Syllabus
Brief review of three-dimensional turbulence; Kolmogorov theory; Richardson cascade
Basic consequences of two-dimensionality; inverse cascade
Self-similarity and its violation; coherent structures
Transition to turbulence; dynamical systems modeling; bifurcations and chaos
Continuous and discrete vorticity; Onsager vortex gas
Quasi-2D systems; applications to selected geophysical flows; bifurcations and climate change
Experimental methods of flow visualization; Particle Image Velocimetry
Annotation
In complex nonlinear systems continuous change of a parameter can lead to sudden and qualitative change of the system behavior through so-called bifurcations. Even a relatively small change in, for example, the mean temperature of the oceans can lead to drastic changes of the climate and associated global flows, which, on the largest scale, are approximately two-dimensional.