Magneto-Fluid Dynamics Seminar
The Eulerian space-time correlation of Magnetohydrodynamic (MHD) turbulence and the interpretation of Parker Solar Probe measurements
Speaker: Jean Perez, Florida Tech
Location: Warren Weaver Hall 905
Date: Tuesday, November 12, 2019, 11 a.m.
In-situ measurements by virtually every spacecraft to date at heliocentric distances above 0.3 Astronomical Units (AU) have found that the turbulent velocity and magnetic fields in the solar wind are predominantly non-compressive fluctuations spanning a broad range of MHD scales. The analysis of these data combined with theory and numerical simulations have helped us shape our understanding of solar wind turbulence beyond 0.3~AU in part due to the validity of the Taylor's Hypothesis (TH), which posits that temporal variation of spacecraft signals is solely due to the spatial variation of a frozen structure passing by the observation point. The Parker Solar Probe (PSP) mission launched last year will explore the solar wind up to seven times closer to the Sun than any previous mission, covering regions where TH is expected to break down. In these regions, a better understanding of the Eulerian space-time correlation is critical for the proper interpretation of time signals from this groundbreaking mission. However, a first-principle derivation of this quantity has remained elusive in turbulence theory due to the statistical closure problem, in which dynamical equations for correlations at order $n$ depend on correlations of order $n+1$. In this talk we will present recent progress in understanding the Eulerian two-time two-point (space-time) correlation for strong and weak incompressible MHD turbulence. In the strong turbulence regime, we propose a model for the space-time correlation that extends Kraichnan's sweeping model for incompressible hydrodynamic (HD) turbulence and validate it against high-resolution numerical simulations. In the weak turbulence regime, an asymptotic wave-turbulence closure is used for the first time to determine the structure of space-time correlations in weak MHD turbulence from the nonlinear equations describing the dynamics. The wave-turbulence closure that we present may find applications in other weak turbulence regimes found in fluids and plasmas.