The evolution of cross helicity in driven/dissipative two-dimensional magnetohydrodynamics

A numerical study of the evolution of cross helicity in driven/dissipative magnetohydrodynamics (MHD) is presented. The magnetofluid is incompressible and a two-dimensional (2-D) periodic geometry is considered. Cross helicity, a measure of the correlation between fluctuations in the magnetic field and the velocity field, is injected by use of correlated Gaussian forcing over a finite bandwidth in wavenumber. Numerical experiments include the driving of initially uncorrelated spectra with highly correlated forcing and the driving of correlated spectra with anticorrelated forcing. A recurring and persistent feature of the simulations is the appearance of oppositely signed cross helicity at small scales relative to large scales. A simple argument based on the Elsässer variables and used previously in the context of decaying turbulence explains many of the observed features. The effect of a uniform external magnetic field is considered and the relation to purely decaying 2-D MHD turbulence is discussed.