Two-Dimensional Turbulence and Transport

Abstract

The Navier–Stokes equation is an equation of the motion of a fluid element in the absence of a pressure-gradient force and viscosity. In an incompressible fluid, the fluid mass density ${\rho_{\rm{m}}}$ is constant. If we further assume that ${\rho_{\rm{m}}}$ is uniform, the equation may be expressed as

$$ \frac{{{\text{d}}\vec{u}}}{{{\hbox{d}}t}} = \frac{{\partial \vec{u}}}{{\partial t}} + (\vec{u}\,\nabla )\vec{u} = - \nabla T + {\nu_{\rm{F}}}{\nabla^2}\vec{u}, $$

(15.1.1)

Further Reading

1.1 Two-Dimensional Turbulence

• D. Biskamp, Magnetohydrodynamic Turbulence (Cambridge University Press, Cambridge, 2004)

• S. Kida, M. Takaoka, Annu. Rev. Fluid Mech. 26, 169 (1994)

• R.H. Kraichnan, D. Montgomery, Rep. Prog. Phys. 43, 547 (1980)

• J. Sommeria, Les Houches Series (Nova Science publisher, New York, 2010)

• P. Tabeling, Phys. Rep. 362, 1–62 (2002)

1.2 Magnetized Plasma Physics

• R. Dandy, Physics of Plasma (Cambridge University Press, Cambridge, 2001)

• P.H. Diamond, S.-I. Itoh, K. Itoh, Modern Plasma Physics, vol. 1 (Cambridge University Press, Cambridge, 2010)

• W. Horton, Y.-H. Ichikawa, Chaos and Structures in Nonlinear Plasma (Word Scientific, Singapore, 1994)

• B.B. Kadomtsev, Tokamak Plasma: A Complex System (IOP Publishing, Bristol, 1991)

• J.A. Krommes, Phys. Rep. 360, 1–352 (2002)

• M. N. Rosenbluth, R. Z. Sagdeev (eds.) Handbook of Plasma Physics, (North-Holland, Amsterdam 1984)

• Toscani Boffi, Rionero (eds) Mathematical Aspects of Fluid and Plasma Dynamics. Proc. Salice Terme 1988, (Springer, 1991)

• J.A. Wesson, Tokamaks (Oxford University Press, Oxford, 1987)

1.3 Magnetohydrodynamic Turbulence and Dynamo

• S. Childress, A.D. Gilbert, Stretch, Twist, Fold: The Fast Dynamo (Springer, Berlin, 1995)

• E. Falgarone, T. Passot (eds.), Turbulence and Magnetic Fields in Astrophysics (Springer, Berlin, 2003)

• E. Parker, Cosmical Magnetic Fields (Oxford University Press, Oxford, 1980)

• E. Priest, T. Forbes, Magnetic Reconnection (Cambridge University Press, Cambridge, 2000)

• J.E. Pringle, A. King Astrophysical Flows (Cambridge University Press, Cambridge)

• A. Ruzmaikin, A. Shukurov, D. Sokoloff, Magnetic Fields of Galaxies (Springer, Berlin, 1988)

• D. D. Schnack Lectures in Magnetohydrodynamics. With an Appendix on Extended MHD (Springer, 2009)

• A.M. Soward et al. (eds.), Fluid Dynamics and Dynamos in Astrophysics (CRC, FL, USA, 2002)

• YaB Zeldovich et al., Magnetic Fields in Astrophysics (Springer, Berlin, 2005)