Strategies for determining the cascade rate in MHD turbulence: isotropy, anisotropy, and spacecraft sampling

TL;DR

This paper evaluates methods for accurately determining cascade rates in MHD turbulence, considering isotropy, anisotropy, and spacecraft sampling effects, with implications for solar wind turbulence analysis.

Contribution

It analyzes the accuracy of third-order laws in MHD turbulence, exploring the effects of symmetry assumptions and sampling strategies through simulations.

Findings

Isotropic assumptions can lead to inaccuracies in cascade rate estimates.

Sampling strategies significantly influence the reliability of third-order law applications.

Simulation results help identify conditions for accurate dissipation rate measurements.

Abstract

``Exact'' laws for evaluating cascade rates, tracing back to the Kolmogorov ``4/5'' law, have been extended to many systems of interest including magnetohydrodynamics (MHD), and compressible flows of the magnetofluid and ordinary fluid types. It is understood that implementations may be limited by the quantity of available data and by the lack of turbulence symmetry. Assessment of the accuracy and feasibility of such ``third-order'' (or Yaglom) relations is most effectively accomplished by examining the von Karman-Howarth equation in increment form, a framework from which the third-order laws are derived as asymptotic approximations. Using this approach, we examine the context of third-order laws for incompressible MHD in some detail. The simplest versions rely on the assumption of isotropy and the presence of a well-defined inertial range, while related procedures generalize the same idea to arbitrary rotational symmetries. Conditions for obtaining correct and accurate values of the dissipation rate from these laws based on several sampling and fitting strategies are investigated using results from simulations. The questions we address are of particular relevance to sampling of solar wind turbulence by one or more spacecraft.