Physics 777 Plasma Physics and Magnetohydrodynamics (MHD) Instructor: Gregory Fleishman Lecture 8. Weak Turbulence and Magnetic Reconnection 21 October 2008

Plan of the Lecture MHD turbulence, general ideas and approaches Plasma Nonlinearity and Wave-Wave Interactions Spectral Description of the Turbulence; Random Phase Approximation, Magnetic Reconnection in the Plasma

What is the turbulence? Reynolds number: Re=VL/  V 2 /L) / ( V/L 2 )  V 2 /L V/L 2 When Re << Re critical, flow = laminar When Re >> Re critical, flow = turbulent = - + l b Credit: J.Cho Section 1. MHD turbulence, general ideas and approaches

Example: wake behind a sphere Re~15,000 critical Re = 40~50 Credit: J.Cho

water ~ 0.01 (cgs) If v=10cm/sec & D=1 cm, Re~1000. ==> turbulence! Example: cylinder in water Credit: J.Cho

Orion nebula Interstellar gas Astrophysical fluids are turbulent and magnetized (Re > ) Credit: J.Cho

Spectra: Cho & Vishniac (2000) B0B0 See also Muller & Biskamp (2000); Maron & Goldreich (2001) |B| Credit: J.Cho

Anisotropy B Smaller eddies are more elongated  Relation between parallel size and perp size?  Critically balanced turbulence Credit: J.Cho Credit: J. M. Stone l || ~l  2/3

Section 2. Plasma Nonlinearity and Wave-Wave Interactions Credit: E.Kontar

Section 3. Spectral Description of the Turbulence Structural functions of the turbulence Spectral description Random phase approximation Statistically uniform turbulence Isotropic and anisotropic turbulence

Section 4. Magnetic Reconnection in the Plasma

Section 7. Homework See the web page