Vortex Flows

The vorticity vector is the curl of fluid velocity (Section 2.6) and is twice the effective local angular velocity of the fluid (Section 1.4). Vorticity plays a central role in understanding fluid flow phenomena, in particular, at high Reynolds numbers (Chapter 21). A case in point is the vortex stretching process underlying the energy transport phenomena in turbulent flows. Moreover, vorticity provides a vital tool while discussing the analytic structure underlying the theoretical formulations of fluid dynamics. It turns out that the vorticity vector is the appropriate canonical variable in the Hamiltonian formulations of fluid flows (Section 3.2). These formulations afford interesting alternative geometric perspectives (Section 3.2) on the Euler equations of fluid flows (Section 5.2).