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

2. 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

3. 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

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

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

6. Orion nebula Interstellar gas Astrophysical fluids are turbulent and magnetized (Re > 10 10 ) Credit: J.Cho

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

9. 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

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

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

19. Section 4. Magnetic Reconnection in the Plasma

28. Section 7. Homework See the web page