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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. |
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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. |
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Figure 3:
Three examples of vortices taken from the pictures by Leonardo da Vinci (cf. Frisch, 1995). |
| 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). |
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Figure 5:
Turbulence in the atmosphere of Jupiter as observed by Voyager. |
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Figure 6:
High resolution numerical simulations of 2D MHD turbulence at resolution |
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Figure 7:
Concentration field |
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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). |
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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 |
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Figure 10:
A sample of fast solar wind at distance |
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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). |
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Figure 12:
Magnetic intensity fluctuations as observed by Helios 2 in the inner solar wind at |
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Figure 13:
Time evolution of the variables |
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Figure 14:
The Lorenz butterfly attractor, namely the time behavior of the variables |
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Figure 15:
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 |
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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). |
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Figure 17:
High velocity streams and slow wind as seen in the ecliptic during solar minimum as function of time |
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Figure 18:
High velocity streams and slow wind as seen in the ecliptic during solar maximum. Data refer to Helios 2 observations in 1979. |
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Figure 19:
High velocity streams and slow wind as seen in the ecliptic during solar minimum |
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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). |
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Figure 21:
The magnetic energy spectrum as obtained by Coleman (1968). |
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Figure 22:
A composite figure of the magnetic spectrum obtained by Russell (1972). |
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Figure 23:
Power density spectra of magnetic field fluctuations observed by Helios 2 between |
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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 |
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Figure 25:
Correlation function just for the |
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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 |
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Figure 27:
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Figure 28:
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 |
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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). |
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Figure 30:
Alfvénic correlation in fast and slow wind. Notice the different degree of correlation between these two types of wind. |
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Figure 31:
Histograms of normalized cross-helicity |
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Figure 32:
Values of the Alfvén ratio |
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Figure 33:
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Figure 34:
Scatter plot between the |
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Figure 35:
Power density spectra |
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Figure 36:
Power density spectra |
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Figure 37:
Ratio of |
| Figure 38:
Upper panel: solar wind speed and solar wind speed multiplied by |
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Figure 39:
Ratio of |
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Figure 40:
Left column: |
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Figure 41:
Power density spectra for |
| Figure 42:
Left panel: wind speed profile is shown in the top panel. Power density associated with |
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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). |
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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). |
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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). |
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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). |
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Figure 47:
Spectral exponents for the |
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Figure 48:
Spectral exponents for the |
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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). |
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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 |
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Figure 51:
(a) Scale dependence of power anisotropy at |
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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 |
| Figure 53:
Trace of |
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Figure 54:
Normalized cross-helicity and Alfvén ratio at |
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Figure 55:
Left panel: values of hourly variance of |
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Figure 56:
2D histograms of normalized cross-helicity |
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Figure 57:
Results from the multiple regression analysis showing radial and latitudinal dependence of the power |
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Figure 58:
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Figure 59:
Time evolution of the power density spectra of |
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Figure 60:
Radial evolution of |
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Figure 61:
Spectra of |
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Figure 62:
Top left panel: time evolution of |
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Figure 63:
The first two rows show magnetic field compression (see text for definition) for fast (left column) and slow (right column) wind at |
| 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. |
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Figure 65:
From top to bottom: field intensity |
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Figure 66:
Correlation coefficient between number density |
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Figure 67:
Histograms of |
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Figure 68:
Solar rotation histograms of |
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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 |
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Figure 70:
Relative amplitude of density fluctuations vs. turbulent Mach number for polar wind. Solid and dashed lines indicate the |
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Figure 71:
Wind speed profile |
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Figure 72:
Structure functions for the magnetic field intensity |
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Figure 73:
Structure functions |
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Figure 74:
Left column: normalized PDFs for the magnetic fluctuations observed in the solar wind turbulence. Right panel: distribution function of waiting times |
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Figure 75:
Left column: normalized PDFs of velocity fluctuations in atmospheric turbulence. Right panel: distribution function of waiting times |
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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 |
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Figure 77:
Differences for the longitudinal velocity |
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Figure 78:
Differences for the magnetic intensity |
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Figure 79:
We show the kinetic energy spectrum |
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Figure 80:
We show the magnetic energy spectrum |
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Figure 81:
Time behavior of the real part of velocity variable |
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Figure 82:
Time behavior of the real part of magnetic variable |
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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 |
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Figure 84:
Normalized PDFs of fluctuations of the longitudinal velocity field at four different scales |
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Figure 85:
We show the normalized PDFs of fluctuations of the magnetic field magnitude at four different scales |
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Figure 86:
Scaling laws of the parameter |
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Figure 87:
From top to bottom, we show |
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Figure 88:
Left column, from top to bottom: we show magnetic field intensity, maximum |
| 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 |
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Figure 90:
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 |
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Figure 91:
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 |
| 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 |
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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 |
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Figure 94:
Flatness |
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Figure 95:
Flatness |
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Figure 96:
Values of |
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Figure 97:
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Figure 98:
Magnetic field auto-correlation function at |
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Figure 99:
Some examples of Mexican Hat wavelet, for different values of the parameters |
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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. |
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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. |
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Figure 102:
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