Intermittent Anisotropic Turbulence Detected by THEMIS in the Magnetosheath

Abstract

Following our previous study of Time History of Events and Macroscale Interactions during Substorms (THEMIS) data, we consider intermittent turbulence in the magnetosheath depending on various conditions of the magnetized plasma behind the Earth’s bow shock and now also near the magnetopause. Namely, we look at the fluctuations of the components of the Elsässer variables in the plane perpendicular to the scale-dependent background magnetic fields and along the local average ambient magnetic fields. We have shown that Alfvén fluctuations often exhibit strong anisotropic non-gyrotropic turbulent intermittent behavior resulting in substantial deviations of the probability density functions from a normal Gaussian distribution with a large kurtosis. In particular, for very high Alfvénic Mach numbers and high plasma beta, we have clear anisotropy with non-Gaussian statistics in the transverse directions. However, along the magnetic field, the kurtosis is small and the plasma is close to equilibrium. On the other hand, intermittency becomes weaker for moderate Alfvén Mach numbers and lower values of the plasma parameter beta. It also seems that the degree of intermittency of turbulence for the outgoing fluctuations propagating relative to the ambient magnetic field is usually similar as for the ingoing fluctuations, which is in agreement with approximate equipartition of energy between these oppositely propagating Alfvén waves. We believe that the different characteristics of this intermittent anisotropic turbulent behavior in various regions of space and astrophysical plasmas can help identify nonlinear structures responsible for deviations of the plasma from equilibrium.

Intermittent turbulence in the heliosheath and the magnetosheath plasmas based on Voyager and THEMIS data

“…1 and 2 of the work by Macek et al, 2017, cases 3, 5, 15, and 16 listed in Table 2), the dependence of the parallel and perpendicular components of kurtosis on timescale τ for both the outgoing (z + ) and ingoing fluctuations (z − ) is now presented in Figs. 14 and 15, taken from (Macek et al, 2017). We can see that kurtosis behind the bow shock, Fig. 14, cases (a) and (b) in Table 2, could sometimes (for β ∼ 1) be smaller than that near the magnetopause, Fig.…”

“…1 and 2 of the paper by Macek et al (2017), we can calculate the Elsässer variables, z ± = V ± V A , where the characteristic Alfvénic velocity is given by V A = B/(µ 0 ρ) 1/2 (Elsasser, 1950). It is worth noting that the sign is taken here relative to the local average magnetic field B o , which certainly depends on the timescale τ responsible for turbulence (Kiyani et al, 2013), as recently noted by Gerick et al (2017).…”

“…1 and 2 of the paper by Macek et al (2017), namely near the bow shock, cases (a) and (b), and near the magne- Figure 10. Kurtosis of the increments of the Elsässer vectors, δz ± , in the magnetosheath vs. the total plasma beta β for the components δz ± (parallel to the mean field vector B o , panels a and b) and two components perpendicular to the field: (1) δz ± ⊥1 (in the plane containing B o and the X axis in the GSE system, panels c and d), and (2) δz ± ⊥2 (perpendicular to the plane, panels e and f) near the bow shock (BS, red circles) and near the magnetopause (MP, white triangles), as observed by THEMIS for samples listed in Table 2. topause, cases (c) and (d), for a given timescale τ = 9 s, are illustrated in Figs.…”

“…4 we continue our study in the entire magnetosheath also near the magnetopause. However, since it would be difficult to obtain the full multifractal spectrum using the THEMIS data, at present we only examine how the degree of multifractality resulting in deviation from the normal distribution, which is also a level of intermittency, depends on the characteristics of the solar wind and magnetospheric plasmas (Macek et al, 2017). The data under study are briefly described in Sect.…”

Intermittent turbulence in the heliosheath and the magnetosheath plasmas based on Voyager and THEMIS data

“…(2) f (D 1 ) = D 1 ; and (3) the line joining the origin to the point on the f (α) curve where α = D 1 is tangent to the curve, as taken from Ott (1993). one needs to specify two scales l 1 and l 2 (l 1 + l 2 ≤ 1) associated with probability measures p and 1 − p. In fact, fractals and multifractals could be considered a convenient mathematical language useful for understanding dynamics of turbulence, as already postulated by Mandelbrot (1982). In fact, in this review we will provide some arguments that this surprisingly simple mathematical rule provides a very efficient tool for phenomenological analysis of complex turbulent media.…”