Ensemble Space-Time Correlation of Plasma Turbulence in the Solar Wind

Abstract

Single point measurement turbulence cannot distinguish variations in space and time. We employ an ensemble of one-and two-point measurements in the solar wind to estimate the space-time correlation function in the comoving plasma frame. The method is illustrated using near Earth spacecraft observations, employing ACE, Geotail, IMP-8, and Wind datasets. New results include an evaluation of both correlation time and correlation length from a single method, and a new assessment of the accuracy of the familiar frozen-in flow approximation. This novel view of the spacetime structure of turbulence may prove essential in exploratory space missions such as Solar Probe Plus and Solar Orbiter for which the frozen-in flow hypothesis may not be a useful approximation.Introduction. The solar wind provides a natural laboratory for fundamental study of plasma turbulence in parameters ranges difficult to achieve in the laboratory (e.g., [1]), and often accessible only through remote sensing [2,3]. Fluctuations in space and time are characteristic of turbulence and each have significant influence in space and astrophysical contexts. The two point correlation functions and associated spectra [4,5] are essential turbulence diagnostics in applications such as plasma heating [6], solar wind acceleration [7], the scattering and transport of energetic particles [8,9], magnetic field connectivity [10,11] and geospace prediction (space weather) [12]. Time correlation enters these applications as well, but in somewhat different ways [9,11], as is also well established in turbulence theory [13]. However, for most in situ interplanetary observations, made by a single spacecraft, there is an almost complete ambiguity between spatial structure and temporal structure. For fast flows, the Taylor frozen-in flow approximation [14] (or, Taylor hypothesis) provides an estimate of purely spatial statistics, with quantifiable limitations on accuracy [15][16][17][18][19]. The time correlation and the space correlation have not been previously treated on the same footing in interplanetary datasets, as far as we are aware. Here we employ a multispacecraft methodology to present a novel view of the space-time correlation of interplanetary turbulence. We show how numerous one-and two-spacecraft measurements may be combined, without use of the Taylor hypothesis, to determine correlation functions in which length and time separations are treated as independent. This method can provide a wealth of information about turbulence structure and dynamics, and may become a valuable tool for interpreting present and future interplanetary datasets.Background. We consider space-time structure of fluctuations in interplanetary space. For simplicity we dis-

A Quarter Century ofWindSpacecraft Discoveries

“…The same method also reveals a Eulerian decorrelation time of about 2.9 h in the solar wind near one AU (Matthaeus et al, 2010). Later combinations of ACE, Geotail, and IMP-8 data with Wind data refined this picture, finding slightly smaller correlation lengths and different correlation lengths in fast and slow solar-wind streams (Matthaeus et al, 2016;Wicks et al, 2009Wicks et al, , 2010. Wind also supported other turbulence studies through, for example,…”

A Quarter Century of Wind Spacecraft Discoveries

“…The same method also reveals a Eulerian decorrelation time of about 2.9 h in the solar wind near one AU (Matthaeus et al, 2010). Later combinations of ACE, Geotail, and IMP-8 data with Wind data refined this picture, finding slightly smaller correlation lengths and different correlation lengths in fast and slow solar-wind streams (Matthaeus et al, 2016;Wicks et al, 2009Wicks et al, , 2010. Wind also supported other turbulence studies through, for example, WILSON ET AL.…”

Magnetohydrodynamic and kinetic scale turbulence in the near-Earth space plasmas: a (short) biased review

“…= plas + kV cos kV , scales . Note finally that other recent papers have raised the possibility of violating the Taylor hypothesis by MHD scales fluctuations taken in the inner heliosphere as those expected from the PSP mission (Matthaeus et al 2016;Bourouaine and Perez 2018).…”