcanic war, and recently re-built by Italian people.
View Image Figure 2:
Turbulence as observed passing an obstacle in the same river of Figure 1, allows us to look at a clear example of wake.
View Image Figure 3:
Three examples of vortices taken from the pictures by Leonardo da Vinci (cf. Frisch, 1995).
View Image Figure 4:
Turbulence as observed in a turbulent water jet (Van Dyke, 1982) reported in the book by Frisch (1995) (photograph by P. Dimotakis, R. Lye, and D. Papantoniu).
View Image Figure 5:
Turbulence in the atmosphere of Jupiter as observed by Voyager.
View Image Figure 6:
High resolution numerical simulations of 2D MHD turbulence at resolution 2048 × 2048 (courtesy by H. Politano). Here the authors show the current density J (x, y), at a given time, on the plane (x,y).
View Image Figure 7:
Concentration field c(x,y), at a given time, on the plane (x, y). The field has been obtained by a numerical simulation at resolution 2048 × 2048. The concentration is treated as a passive scalar, transported by a turbulent field. Low concentrations are reported in blue while high concentrations are reported in yellow (courtesy by A. Noullez).
View Image Figure 8:
The original pictures by O. Reynolds which show the transition to a turbulent state of a flow in a pipe, as the Reynolds number increases from top to bottom (see the website Reynolds, 1883).
View Image Figure 9:
Turbulence as measured in the atmospheric boundary layer. Time evolution of the longitudinal velocity and temperature are shown in the upper and lower panels, respectively. The turbulent samples have been collected above a grass-covered forest clearing at 5 m above the ground surface and at a sampling rate of 56 Hz (Katul et al., 1997).
View Image Figure 10:
A sample of fast solar wind at distance 0.9 AU measured by the Helios 2 spacecraft. From top to bottom: speed, number density, temperature, and magnetic field, as a function of time.
View Image Figure 11:
Turbulence as measured at the external wall of a device designed for thermonuclear fusion, namely the RFX in Padua (Italy). The radial component of the magnetic field as a function of time is shown in the figure (courtesy by V. Antoni).
View Image Figure 12:
Magnetic intensity fluctuations as observed by Helios 2 in the inner solar wind at 0.9 AU, for different blow-ups. The apparent self-similarity is evident here.
View Image Figure 13:
Time evolution of the variables x(t), y(t), and z(t) in the Lorenz’s model (see Equation (18View Equation)). This figure has been obtained by using the parameters Pr = 10, b = 8/3, and R = 28.
View Image Figure 14:
The Lorenz butterfly attractor, namely the time behavior of the variables z(t) vs. x(t) as obtained from the Lorenz’s model (see Equation (18View Equation)). This figure has been obtained by using the parameters Pr = 10, b = 8/3, and R = 28.
Watch/download Movie Figure 15: (Movie)
Animation built on SOHO/EIT and SOHO/SUMER observations of the solar-wind source regions and magnetic structure of the chromospheric network. Outflow velocities, at the network cell boundaries and lane junctions below the polar coronal hole, reach up to 10 km s-1 are represented by the blue colored areas (original figures from Hassler et al., 1999).
View Image Figure 16:
Helmet streamer during a solar eclipse. Slow wind leaks into the interplanetary space along the flanks of this coronal structure. (Figure taken from High Altitude Observatory, 1991).
View Image Figure 17:
High velocity streams and slow wind as seen in the ecliptic during solar minimum as function of time [yyddd]. Streams identified by labels are the same corotating stream observed by Helios 2, during its primary mission to the sun in 1976, at different heliocentric distances. These streams, named “The Bavassano-Villante streams” after Tu and Marsch (1995a), have been of fundamental importance in understanding the radial evolution of MHD turbulence in the solar wind.
View Image Figure 18:
High velocity streams and slow wind as seen in the ecliptic during solar maximum. Data refer to Helios 2 observations in 1979.
View Image Figure 19:
High velocity streams and slow wind as seen in the ecliptic during solar minimum
View Image Figure 20:
Left panel: a simple sketch showing the configuration of a helmet streamer and the density profile across this structure. Right panel: Helios 2 observations of magnetic field and plasma parameters across the heliospheric current sheet. From top to bottom: wind speed, magnetic field azimuthal angle, proton number density, density fluctuations and normalized density fluctuations, proton temperature, magnetic field magnitude, total pressure, and plasma beta, respectively (adopted from Bavassano et al., 1997, © 1997 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 21:
The magnetic energy spectrum as obtained by Coleman (1968).
