The development of anisotropy in an initially isotropie spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops through the combined effects of an externally imposed d.c. magnetic field and viscous and resistive dissipation at high wavenumbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wavenumbers.

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Operated by the Universities Space Research Association a ,bTh~~Ca dz:.resn ICASE Fluid MechanicsDue to increasing research being conducted at ICASE in the field of fluid mechanics, future ICASE reports in this area of research will be printed with a green cover. Applied and numerical mathematics reports will have the familiar blue cover, while computer science reports will have yellow covers. In all other aspects the reports will remain the same; in particular, they will continue to be submitted to the appropriate journals or conferences for formal publication.

The statistical theory of absolute equilibrium ensembles is extended to describe ideal, three-dimensional, magnetohydrodynamic (MHD) turbulence with and without rotation, and with and without a mean magnetic field. Results from seven long-time numerical simulations of five general cases on a 32 3 grid are presented. One notable result is the discovery of a new ideal invariant, the 'parallel helicity,' which arises when rotation and mean magnetic field vectors are aligned. Although the basic equations and statistical theory are symmetric under parity or charge reversal, the presence of invariant cross, magnetic or parallel helicity dynamically breaks this symmetry. Ideal MHD turbulence is, in general, nonergodic due to the decomposability of the constant energy surface in phase space. Non-ergodicity can be manifested in the appearance of coherent structure as long as magnetic or parallel helicity is invariant. The fact that MHD turbulence inherently contains coherent structure in certain general cases may have important implications for dynamo theory.