title: Robustness of the inverse cascade in two-dimensional turbulence.
abstract: We study quasisteady inverse cascades in unbounded and bounded two-dimensional turbulence driven by time-independent injection and dissipated by molecular viscosity. It is shown that an inverse cascade that carries only a fraction r of the energy input to the largest scales requires the enstrophy-range energy spectrum to be steeper than k(-5) (ruling out a direct cascade) unless 1-r<<1. A direct cascade requires the presence of an inverse cascade that carries virtually all energy to the largest scales (1-r<<1). These facts underlie the robustness of the Kolmogorov-Kraichnan k(-5/3) inverse cascade, which is readily observable in numerical simulations without an accompanying direct enstrophy cascade. We numerically demonstrate an instance where the k(-5/3) inverse-cascading range is realizable with 79% of the energy injection dissipated within the energy range and virtually all of the enstrophy dissipated in the vicinity of the forcing region. As equilibrium is approached, the respective logarithmic slopes -alpha and -beta of the ranges of wave numbers lower and higher than the forcing wave number satisfy alpha+beta approximately 8. These results are consistent with recent theoretical predictions.
authors.affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1.
authors.forename: Chuong V
authors.initials: CV
authors.lastname: Tran
authors.forename: John C
authors.initials: JC
authors.lastname: Bowman