View Image Figure 22:
A composite figure of the magnetic spectrum obtained by Russell (1972).
View Image Figure 23:
Power density spectra of magnetic field fluctuations observed by Helios 2 between 0.3 and 1 AU within the trailing edge of the same corotating stream shown in Figure 17, during the first mission to the Sun in 1976. The spectral break (blue dot) shown by each spectrum, moves to lower and lower frequency as the heliocentric distance increases.
View Image Figure 24:
Power density spectra of the three components of IMF after rotation into the minimum variance reference system. The black curve corresponds to the minimum variance component, the blue curve to the maximum variance, and the red one to the intermediate component. This case refers to fast wind observed at 0.3 AU and the minimum variance direction forms an angle of ~ 8o with respect to the ambient magnetic field direction. Thus, most of the power is associated with the two components quasi-transverse to the ambient field
View Image Figure 25:
Correlation function just for the Z component of interplanetary magnetic field as observed by Helios 2 during its primary mission to the Sun. The blue color refers to data recorded at 0.9 AU while the red color refers to 0.3 AU. Solid lines refer to fast wind, dashed lines refer to slow wind.
View Image Figure 26:
Contour plot of the 2D correlation function of interplanetary magnetic field fluctuations as a function of parallel and perpendicular distance with respect to the mean magnetic field. The separation in r|| and r _L is in units of 1010 cm (adopted from Matthaeus et al., 1990, © 1990 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 27:
sm vs. frequency and wave number relative to an interplanetary data sample recorded by Voyager 1 at approximately 1 AU (adopted from Matthaeus and Goldstein, 1982b, © 1982 American Geophysical Union, reproduced by permission of American Geophysical Union).
Watch/download Movie Figure 28: (Movie)
Numerical simulation of the incompressible MHD equations in three dimensions, assuming periodic boundary conditions (see details in Mininni et al., 2003a). The left panel shows the power spectra for kinetic energy (green), magnetic energy (red), and total energy (blue) vs. time. The right panel shows the spatially integrated kinetic, magnetic, and total energies vs. time. The vertical (orange) line indicates the current time. These results correspond to a 1283 simulation with an external force applied at wave number kforce = 10 (movie kindly provided by D. Gómez).
View Image Figure 29:
Alfvénic correlation in fast solar wind. Left panel: large scale Alfvénic fluctuations found by Bruno et al. (1985). Right panel: small scale Alfvénic fluctuations for the first time found by Belcher and Solodyna (1975) (© 1975, 1985 American Geophysical Union, reproduced and adapted by permission of American Geophysical Union).
View Image Figure 30:
Alfvénic correlation in fast and slow wind. Notice the different degree of correlation between these two types of wind.
View Image Figure 31:
Histograms of normalized cross-helicity sc showing its evolution between 0.3 (circles), 2 (triangles), and 20 (squares) AU for different time scales: 3 h (top panel), 9 h (middle panel), and 81 h (bottom panel) (adopted from Roberts et al., 1987b, © 1987 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 32:
Values of the Alfvén ratio rA as a function of frequency and heliocentric distance, within slow (left column) and fast (right column) wind (adopted from Marsch and Tu, 1990a, © 1990 American Geophysical Union, reproduced by permission of American Geophysical Union).
Watch/download Movie Figure 33: (Movie)
1283 numerical simulation, as in Figure 28, but with an external force applied at wave number kforce = 3 (movie kindly provided by D. Gómez).
