Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics

Abstract

Alfvénic interactions which transfer energy from large to small spatial scales lie at the heart of magnetohydrodynamic turbulence. An important feature of the turbulence is the generation of negative residual energy -- excess energy in magnetic fluctuations compared to velocity fluctuations. By contrast, an MHD Alfvén wave has equal amounts of energy in fluctuations of each type. Alfvénic quasimodes that do not satisfy the Alfvén wave dispersion relation and exist only in the presence of a nonlinear term can contain either positive or negative residual energy, but until now an intuitive physical explanation for why negative residual energy is preferred has remained elusive. This paper shows that the equations of reduced MHD are symmetric in that they have no intrinsic preference for one sign of the residual energy over the other. An initial state that is not an exact solution to the equations can break this symmetry in a way that leads to net-negative residual energy generation. Such a state leads to a solution with three distinct parts: nonresonant Alfvénic quasimodes, normal modes produced to satisfy initial conditions, and resonant normal modes that grow in time. The latter two parts strongly depend on initial conditions; the resulting symmetry breaking leads to net-negative residual energy both in Alfvénic quasimodes and $\omega =k_{\parallel }{V}_A=0$ modes. These modes have net-positive residual energy in the equivalent boundary value problem, suggesting that the initial value setup is a better match for solar wind turbulence.

arXiv comment19 pages, 1 figure

References in corpus (26)

• Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas
• A weak turbulence theory for incompressible MHD
• The multi-scale nature of the solar wind
• Probing Turbulence in the Coma Galaxy Cluster
• On the Spectrum of Magnetohydrodynamic Turbulence
• Evolving turbulence and magnetic fields in galaxy clusters
• Recent progress in astrophysical plasma turbulence from solar wind observations
• Spectral energy dynamics in magnetohydrodynamic turbulence
• Spectrum of Kinetic Alfven Turbulence
• Finite dissipation and intermittency in magnetohydrodynamics
• Alfven Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: an Analytical Treatment
• Scale-Locality of Magnetohydrodynamic Turbulence
• Residual Energy Spectrum of Solar Wind Turbulence
• Alfven Wave Collisions, The Fundamental Building Block of Plasma Turbulence I: Asymptotic Solution
• Spectral scaling laws in MHD turbulence simulations and in the solar wind
• Direct Evidence of the Transition from Weak to Strong MHD Turbulence
• Development of Anisotropy in Incompressible Magnetohydrodynamic Turbulence
• Spectrum of weak magnetohydrodynamic turbulence
• Kinetic Turbulence in Astrophysical Plasmas: Waves and/or Structures?
• Constraints on ion vs. electron heating by plasma turbulence at low beta
• Anisotropic fluxes and nonlocal interactions in MHD turbulence
• Alfven Wave Collisions, The Fundamental Building Block of Plasma Turbulence II: Numerical Solution
• Residual Energy in Magnetohydrodynamic Turbulence
• Impact of Residual Energy on Solar Wind Turbulent Spectra
• Alfvén-dynamo balance and magnetic excess in MHD turbulence
• The Alfvenic nature of energy transfer mediation in localized, strongly nonlinear Alfven wavepacket collisions

Cited by in corpus (1)

• Understanding Plasma Turbulence Through Exact Coherent Structures