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In the first part of this talk I'll review basic results about two-dimensional turbulence emphasizing the absence of a dissipative anomaly in two-dimensional (2D) fluid mechanics, and the energy-conserving long-time behavior of solutions of the 2D equations of motion. Arguments dating back to Onsager predict the formation of an ensemble of vortices separated by potential flow. Close encounters between like-signed vortices lead to irreversible merger into larger vortices. A simple scaling argument predicts relations between different quantities, such as the decay of the vortex density and the expansion in radius of a typical vortex. In the second part of the talk I turn to forced 2D turbulence and the problem of vortex condensation into the gravest mode of a finite box. I show that for most forcing functions the amplitude of the condensate in the inviscid limit is independent of viscosity. This non-singular inviscid limit is compatible with the energy power integral because the flow adjusts so that the work done on the 2D fluid by a prescribed force is linearly proportional to viscosity in the inviscid limit.

Bill Young is a member of the National Academy of Sciences and a Fellow of the American Meteorological Society and the American Geophysical Union.