View Image Figure 34:
Scatter plot between the z-component of the Alfvén velocity and the proton velocity fluctuations at about 2 mHz. Data refer to Helios 2 observations at 0.29 AU (left panel) and 0.88 AU (right panel) (adapted from Bavassano and Bruno, 2000; © 2000 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 35:
Power density spectra ± e computed from ± dz fluctuations for different time intervals indicated by the arrows (adopted from Tu et al., 1990, © 1990 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 36:
Power density spectra e- and e+ computed from dz- and dz+ fluctuations. Spectra have been computed within fast (H) and slow (L) streams around 0.4 and 0.9 AU as indicated by different line styles. The thick line represents the average power spectrum obtained from all the about 50 - espectra, regardless of distances and wind speed. The shaded area is the 1s width related to the average (adopted from Tu and Marsch, 1990b, © 1990 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 37:
Ratio of - eover + ewithin fast wind at 0.3 and 0.9 AU in the left and right panels, respectively (adopted from Marsch and Tu, 1990a, © 1990 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 38:
Upper panel: solar wind speed and solar wind speed multiplied by sc. In the lower panels the authors reported: sc, rE, e-, e+, magnetic compression, and number density compression, respectively (adopted from Bruno and Bavassano, 1991, © 1991 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 39:
Ratio of e-over e+within fast wind between 1 and 5 AU as observed by Ulysses in the ecliptic (adopted from Bavassano et al., 2001, © 2001 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 40:
Left column: e+and e-spectra (top) and sc (bottom) during a slow wind interval at 0.9 AU. Right column: kinetic e v and magnetic e B energy spectra (top) computed from the trace of the relative spectral tensor, and spectrum of the Alfvén ratio rA (bottom) (adopted from Tu and Marsch, 1991).
View Image Figure 41:
Power density spectra for + eand - eduring a high velocity stream observed at 0.3 AU. Best fit lines for different frequency intervals and related spectral indices are also shown. Vertical lines fix the limits of five different frequency intervals analyzed by Bruno et al. (1996) (adopted from Bruno et al., 1996).
View Image Figure 42:
Left panel: wind speed profile is shown in the top panel. Power density associated with e+(thick line) and e-(thin line), within the 5 frequency bands chosen, is shown in the lower panels. Right panel: wind speed profile is shown in the top panel. Values of the angle between the minimum variance direction of + dz (thick line) and - dz (thin line) and the direction of the ambient magnetic field are shown in the lower panels, relatively to each frequency band (adopted from Bruno et al., 1996).
View Image Figure 43:
Large scale solar wind profile as a function of latitude during minimum (left panel) and maximum (right panel) solar cycle phases. The sunspot number is also shown at the bottom panels (adopted from McComas et al., 2003, © 2003 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 44:
Magnetic field and velocity hourly correlation vs. heliographic latitude (adopted from Smith et al., 1995, © 1995American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 45:
Normalized magnetic field components and magnitude hourly variances plotted vs. heliographic latitude during a complete latitude survey by Ulysses (adopted from Forsyth et al., 1996, © 1996 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 46:
Spectral indexes of magnetic fluctuations within three different time scales as indicated in the plot. The bottom panel shows heliographic latitude and heliocentric distance of Ulysses (adopted from Horbury et al., 1995c, © 1995 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 47:
Spectral exponents for the B z component estimated from the length function computed from Ulysses magnetic field data, when the s/c was at about 4 AU and o ~ - 50 latitude. Different symbols refer to different time intervals as reported in the graph (figure adopted from  Horbury et al., 1995a).
View Image Figure 48:
Spectral exponents for the Bz component estimated from the length function computed from Helios and Ulysses magnetic field data. Ulysses length function (dotted line) is the same shown in the paper by Horbury et al. (1995a) when the s/c was at about 4 AU and o ~ -50 latitude (adopted from Marsch and Tu, 1996, © 1996 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 49:
Hourly variances of the components and the magnitude of the magnetic field vs. radial distance from the Sun. The meaning of the different symbols is also indicated in the upper right corner (adopted from Forsyth et al., 1996, © 1996 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 50:
(a) Scale dependence of radial power, (b) latitudinal power, (c) radial spectral index, (d) latitudinal spectral index, and (e) spectral index computed at 2.5 AU. Solid circles refer to the trace of the spectral matrix of the components, open squares refer to field magnitude. Correspondence between wave number scale and time scale is based on a wind velocity of 750 km s-1 (adopted from Horbury and Balogh, 2001, © 2001 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 51:
