The application of Kraichnan-Leith-Batchelor similarity theory to inverse cascades in generalized two-dimensional turbulence

This thesis examines how well Kraichnan-Leith-Batchelor (KLB) similarity theory describes turbulent inverse cascades in &;Comparing simulations forced at well-resolved and poorly-resolved scales shows that the simulated inverse cascades are non-universal in that their statistical characteristics and vortex populations depend on the resolution of the forcing scale. For well-resolved forcing coherent vortices form in the alpha = 1 and alpha = 2 flows, steepening the spectra past the KLB predictions and generating non-Gaussian and intermittent statistics. Separating the flows into coherent and residual components reveals that a Gaussian and non-intermittent turbulent background satisfying KLB scaling exists for alpha = 2, but further work is necessary to determine whether this is the case for alpha = 1. KLB theory thus describes inverse cascades in specific models under specific forcing conditions, as well as the incoherent part of the field in certain models. For well-resolved forcing coherent vortices disrupt the scaling, while in other models KLB inverse cascades are not realizable at all. The question of whether KLB theory describes inverse cascades thus has a complex answer, which depends on the 2D fluid model in question and the particular flow details.