Magnetohydrodynamic turbulence in a strongly magnetised plasma
  I present a review of incompressible magnetohydrodynamic (MHD) turbulence in
a strongly magnetised plasma. The approach is phenomenological even where a
more rigorous theory is available, so that a reader armed with paper, pencil
and some determination may be able to work through most of the physics. The
focus is on the inertial-range spectra for very large (fluid and magnetic)
Reynolds numbers. These theories of the inertial-range are built on two
important facts: (i) Kraichnan's insight that the turbulent cascades are a
result of nonlinear interactions between oppositely directed wavepackets of
Elsasser fields; (ii) these oppositely directed wavepackets do not exchange
energy, but contribute only to changing each other's spatial structures. I
begin with a description and critique of the Iroshnikov-Kraichnan theory, and
explore the fundamental departures necessitated by the anisotropic nature of
the turbulence. Derivations of the inertial-range spectra of four regimes of
MHD turbulence -- the balanced weak, balanced strong, imbalanced weak and the
imbalanced strong cascades -- are then presented. The need for studying the
spectra of imbalanced turbulence when the waves on the outer scale have a short
correlation time is briefly discussed.