(a) Scale dependence of power anisotropy at 2.5 AU plotted as the log10 of the ratio of BR (solid circles), BT (triangles), BN (diamonds), and |B| (squares) to the trace of the spectral matrix; (b) the radial, and (c) latitudinal behavior of the same values, respectively (adopted from Horbury and Balogh, 2001, © 2001 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 52:
Power spectra of magnetic field components (solid circles) and magnitude (open squares) from Ulysses (solid line) and Helios 1 (dashed line). Spectra have been extrapolated to 1 AU using radial trends in power scalings estimated from Ulysses between 1.4 and 4.1 AU and Helios between 0.3 and 1 AU (adopted from Horbury and Balogh, 2001, © 2001 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 53:
Trace of e+(solid line) and e-(dash-dotted line) power spectra. The central and right panels refer to Ulysses observations at 2 and 4 AU, respectively, when Ulysses was embedded in the fast southern polar wind during 1993 - 1994. The leftmost panel refers to Helios observations during 1978 at 0.3 AU (adopted from Goldstein et al., 1995a, © 1995 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 54:
Normalized cross-helicity and Alfvén ratio at 2 and 4 AU, as observed by Ulysses at o - 80 and o -40 latitude, respectively (adopted from Goldstein et al., 1995a, © 1995 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 55:
Left panel: values of hourly variance of dz± (i.e., e±) vs. heliocentric distance, as observed by Ulysses. Helios observations are shown for comparison and appear to be in good agreement. Right column: Elsässer ratio (top panel) and Alfvén ratio (bottom panel) are plotted vs. radial distance while Ulysses is embedded in the polar wind (adopted from Bavassano et al., 2000a,b, © 2000 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 56:
2D histograms of normalized cross-helicity sc (here indicated by sC) and normalized residual energy sr (here indicated by sR) for different heliospheric regions (ecliptic wind, mid-latitude wind with strong velocity gradients, polar wind) (adopted from Bavassano et al., 1998, © 1998 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 57:
Results from the multiple regression analysis showing radial and latitudinal dependence of the power e+ associated with outward modes (see Appendix 13.3.1). The top panel refers to the same dataset used by Horbury and Balogh (2001). The bottom panel refers to a dataset omni-comprehensive of south and north passages free of strong compressive events (Bavassano et al., 2000a). Values of e+ have been normalized to the value o e+ assumed by this parameter at 1.4 AU, closest approach to the Sun. The black line is the total regression, the blue line is the latitudinal contribution and the red line is the radial contribution (adopted from Bavassano et al., 2002a, © 2002 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 58:
e+(red) and e-(blue) radial gradient for different latitudinal regions of the solar wind. The first three columns, labeled EQ, refer to ecliptic observations obtained with different values of the upper limit of TBN defined as the relative fluctuations of density and magnetic intensity. The last two columns, labeled POL, refer to observations of polar turbulence outside and inside 2.6 AU, respectively (adopted from Bavassano et al., 2001, © 2001 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 59:
Time evolution of the power density spectra of z+ and z- showing the turbulent evolution of the spectra due to velocity shear generation (adopted from Roberts et al., 1991).
View Image Figure 60:
Radial evolution of + eand - espectra obtained from the Marsch and Tu (1993a) model, in which a parametric decay source term was added to the Tu’s model (Tu et al., 1984) that was, in turn, extended by including both spectrum equations for e+and e -and solved them self-consistently (adopted from Marsch and Tu, 1993a, © 1993 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 61:
Spectra of + e(thick line), - e(dashed line), and r e (thin line) are shown for 6 different times during the development of the instability. For t > 50 a typical Kolmogorov slope appears. These results refer to b = 1 (figure adopted from Malara et al., 2001).
View Image Figure 62:
Top left panel: time evolution of + e(solid line) and - e(dashed line). Middle left panel: density (solid line) and magnetic magnitude (dashed line) variances. Bottom left panel: normalized cross helicity sc. Right panel: Ulysses observations of sc radial evolution within the polar wind (left column is from Malara et al., 2001, right panel is a courtesy of B. Bavassano).
View Image Figure 63:
The first two rows show magnetic field compression (see text for definition) for fast (left column) and slow (right column) wind at 0.3 AU (upper row) and 0.9 AU (middle row). The bottom panels show the ratio between compression at 0.9 AU and compression at 0.3 AU. This ratio is generally greater than 1 for both fast and slow wind.
View Image Figure 64:
From left to right: normalized spectra of proton temperature (adopted from Tu et al., 1991), number density, and magnetic field intensity fluctuations (adopted from Marsch and Tu, 1990b, © 1990 American Geophysical Union, reproduced by permission of American Geophysical Union) Different lines refer to different heliocentric distances for both slow and fast wind.
