Linear Mode Decomposition in Magnetohydrodynamics Revisited

Abstract

Small-amplitude fluctuations in the magnetized solar wind are measured typically by a single spacecraft. In the magnetohydrodynamics (MHD) description, fluctuations are typically expressed in terms of the fundamental modes admitted by the system. An important question is how to resolve an observed set of fluctuations, typically plasma moments such as the density, velocity, pressure, and magnetic field fluctuations, into their constituent fundamental MHD modal components. Despite its importance in understanding the basic elements of waves and turbulence in the solar wind, this problem has not yet been fully resolved. Here, we introduce a new method that identifies between wave modes and advected structures such as magnetic islands or entropy modes and computes the phase information associated with the eligible MHD modes. The mode-decomposition method developed here identifies the admissible modes in an MHD plasma from a set of plasma and magnetic field fluctuations measured by a single spacecraft at a specific frequency and an inferred wavenumber k m . We present data from three typical intervals measured by the Wind and Solar Orbiter spacecraft at ∼1 au and show how the new method identifies both propagating (wave) and nonpropagating (structures) modes, including entropy and magnetic island modes. This allows us to identify and characterize the separate MHD modes in an observed plasma parcel and to derive wavenumber spectra of entropic density, fast and slow magnetosonic, Alfvénic, and magnetic island fluctuations for the first time. These results help identify the fundamental building blocks of turbulence in the magnetized solar wind.

MHD Inertial and Energy-containing Range Turbulence Anisotropy in the Young Solar Wind

“…We find that solar wind fluctuations in the young solar wind, i.e., near the Sun, are predominantly 2D and not slab, consistent with previous findings from theoretical and observational studies (Zank & Matthaeus 1992b, 1993Bieber et al 1996;Zank et al 2017;Adhikari et al 2022). This conclusion is contrary to the prior results of Bandyopadhyay & McComas (2021) and Zhao et al (2022), indicating that a closer analysis is warranted, possibly using the mode-decomposition analysis developed recently by Zank et al (2023), which is distinct from both these analyses and that presented here. An intriguing prospect is to extend this analysis from the sub-Alfvénic region to the super-Alfvénic region, including distances up to 1 au.…”

Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations

“…Observationally, the presence of quasi-2D turbulence is demonstrated by the "Maltese-cross"-like structure of the correlation function (Matthaeus et al 1990;Dasso et al 2005), by the anisotropic turbulence measurements (Bandyopadhyay & McComas 2021;Zhao et al 2022a), and its consistency with cosmic-ray mean free paths (Bieber et al 1994;Zhao et al 2017). Multi-SC observations also provide evidence of low-frequency fluctuations (Sahraoui et al 2010) and nonpropagating modes (Zank et al 2023;Zhao et al 2023) in the solar wind.…”

Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

“…In a similar vein, one would like to distinguish between density fluctuations (e.g., Kontar et al 2023) generated by compressible fast and slow magnetosonic (MS) waves and advected density fluctuations (entropy modes). Zank et al (2023) revisited and developed a very general mode decomposition method that identifies wave modes and advected structures, such as magnetic islands or entropy modes, while evaluating the corresponding phase information. By utilizing the newly developed mode decomposition technique, we reanalyze the first sub-Alfvénic solar wind interval observed by PSP.…”

“…It should be noted that a classical mode decomposition analysis (Glassmeier et al 1995) was applied to various plasma intervals observed during the first PSP encounter by Chaston et al (2020) and Zhao et al (2021b). Unlike the method introduced by Zank et al (2023), the classical method projects the observed fluctuations onto a subspace of possible MHD modes comprising only three possible modes, the planar Alfvén, and fast and slow MS modes, and all three modes share the same wavevector (Zhao et al 2021b). The classical approach does not include advected modes (entropy modes, magnetic islands, Alfvén vortices) nor the full spherical Alfvén mode, all of which are incorporated in the analysis presented in Zank et al (2023), together with the fast and slow MS modes.…”