NEW ONE-DIMENSIONAL MODEL-EQUATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE

New one-dimensional model equations of magnetohydrodynamic turbulence depending on the position x and the time t are proposed considering th e x component of the velocity u(x,r) and the y and z components of the magnetic field b(y)(x,t) and b(z)(x,r). It is found that the model eq uations conserve the total energy and the quantity similar to the cros s helicity, and that they have a similarity solution, u(x,t)similar to x/t and b(y)(x,t), b(z)(x,t)similar to C/t in the inviscid limit. A s hock type solution is obtained where both the velocity and the magneti c fields have a jump in a narrow viscous or diffusive region. Numerica l simulations are also carried out and the results show that the k(-2) energy spectrum develops both for the velocity and the magnetic field s. (C) 1997 American Institute of Physics.