View Image Figure 65:
From top to bottom: field intensity |B |; proton and alpha particle velocity vp and va; corrected proton velocity vpc = vp- dvA, where vA is the Alfvén speed; proton and alpha number density np and na; proton and alpha temperature Tp and Ta; kinetic and magnetic pressure Pk and Pm, which the authors call Pgas and Pmag; total pressure Ptot and b = Pgas/Pmag (adopted from Thieme et al., 1989).
View Image Figure 66:
Correlation coefficient between number density n and total pressure pT plotted vs. the correlation coefficient between kinetic pressure and magnetic pressure for both Helios relatively to fast wind (adopted from Marsch and Tu, 1993b).
View Image Figure 67:
Histograms of r(N - Pt) and r(Pm - Pk) per solar rotation. The color bar on the left side indicates polar (red), mid-latitude (blue), and low latitude (green) phases. Moreover, universal time UT, heliocentric distance, and heliographic latitude are also indicated on the left side of the plot. Occurrence frequency is indicated by the color bar shown on the right hand side of the Figure (figure adopted from Bavassano et al., 2004).
View Image Figure 68:
Solar rotation histograms of B - N and B - T in the same format of Figure 67 (figure adopted from Bavassano et al., 2004).
View Image Figure 69:
Scatter plots of the relative amplitudes of total pressure vs. density fluctuations for polar wind samples P1 to P4. Straight lines indicate the Tu and Marsch (1994) model predictions for different values of a, the relative PBS/W contribution to density fluctuations (figure adopted from Bavassano et al., 2004).
View Image Figure 70:
Relative amplitude of density fluctuations vs. turbulent Mach number for polar wind. Solid and dashed lines indicate the M and M 2 scalings, respectively (figure adopted from Bavassano et al., 2004).
View Image Figure 71:
Wind speed profile V and |sc|V are shown in the top panel. The lower three panels refer to correlation coefficient, phase angle and coherence for the three components of dV and dB fluctuations, respectively. The successive panel indicates the value of the angle between magnetic field and velocity fluctuations minimum variance directions. The bottom panel refers to the heliocentric distance (adopted from Bruno and Bavassano, 1993).
View Image Figure 72:
Structure functions for the magnetic field intensity Sn(r) for two different orders, n = 3 and n = 5, for both slow wind and fast wind, as a function of the time scale r. Data come from Helios 2 spacecraft at 0.9 AU.
View Image Figure 73:
Structure functions Sn(r) for two different orders, n = 3 and n = 5, for both slow wind and high wind, as a function of the fourth-order structure function S4(r). Data come from Helios 2 spacecraft at 0.9 AU.
View Image Figure 74:
Left column: normalized PDFs for the magnetic fluctuations observed in the solar wind turbulence. Right panel: distribution function of waiting times Dt between structures at the smallest scale. The parameter b is the scaling exponent of the scaling relation PDF (Dt) ~ Dt-b for the distribution function of waiting times.
View Image Figure 75:
Left column: normalized PDFs of velocity fluctuations in atmospheric turbulence. Right panel: distribution function of waiting times Dt between structures at the smallest scale. The parameter b is the scaling exponent of the scaling relation - b PDF (Dt) ~ Dt for the distribution function of waiting times. The turbulent samples have been collected above a grass-covered forest clearing at 5 m above the ground surface and at a sampling rate of 56 Hz (Katul et al., 1997).
View Image Figure 76:
Left column: normalized PDFs of the radial magnetic field collected in RFX magnetic turbulence (Carbone et al., 2000). Right panel: distribution function of waiting times Dt between structures at the smallest scale. The parameter b is the scaling exponent of the scaling relation P DF (Dt) ~ Dt -b for the distribution function of waiting times.
View Image Figure 77:
Differences for the longitudinal velocity dut = u(t + t )- u(t) at three different scales t, as shown in the figure.
View Image Figure 78:
Differences for the magnetic intensity db = B(t + t )- B(t) t at three different scales t, as shown in the figure.
View Image Figure 79:
We show the kinetic energy spectrum |un(t)|2 as a function of log2 kn for the MHD shell model. The full line refer to the Kolmogorov spectrum k -2/3 n.
