Wavelet determination of magnetohydrodynamic-range power spectral exponents in solar wind turbulence seen by Parker Solar Probe

¹ Centre for Fusion, Space and Astrophysics, Physics Department, University of Warwick, Coventry CV4 7AL, UK
e-mail: Xueyi.Wang@warwick.ac.uk
² Department of Mathematics and Statistics, University of Tromsø, Tromsø 9037, Norway
³ International Space Science Institute, Bern 3012, Switzerland

Received: 17 April 2023
Accepted: 23 August 2023

Abstract

Context. The high Reynolds number solar wind flow provides a natural laboratory for the study of turbulence in situ. Parker Solar Probe samples the solar wind between 0.17 AU and 1 AU, providing an opportunity to study how turbulence evolves in the expanding solar wind.

Aims. We aim to obtain estimates of the scaling exponents and scale breaks of the power spectra of magnetohydrodynamic (MHD) turbulence at sufficient precision to discriminate between Kolmogorov and Iroshnikov-Kraichnan (IK) turbulence, both within each spectrum and across multiple samples at different distances from the Sun and at different plasma β.

Methods. We identified multiple long-duration intervals of uniform solar wind turbulence, sampled by PSP/FIELDS and selected to exclude coherent structures, such as pressure pulses and current sheets, and in which the primary proton population velocity varies by less than 20% of its mean value. The local value of the plasma β for these datasets spans the range 0.14 < β < 4. All selected events span spectral scales from the approximately ‘1/f’ range at low frequencies, through the MHD inertial range (IR) of turbulence, and into the kinetic range, below the ion gyrofrequency. We estimated the power spectral density (PSD) using a discrete Haar wavelet decomposition, which provides accurate estimates of the IR exponents.

Results. Within 0.3 AU of the Sun, the IR exhibits two distinct ranges of scaling. The inner, high-frequency range has an exponent consistent with that of IK turbulence within uncertainties. The outer, low-frequency range is shallower, with exponents in the range from –1.44 to –1.23. Between 0.3 and 0.5 AU, the IR exponents are closer to, but steeper than, that of IK turbulence and do not coincide with the value –3/2 within uncertainties. At distances beyond 0.5 AU from the Sun, the exponents are close to, but mostly steeper than, that of Kolmogorov turbulence, –5/3: uncertainties inherent in the observed exponents exclude the value –5/3. Between these groups of spectra we find examples, at 0.26 AU and 0.61 AU, of two distinct ranges of scaling within the IR with an inner, high-frequency range with exponents ∼ − 1.4, and a low-frequency range with exponents close to the Kolmogorov value of –5/3.

Conclusions. Since the PSD-estimated scaling exponents are a central predictor in turbulence theories, these results provide new insights into our understanding of the evolution of turbulence in the solar wind.