University:
Boston University
Course:
CAS AS 311 | Planetary Physics
Academic year:

2024
Views:

357

Pages:

19
Author:

Annabel Combs

Introduction to Turbulence and Heating in the Solar Wind Outline I. Introduction to Turbulence II. Measurements of Turbulence in the Solar Wind. III. Magnetohydrodynamics (MHD) IV. Alfven Waves, the Origin of the Solar Wind, and Solar Probe Plus V. Introduction to phenomenological theories of MHD turbulence. What Is Turbulence? Operational definition for turbulence in plasmas and fluids: turbulence consists of disordered motions spanning a large range of lengthscales and/or timescales. “Energy Cascade” in Hydrodynamic Turbulence Plasma Turbulence Vs. Hydro Turbulence • In plasmas such as the solar wind, turbulence involves electric and magnetic fields as well as velocity fluctuations. • In some cases the basic building blocks of turbulence are not eddies but plasma waves or wave packets. Where Does Turbulence Occur? • Atmosphere (think about your last plane flight). • Oceans. • Sun, solar wind, interstellar medium, intracluster plasmas in clusters of galaxies... What Causes Turbulence? • Instabilities: some source of free energy causes the amplification of fluctuations which become turbulent. Example: convection in stars. • Stirring. Example: stirring cream into coffee. • Requirement: the medium can’t be too viscous. (Stirring a cup of coffee causes turbulence, but stirring a jar of honey does not.) What Does Turbulence Do? • Turbulent diffusion or mixing. Examples: cream in coffee, pollutants in the atmosphere. • Turbulent heating. When small-scale eddies (or wave packets) dissipate, their energy is converted into heat. Example: the solar wind. Outline I. Introduction to Turbulence II. Measurements of Turbulence in the Solar Wind. III. Magnetohydrodynamics (MHD) IV. Alfven Waves, the Origin of the Solar Wind, and Solar Probe Plus V. Introduction to phenomenological theories of MHD turbulence. In Situ Measurements RTN coordinates (E.g., Helios, ACE, Wind, STEREO...) Quantities measured include v, B, E, n, and T Spacecraft Measurements of the Magnetic Field and Velocity Data from the Mariner 5 spacecraft (Belcher & Davis 1971) Is This Turbulence? • The velocity and magnetic field in these measurements appear to fluctuate in a random or disordered fashion. • But how do we tell whether there are “velocity fluctuations spanning a large range of scales,” as in our operational definition of turbulence? • One way: by examining the power spectrum of The Magnetic Power Spectrum Fourier transform of magnetic field •powerB(t) is the magnetic field vector measured at the spectrum spacecraft location. • T is the duration of the measurements considered. (When power spectra are computed using real data, T can not be increased indefinitely; the resulting power spectra are then approximations of the above formulas.) The Magnetic Power Spectrum • B(f) can be thought of as the part of B that ~ oscillates with frequency f. • When turbulence is present, P(f) is nonnegligible over a broad range of frequencies. Typically, P(f) has a powerlaw scaling over frequencies varying by Turbulence? Magnetic Power Spectra in the Solar Wind Yes - the magnetic fluctuations measured by the spacecraft span a broad range of timescales. (Bruno & Carbone 2005) Similar spectra are observed at all locations What Causes the Time Variation Seen in Spacecraft Measurements? • Consider a traveling plasma wave (more on plasma waves soon). Imagine you’re viewing this wave as you move away from the Sun at the same velocity as the solar wind. From your perspective, the time variation of the magnetic field is the result of the wave pattern moving past you at the wave phase speed relative to the solar-wind plasma, vphase, which is typically ≈30 km/s in the solar wind near Earth. • If the wavenumber of the wave is k, the angular But What if You Measure B Using a “Stationary” Spacecraft That Does Not Move with the Solar Wind? • Near Earth, the speed at which the solar wind flows past a satellite is highly supersonic, typically >10vphase, • where vphase is the phase speed in the plasma rest frame. “Taylor’s Frozen-in Flow Hypothesis”: Time variation measured by a spacecraft results primarily from the advection of spatially varying quantities past the spacecraft at high speed. The “intrinsic time variation” in the solar-wind frame has almost no effect on the measurements. The spacecraft would see almost the same thing if the fields were static in the solar-wind frame. ∝e • If a wave with wavevector k is advected past the spacecraft (i.e., δB ik⋅x), and the wave is static in the solar-wind frame, the spacecraft measures a magnetic oscillation with angular frequency ω = 2πf = k⋅vsolarwind. • Frequencies measured by a spacecraft thus tell us about k (spatial structure) rather than the intrinsic time variation that would be seen in the plasma rest frame. Taylor’s Frozen-in Flow Hypothesis (Bruno & Carbone 2005) The frequency spectra measured by satellites correspond to wavenumber spectra in the solar-wind frame. Question: in the data below, the v and B fluctuations are highly correlated --- what does this mean? We’ll come back to this... Data from the Mariner 5 spacecraft (Belcher & Davis 1971)

Introduction to Turbulence and Heating in the Solar Wind

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