View Image Figure 80:
We show the magnetic energy spectrum 2 |bn(t)| as a function of log2kn for the MHD shell model. The full line refer to the Kolmogorov spectrum k -n2/3.
View Image Figure 81:
Time behavior of the real part of velocity variable u (t) n at three different shells n, as indicated in the different panels.
View Image Figure 82:
Time behavior of the real part of magnetic variable b (t) n at three different shells n, as indicated in the different panels.
View Image Figure 83:
In the first three panels we report PDFs of both velocity (left column) and magnetic (right column) shell variables, at three different shells ln. The bottom panels refer to probability distribution functions of waiting times between intermittent structures at the shell n = 12 for the corresponding velocity and magnetic variables.
View Image Figure 84:
Normalized PDFs of fluctuations of the longitudinal velocity field at four different scales t. Solid lines represent the fit made by using the log-normal model (adopted from Sorriso-Valvo et al., 1999, © 1999 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 85:
We show the normalized PDFs of fluctuations of the magnetic field magnitude at four different scales t as indicated in the different panels. Solid lines represent the fit made by using the log-normal model (adopted from Sorriso-Valvo et al., 1999, © 1999 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 86:
Scaling laws of the parameter c2(t) as a function of the scales t, obtained by the fits of the PDFs of both velocity and magnetic variables (see Figures 84 and 85). Solid lines represent fits made by power laws (adopted from Sorriso-Valvo et al., 1999, © 1999 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 87:
From top to bottom, we show 81 s averages of velocity wind profile in km s-1, magnetic field intensity in nT, the logarithmic value of magnetic (blue line), thermal(red line), and total pressure (black line) in dyne/ cm2 and field intensity residuals in nT. The two vertical boxes delimit the two time intervals # 1 and #2 which were chosen for comparison. While the first interval shows strong magnetic intermittency, the second one does not (adopted from Bruno et al., 2001).
View Image Figure 88:
Left column, from top to bottom: we show magnetic field intensity, maximum c3, intermediate c 2 and minimum c 1 variance components for magnetic field (blue color) and wind velocity relative to the time interval #1 shown in Figure 87. Right below, we show the hodogram on the maximum variance plane c3 - c2, as a function of time (blue color line). The red lines are the projection of the blue line. The large arc, from A to B, corresponds to the green segment in the profile of the magnetic field components shown in the upper panel. The same parameters are shown for interval # 2 (Figure 87), in the same format, on the right hand side of the figure. The time resolution of the data is 81 s (adopted from Bruno et al., 2001).
View Image Figure 89:
Trajectory followed by the tip of the magnetic field vector (blue color line) in the minimum variance reference system for interval # 1 (left) and # 2 (right). Projections on the three planes (red color lines) formed by the three eigenvectors c1,c2,c3, and the average magnetic field vector, with its projections on the same planes, are also shown. The green line extending from label A to label B refers to the arc-like discontinuity shown in Figure 88. The time resolution of the magnetic field averages is 6 s (adopted from Bruno et al., 2001). (To see animations relative to similar time intervals click on Figures 90 for a time series affected by the intermittency phenomenon or at 91 for non-intermittent and intermittent samples.
Watch/download Movie Figure 90: (Movie)
Trajectory followed by the tip of the magnetic field vector in the minimum variance reference system during a time interval not characterized by intermittency. The duration of the interval is 2000 × 6 s but the magnetic field vector moves only for 100 × 6 s in order to make a smaller file (movie kindly provided by A. Vecchio).
Watch/download Movie Figure 91: (Movie)
Trajectory followed by the tip of the magnetic field vector in the minimum variance reference system during a time interval characterized by intermittent events. The duration of the interval is 2000 × 6 s but the magnetic field vector moves only for 100 × 6 s in order to make a smaller file (movie kindly provided by A. Vecchio).
View Image Figure 92:
Simple visualization of hypothetical flux tubes which tangle up in space. Each flux tube is characterized by a local field direction, and within each flux tube the presence of Alfvénic fluctuations makes the magnetic field vector randomly wander about this direction. Moreover, the large scale is characterized by an average background field direction aligned with the local interplanetary magnetic field. Moving across different flux-tubes, characterized by a different values of |B |, enhances the intermittency level of the magnetic field intensity time series (adopted from Bruno et al., 2001).
