Hamilton Colloquium Series - William Young, Scripps Institution of Oceanography, UC, San Diego - "Two Dimensional Turbulence"

Thu, Mar 14, 2013, 4:30 pm to 5:30 pm
Jadwin A10
In the first part of this talk I will review basic results about two-dimensional turbulence emphasizing the absence of a dissipative anomaly in D=2, and the energy-conserving long-time behavior of solutions of the inviscid equations of motion. Arguments dating back to Onsager predict the formation of an en-semble of vortices separated by potential flow. Close encounters between like-signed vortices lead to irreversible merger into larger vortices. A simple scal-ing argument predicts relations between different quantities, such as the de-cay of the vortex density and the expansion in radius of a typical vortex. In the second part of the talk I will turn to forced two-dimensional turbulence and the problem of vortex condensation into the gravest mode of a finite box. I will 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 two-dimensional fluid by a prescribed force is linearly proportional to viscosity in the inviscid limit.