Turbulence and Reconnection

Transcription

1 Turbulence and Reconnection Jeff Tessein July 10, 2011 NASA turbulence study at Wallops Island, Virginia

2 Outline Turbulence (length scales, Reynolds decomposition) Navier-Stokes Equation Turbulence Spectrum Observations Reconnnection Turbulence and Reconnection The Dissipation of Solar Wind Turbulence

3 Introduction to Turbulence Large Reynolds number Dissipation: energy injection required to maintain a turbulent flow 3D vorticity fluctuations: Vortex lines do not break v Feature of the flow, not a fluid property Turbulence is observed in: Corona, solar wind, outer heliosphere, intergalactic fields Weather systems, wind tunnels, fusion plasmas

4 Turbulent Flows Key characteristics of turbulent flows: disorder, efficient mixing, vorticity, large range of scales Right: Hot, turbulent smoke from a cigarette. Left: Breakdown of a drop of ink in water (Tennekes & Lumley 1970)

5 Newton's 2 Law for fluids Navier-Stokes Equation u 2 u u= p u F t TROUBLE Reynolds number: u u 2 u Reynolds decomposition: Ũ = Ū+u' (mean and fluctuating components)

6 Turbulence Spectrum Inertial range slope not always -5/3 There is a cascade from large to small scales Below: Sample energy spectrum from the solar wind using ACE data (Hamilton et. al. 1998). Note the spectral break where the inertial ranges transitions in to the dissipation range.

7 Reconnection Magnetic fields generated by stars and planets through the dynamo Massive amount of energy stored in magnetic fields can be released explosively Magnetic fields lines have tension: rubber band Magnetic reconnection is the fast release of this magnetic energy Examples: Meeting of Earth and Sun magnetic field, solar prominences, substorms Process occurs at a reconnection site where two oppositely directed magnetic field lines interact

8 Reconnection and Turbulence Right: Reconnection occurring in the solar wind. Reynolds number in the solar wind is of order 106. Left: Reconnnection occurs in a tuburlent simulation. Reconnection sites are represented by X. Rm =5000. From Servidio et. al Right: Example of reconnecting field lines in the solar corona. The corona is turbulent. Reynolds number in the corona is of order 104. Image from Burch & Drake 2009.

9 11. The Dissipation of Solar Wind Turbulence I. Observations: 1. General observations of turbulent fluctuations. 2. Plasma heating by dissipation of turbulence. 3. Observational Analysis Methods. II. THEORY/SIMULATION: 1. What are the salient properties and measurable predictions of various models for the turbulent fluctuations in the dissipation range? 2. What numerical approaches are most useful for investigations of the solar wind dissipation range, and what are their primary advantages and limitations? 3. What theoretical arguments support a small but non zero amount of fluctuation energy in wave vectors that have mainly parallel components? 4. Contrast the role of homogeneous vs inhomogeneous dissipation processes for the turbulence in the solar wind. 5. What implications do the various theories for imbalanced/non-zero cross helicity plasma turbulence have for the physical mechanisms responsible for dissipation of the turbulence? 6. How do temperature anisotropies, including related instabilities, likely affect our interpretations of turbulent fluctuations and heating in the dissipation range? III. GENERAL: 1. Discuss the controversial topic of the quasi-linear vs. inherently nonlinear (coherent structures and discontinuities) views of plasma turbulence.

10 References Burch, L. and J. F. Drake "Reconnecting magnetic fields", American Scientist, vol. 97, no. 5, pp , Hamilton, K., C. W. Smith, B. J. Vasquez, and R. J. Leamon (2008), Anisotropies and helicities in the solar wind inertial and dissipation ranges at 1 AU, J. Geophys. Res., 113, A01106, doi: /2007ja Servidio, S. and Matthaeus, W. H. and Shay, M. A. and Cassak, P. A. and Dmitruk, P. (2009), Magnetic Reconnection in Two-Dimensional Magnetohydrodynamic Turbulence, Phys Rev Lett, 102, 11, , doi: /physrevlett @article{ , Tennekes, H. and J.L. Lumley. A First Course in Turbulence. Cambridge, Massachusetts: The MIT Press, 1970.