Inertial-Range Energy Transfer Free from Isotropic Assumption in Turbulent Space Plasma1

TL;DR

This paper compares two methods, DA and LPDE, for measuring 3D energy transfer in turbulent space plasmas, highlighting their sensitivities and implications for multi-spacecraft missions.

Contribution

It systematically evaluates the effectiveness of DA and LPDE methods in quantifying anisotropic energy cascades without assuming isotropy in space plasmas.

Findings

DA shows polar and azimuthal dependence but is configuration-insensitive.

LPDE is affected by spacecraft separation and shape, less by sampling trajectory.

Both methods are valuable for understanding turbulence in space physics.

Abstract

The idea of an energy cascade in the inertial range is often invoked in turbulent space plasmas to estimate the energy dissipation rate. Laws governing the behavior of third-order structure functions in the inertial range, so-called third-order laws, are among the few rigorous theoretical results quantifying cross-scale energy transfer. The widely used third-order-law derived rate assumes isotropy, which fundamentally conflicts with the anisotropic nature of space plasmas. Elementary questions persist regarding how such anisotropic energy cascades can be quantified using multi-spacecraft constellations. As the heliospheric community increasingly progresses towards multi-spacecraft, multi-scale constellations, such as Plasma Observatory and HelioSwarm, we revisit these crucial issues pertinent to accurately measuring the inertial-range energy transfer. Here we make a systematic comparison between two methods: direction-averaging (DA) and lag polyhedral derivative ensemble (LPDE) to determine the full three-dimensional (3D) dependence of cross-scale energy transfer. We find that DA exhibits both polar and azimuthal dependence, but is insensitive to spacecraft configuration. By contrast, LPDE is strongly affected by spacecraft separation and tetrahedral shape, while being comparatively insensitive to the sampling trajectory. Our findings have direct implications for current and future multi-spacecraft missions. Both DA and LPDE will provide crucial information on the nature of turbulence in space and astrophysics.