On self-consistent finite-mode approximations in (quasi-) two-dimensional hydrodynamics and magnetohydrodynamics

The idea of sine truncations (V. Zeitlin, 1989) in hydrodynamics of incompressible fluid is further developed. For flows with doubly periodic boundary conditions a representation of symplectic diffeomorphisms of the torus as a N→∞ limit of SU(N) groups is used to construct a self-consistent discrete Navier-Stokes equation for vorticity. A Laplacian on the SU(N) group is used as discrete Laplacian for this purpose. Self-consistent finite-mode approximations for 2d magnetohydrodynamics are constructed using the same principle.