An Intermittent Model for the $1/f$ Spectrum in the Pristine Solar Wind

TL;DR

This paper investigates the $1/f$ turbulence spectrum in the solar wind using Parker Solar Probe data, revealing a $1/\tau$ cascade rate dependence and proposing a new intermittent model with $1/\ell$ scaling.

Contribution

It introduces a novel intermittent model explaining the $1/f$ spectrum in solar wind turbulence, supported by observational data and analysis of magnetic field fluctuations.

Findings

Cascade rate follows a $1/\tau$ dependence in the $1/f$ range.

Magnetic field fluctuations show intermittent behavior parallel to the field.

Perpendicular fluctuations are approximately Gaussian, indicating different turbulence characteristics.

Abstract

We present a statistical, observational study of the $1/f$ range of solar wind turbulence, where $f$ denotes frequency, using in situ data from the Parker Solar Probe (PSP). We compute the energy cascade rate using the third order law of incompressible magnetohydrodynamic (MHD) turbulence, incorporating expansion terms to account for solar wind dynamics. Our results reveal a $1/\tau$ dependence of the energy cascade rate, where $\tau$ is the temporal lag, within the $1/f$ range, in contrast to the constant cascade rate in the inertial range. To explain this behavior, we propose a new intermittent model predicting a $1/\ell$ scaling of the cascade rate, where $\ell$ represents the spatial lag. The analysis of the probability density function (PDF) of magnetic field increments confirms the intermittent nature of the parallel fluctuation component, whereas the perpendicular fluctuations are found to be quasi Gaussian. These findings provide new insights into energy transfer processes in the $1/f$ range of solar wind turbulence, with potential applications in planetary magnetosheaths.