Long-time states of inverse cascades in the presence of a maximum length scale

It is shown numerically, both for the two-dimensional Navier-Stokes equations and for two-dimensional magnetohydrodynamics, that the long-time asymptotic state in a forced inverse-cascade situation is one in which the spectrum is completely dominated by its own fundamental. The growth continues until the fundamental is dissipatively limited by its own disspation rate. An algebraic model is proposed for the dynamics of such a final state.