Nonlinear dynamical modeling of solar cycles using dynamo formulation with turbulent magnetic helicity

Abstract

We describe a sequence of two-dimensional numerical simulations of inflection point instability in a stably stratified shear flow near the ground. The fastest growing Kelvin-Helmholtz modes are studied in detail; in particular we investigate the growth inhibiting effect of the ground which is predicted by linear theory and the Reynolds number dependence of the process of growth to finite amplitude. We consider flows which are both above and below the critical Reynolds number (Re = 300) which has been reported by Woods (1969) to mark the boundary between flows which have turbulent final states and those which do not. A global energy budget reveals a fundamental difference in character of the finite amplitude billows in these two Reynolds number regimes. However, for relatively high Reynolds numbers (Re = 10³) we do not find any explicit evidence for secondary instability. Above the transition Reynolds number the modified mean flow induced by wave growth is characterized by a splitting of the original shear layer and of the in version in which it is embedded.