View Image Figure 93:
Composite figure made adapting original figures from the paper by Chang et al. (2004). The first element on the upper left corner represents field-aligned spatio-temporal coherent structures. A cross-section of two of these structures of the same polarity is shown in the upper right corner. Magnetic flux iso-contours and field polarity are also shown. The darkened area represents intense current sheet during strong magnetic shear. The bottom element of the figure is the result of 2D MHD simulations of interacting coherent structures, and shows intermittent spatial distribution of intense current sheets. In this scenario, new fluctuations are produced which can provide new resonance sites, possibly nucleating new coherent structures
View Image Figure 94:
Flatness F vs. time scale t relative to magnetic field fluctuations. The left column (panels A and C) refers to slow wind and the right column (panels B and D) refers to fast wind. The upper panels refer to compressive fluctuations and the lower panels refer to directional fluctuations. Vertical bars represent errors associated with each value of F. The three different symbols in each panel refer to different heliocentric distances as reported in the legend (adopted from Bruno et al., 2003b, © 2003 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 95:
Flatness F vs. time scale t relative to wind velocity fluctuations. In the same format of Figure 94 panels A and C refer to slow wind and panels B and D refer to fast wind. The upper panels refer to compressive fluctuations and the lower panels refer to directional fluctuations. Vertical bars represent errors associated with each value of F (adopted from Bruno et al., 2003b, © 2003 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 96:
Values of c2 (upper panel) and s2 (lower panel) vs. heliocentric distance. These values have been calculated for the projected low frequency beginning of the inertial range relative to each distance (see text for details). R, T, and N components are indicated by asterisks, crosses and circles, respectively (adopted from Pagel and Balogh, 2003, © 2003 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 97:
BY component of the IMF recorded within a high velocity stream.
View Image Figure 98:
Magnetic field auto-correlation function at 1 AU (adopted from Matthaeus and Goldstein, 1982b, © 1982 American Geophysical Union, reproduced by permission of American Geophysical Union).
View Image Figure 99:
Some examples of Mexican Hat wavelet, for different values of the parameters t and ' t.
View Image Figure 100:
The black curve indicates the original time series, the red one refers to the LIMed data, and the blue one shows the difference between these two curves.
View Image Figure 101:
The top reference system is the RTN while the one at the bottom is the Solar Ecliptic reference system. This last one is shown in the configuration used for Helios magnetic field data, with the X axis positive towards the Sun.
View Image Figure 102:
Original reference system [x,y,z] and minimum variance reference system whose axes are V1, V2, and V3 and represent the eigenvectors of M. Moreover, c1, c2, and c3 are the eigenvalues of M.
View Image Figure 103:
Mean field reference system.
View Image Figure 104:
Outline of a top-hat plasma analyzer.
View Image Figure 105:
Unit volume in phase space.
View Image Figure 106:
Outline of a flux-gate magnetometer. The driving oscillator makes an electric current, at frequency f, circulate along the coil. This coil is such to induce along the two bars a magnetic field with the same intensity but opposite direction so that the resulting magnetic field is zero. The presence of an external magnetic field breaks this symmetry and the resulting field /= 0 will induce an electric potential in the secondary coil, proportional to the intensity of the component of the ambient field along the two bars.
View Image Figure 107:
Left panel: This figure refers to any of the two sensitive elements of the magnetometer. The thick black line indicates the magnetic hysteresis curve, the dotted green line indicates the magnetizing field H, and the thin blue line represents the magnetic field B produced by H in each bar. The thin blue line periodically reaches saturation producing a saturated magnetic field B. The trace of B results to be symmetric around the zero line. Right panel: magnetic fields B1 and B2 produced in the two bars, as a function of time. Since B1 and B2 have the same amplitude but out of phase by 180o, they cancel each other.
View Image Figure 108:
Left panel: the net effect of an ambient field HA is that of introducing an offset which will break the symmetry of B with respect to the zero line. This figure has to be compared with Figure 107 when no ambient field is present. The upper side of the B curve saturates more than the lower side. An opposite situation would be shown by the second element. Right panel: trace of the resulting magnetic field B = B1 + B2. The asymmetry introduced by HA is such that the resulting field B is different from zero.
View Image Figure 109:
Time derivative of the curve B = B1 + B2 shown in Figure 108 assuming the magnetic flux is referred to a unitary surface.