Ased collection of fluctuations as is sometimes imagined. Numerical realizations of cascades, as well as observations of turbulence, reveal that nonlinear dynamics leads to local relaxation and the spontaneous creation of regions of reduced nonlinearity, bounded by higher stress concentrations of gradients. This perspective links cascade, relaxation, coherent structures, TalmapimodMedChemExpress Talmapimod intermittency and dissipation in a physically appealing picture that is complementary to the more mathematical view of intermittency in terms of anomalous scaling and fractal descriptions. It also makes clear that there is much more to a turbulence description than what is accessible simply by discussion of the power spectrum itself [59].rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373:…………………………………………………5. Evidence for coherent structures in the solar windGiven the accessibility of the solar wind as a natural laboratory for turbulence studies, it is natural to enquire whether the characterization of intermittent turbulence given above is consistent with interplanetary observations. The most obvious feature of solar wind observations that relates to the picture of cellular flux tube structure of MHD and plasma turbulence is the frequent appearance of discontinuities. These have been studied for decades [60,61], often interpreted as an example of the relevance of simple ideal MHD solutions to the solar wind [60?2]. If, alternatively, the discontinuities are features of turbulence, then a methodology is Y-27632 site needed that can compare properties, preferably statistical properties, of discontinuities in a known turbulence environment, such as MHD simulation, with the observed discontinuities in the solar wind. One such approach is the partial variance of increments (PVI) method, which was designed precisely for this purpose [36,63]. The PVI time series is defined in terms of the vector magnetic field increment B(s, ) = B(s + ) – B(s), which is evaluated along a linear trajectory labelled by s (in space or time) with a lag .4 Then the PVI time series is | B(s, )| , (5.1) PVI(s; ) = | B(s, )|4 The time lag is usually selected to correspond to the inertial range of the fluctuations, or in some cases the smallest time lag available in the dataset. For a given analysis, is fixed, but results for various values of may also be compared.(a)PVI SIM20 10 0 250 500 s/lc 750rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373:…………………………………………………(b)PVI ACE20 10 0 250 500 time/tc 750Figure 6. Spatial signal PVI computed from simulation versus distance s/c at a spatial lag = 0.00625c (solid thin red line), where c is the correlation scale. (b) Time series PVI (normalized to correlation time tc ) computed from ACE data at a time separation of 4 min. The thick dashed blue lines are the values of the thresholds employed for figure 7. (Online version in colour.)where the average is over a suitably large trailing (i.e. times < s) sample computed along the time series. Two sample PVI time series are shown in figure 6, one from a sample of about 750 correlation times of solar wind data and the other from a similar size sample taken from a large two-dimensional MHD turbulence simulation. The simulation is sampled along a linear trajectory analogous to the way that the solar wind data are interpreted using the Taylor hypothesis (spatial lag = time lag ?flow speed). The PVI time series measures the `spikin.Ased collection of fluctuations as is sometimes imagined. Numerical realizations of cascades, as well as observations of turbulence, reveal that nonlinear dynamics leads to local relaxation and the spontaneous creation of regions of reduced nonlinearity, bounded by higher stress concentrations of gradients. This perspective links cascade, relaxation, coherent structures, intermittency and dissipation in a physically appealing picture that is complementary to the more mathematical view of intermittency in terms of anomalous scaling and fractal descriptions. It also makes clear that there is much more to a turbulence description than what is accessible simply by discussion of the power spectrum itself [59].rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373:.........................................................5. Evidence for coherent structures in the solar windGiven the accessibility of the solar wind as a natural laboratory for turbulence studies, it is natural to enquire whether the characterization of intermittent turbulence given above is consistent with interplanetary observations. The most obvious feature of solar wind observations that relates to the picture of cellular flux tube structure of MHD and plasma turbulence is the frequent appearance of discontinuities. These have been studied for decades [60,61], often interpreted as an example of the relevance of simple ideal MHD solutions to the solar wind [60?2]. If, alternatively, the discontinuities are features of turbulence, then a methodology is needed that can compare properties, preferably statistical properties, of discontinuities in a known turbulence environment, such as MHD simulation, with the observed discontinuities in the solar wind. One such approach is the partial variance of increments (PVI) method, which was designed precisely for this purpose [36,63]. The PVI time series is defined in terms of the vector magnetic field increment B(s, ) = B(s + ) - B(s), which is evaluated along a linear trajectory labelled by s (in space or time) with a lag .4 Then the PVI time series is | B(s, )| , (5.1) PVI(s; ) = | B(s, )|4 The time lag is usually selected to correspond to the inertial range of the fluctuations, or in some cases the smallest time lag available in the dataset. For a given analysis, is fixed, but results for various values of may also be compared.(a)PVI SIM20 10 0 250 500 s/lc 750rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373:.........................................................(b)PVI ACE20 10 0 250 500 time/tc 750Figure 6. Spatial signal PVI computed from simulation versus distance s/c at a spatial lag = 0.00625c (solid thin red line), where c is the correlation scale. (b) Time series PVI (normalized to correlation time tc ) computed from ACE data at a time separation of 4 min. The thick dashed blue lines are the values of the thresholds employed for figure 7. (Online version in colour.)where the average is over a suitably large trailing (i.e. times < s) sample computed along the time series. Two sample PVI time series are shown in figure 6, one from a sample of about 750 correlation times of solar wind data and the other from a similar size sample taken from a large two-dimensional MHD turbulence simulation. The simulation is sampled along a linear trajectory analogous to the way that the solar wind data are interpreted using the Taylor hypothesis (spatial lag = time lag ?flow speed). The PVI time series measures the `spikin.
