Abstract
Chapter 7 presents the dynamics of vorticity and its relation to turbulence. Vortex lines, tubes, sheets, and concentrated vortices are analyzed, and the fundamental vorticity theorems are formulated. Concentrated vortex models are discussed, including the forced, free, and Rankine vortices. Cellular flows are introduced, and linked to thermal flow instability. Vorticity in shear flow is discussed, and the conditions for flow induced by vorticity are examined. The vorticity transport equation is derived, and each term is examined for its physical meaning. Vortex stretching, vortex rings, and vortex lines frozen in the fluid are explained. Diffusion of vorticity and vortex shedding are introduced, and Stokes's theorem is proved. Enstrophy and helicity are defined and related to environmental flows. Kelvin's circulation theorem is established, and conservation of helicity is proven.
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