Arbitrary-order Hilbert spectral analysis and intermittency in solar wind density fluctuations

TL;DR

This study applies the arbitrary-order Hilbert spectral analysis to solar wind density data, revealing scaling behaviors and intermittency properties that challenge classical methods and inform turbulence models.

Contribution

It introduces the use of Hilbert spectral analysis for solar wind turbulence, overcoming limitations of traditional methods and providing new insights into multiscaling and monofractal behaviors.

Findings

Classical structure functions fail to detect inertial range power laws due to non-stationarity.

Hilbert spectral analysis accurately estimates scaling exponents close to hydrodynamic turbulence.

Small-scale turbulence exhibits monofractal behavior consistent with fractional Brownian motion.

Abstract

The properties of inertial and kinetic range solar wind turbulence have been investigated with the arbitrary-order Hilbert spectral analysis method, applied to high-resolution density measurements. Due to the small sample size, and to the presence of strong non-stationary behavior and large-scale structures, the classical structure function analysis fails to detect power law behavior in the inertial range, and may underestimate the scaling exponents. However, the Hilbert spectral method provides an optimal estimation of the scaling exponents, which have been found to be close to those for velocity fluctuations in fully developed hydrodynamic turbulence. At smaller scales, below the proton gyroscale, the system loses its intermittent multiscaling properties, and converges to a monofractal process. The resulting scaling exponents, obtained at small scales, are in good agreement with those of classical fractional Brownian motion, indicating a long-term memory in the process, and the absence of correlations around the spectral break scale. These results provide important constraints on models of kinetic range turbulence in the solar wind.