Two-and-a-half-dimensional magnetohydrodynamic turbulence

Abstract

The homogeneous turbulence for which fluctuating magnetic fields and velocity fields are independent of one spatial coordinate but still possess all three components are studied to form a generalized two-and-half dimensional geometry. The integral of the z-vector potential and the magnetic helicity are shown to be ideal invariants, and the basic dynamical variables and the equations of uniform-density incompressible magnetohydrodynamics are defined. The possibility of simultaneous inverse cascades is considered, and Kolmogoroff dimensional analysis is employed to infer omnidirectional inverse cascade spectra. Implications of a selective decay hypothesis, where a tendency exists in the initial value problem for the ideal invariants directly cascaded to higher wavenumbers to be selectively dissipated, and the possibility of a dynamo action in the considered geometry, are examined.