Energy Cascade Rate in Compressible Fast and Slow Solar Wind Turbulence

Abstract

Estimation of the energy cascade rate in the inertial range of solar wind turbulence has been done so far mostly within the incompressible magnetohydrodynamics (MHD) theory. Here, we go beyond that approximation to include plasma compressibility using a reduced form of a recently derived exact law for compressible, isothermal MHD turbulence. Using in-situ data from the THEMIS/ARTEMIS spacecraft in the fast and slow solar wind, we investigate in detail the role of the compressible fluctuations in modifying the energy cascade rate with respect to the prediction of the incompressible MHD model. In particular, we found that the energy cascade rate: i) is amplified particularly in the slow solar wind; ii) exhibits weaker fluctuations in spatial scales, which leads to a broader inertial range than the previous reported ones; iii) has a power law scaling with the turbulent Mach number; iv) has a lower level of spatial anisotropy. Other features of solar wind turbulence are discussed along with their comparison with previous studies that used incompressible or heuristic (non exact) compressible MHD models.

Compressible Magnetohydrodynamic Turbulence in the Earth’s Magnetosheath: Estimation of the Energy Cascade Rate Using in situ Spacecraft Data

“…The results of analysis of all the samples are summarized in Interestingly, the role of the compressibility in increasing the compressible cascade rate can be evidenced by the turbulent Mach number M s = < δv > 2 /c 2 s , where δv is the fluctuating flow velocity. Figure 4 shows a power law-like dependence of | C | on M s as |ε C | ∼ M 4 s , steeper than the one observed in the solar wind [10]. To the best of our knowledge there are no theoretical predictions that relate ε to M s in compressible turbulence.…”

“…In particular the last term in the RHS of equation 2, is written as a first order increment multiplied by an averaged quantity δψ. This term that plays a leading order in the BG13 model [10,33] is likely to converge faster than the usual third-order terms when estimated from spacecraft observations or simulations data.…”

“…Recently, an exact law of compressible isothermal MHD turbulence has been derived [32] (hereafter BG13). It has been successfully used to improve our understanding of the role of density fluctuations in heating the fast and slow solar wind by showing in particular that, even if they are weak and represent only ∼ 5%−20% of the total fluctuations, they nevertheless can enhance significantly the turbulence cascade rate [10,33].…”

“…Thanks to the availability of in situ measurements recorded on board various orbiting spacecraft, the solar wind and the Earth's magnetosheath (i.e., the region of the solar wind downstream of the bow shock) provide a unique laboratory for the observational studies of plasma turbulence. An important feature of magnetosheath turbulence is the high level of density fluctuations in it, which can reach ∼ 50% − 100% [5][6][7][8] in comparison with ∼ 5% − 20% in the solar wind [9,10]. This makes the magnetosheath a key region of the near-Earth space where significant progress can be made in understanding compressible plasma turbulence, which is poorly understood although it is thought to be important in various astrophysical plasmas, such as supernovae remnants or the interstellar medium (ISM) [11][12][13][14][15].…”

“…For Themis spacecraft, the magnetic field data and the plasma moments are measured respectively by the FGM [40] and the ElectroStatic Analyzer (ESA) [41]. In selecting our samples, we eliminated time intervals that contained significant disturbances or velocity shears and considered only time intervals that have a relatively stationary plasma β (as discussed above) [10].…”