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Twotime energy spectrum of weak magnetohydrodynamic turbulence
Author  Perez, Jean; Azelis, Augustus; Bourouaine, Sofiane; 
Keywords  Parker Data Used 
Abstract  In this work a weakturbulence closure is used to determine the structure of the twotime power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. The twotime energy spectrum is a fundamental quantity in turbulence theory from which most statistical properties of a homogeneous turbulent system can be derived. A closely related quantity, obtained via a spatial Fourier transform, is the twopoint twotime correlation function describing the spacetime correlations arising from the underlying dynamics of the turbulent fluctuations. Both quantities are central in fundamental turbulence theories as well as in the analysis of turbulence experiments and simulations. However, a firstprinciples derivation of these quantities has remained elusive due to the statistical closure problem, in which dynamical equations for correlations at order n depend on correlations of order n + 1. The recent launch of the Parker Solar Probe (PSP), which will explore the nearSun region where the solar wind is born, has renewed the interest in the heliophysics community to understand the structure and possible universal properties of spacetime correlations. The weak MHD turbulence regime that we consider in this work allows for a natural asymptotic closure of the twotime spectrum, which may be applicable to other weak turbulence regimes found in fluids and plasmas. An integrodifferential equation for the scaledependent temporal correlation function is derived for incompressible Alfvenic fluctuations whose nonlinear dynamics is described by the reduced MHD equations. 
Year of Publication  2020 
Journal  PHYSICAL REVIEW RESEARCH 
Volume  2 
Number of Pages  023189 
Section  
Date Published  05/2020 
ISBN  
URL  
DOI  10.1103/PhysRevResearch.2.023189 