Convergence of Dirichlet quotients and selective decay of 2D magnetohydrodynamic flows

The selective decay phenomena have been observed by physicists for many dynamic flows such as Navier–Stokes flows, barotropic geophysical flows, and magnetohydrodynamic (MHD) flows in either actual physical experiments or numerical simulations. In the previous paper (M.-Q. Zhan, 2010 [20]), the author showed the validity of the selective decay principle for the 2D magnetohydrodynamic (MHD) flows in the case of small magnetic Prandtl number. In this paper, we shall show the validity of the selective decay principle for the 2D magnetohydrodynamic (MHD) flows for any magnetic Prandtl number with periodic boundary conditions.