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Turbulence and Symmetry
This lecture introduces the concept of turbulence and symmetry in fluid flow past a cylinder, focusing on the Reynolds number and its impact on flow behavior. It discusses the breaking and restoration of symmetries as the Reynolds number increases, highlighting the tendency for statistical symmetries at high Reynolds numbers. The lecture also covers the application of symmetries and conservation laws in compressible fluid dynamics, emphasizing periodic boundary conditions and the behavior of flow fields. Various examples and observations are presented to illustrate the theoretical concepts discussed.