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Carl Rossby proposed in 1939 [4] that, instead of the full three-dimensional vorticity vector, the local vertical component of the absolute vorticity is the most important component for large-scale atmospheric flow, and that the large-scale structure of a two-dimensional non-divergent barotropic flow can be modeled by assuming that is conserved.
Equation (14) is often referred to as the geopotential tendency equation. It relates the local geopotential tendency (term A) to the vorticity advection distribution (term B) and thickness advection (term C).
The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is:
Vorticity is useful for understanding how ideal potential flow solutions can be perturbed to model real flows. In general, the presence of viscosity causes a diffusion of vorticity away from the vortex cores into the general flow field; this flow is accounted for by a diffusion term in the vorticity transport equation.
The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows. Applications of potential flow include: the outer flow field for aerofoils, water waves, electroosmotic flow, and groundwater flow. For flows (or parts thereof) with strong vorticity effects
As the fluid flows outward, the area of flow increases. As a result, to satisfy continuity equation, the velocity decreases and the streamlines spread out. The velocity at all points at a given distance from the source is the same. Fig 2 - Streamlines and potential lines for source flow. The velocity of fluid flow can be given as -
All potential flow solutions are also solutions of the Euler equations, and in particular the incompressible Euler equations when the potential is harmonic. [27] A two-dimensional parallel shear-flow. Solutions to the Euler equations with vorticity are:
Formula for vorticity can give another explanation of the Stokes' Paradox. The functions (), > belong to the kernel of and generate the stationary solutions of the vorticity equation with Robin-type boundary condition. From the arguments above any Stokes' vorticity flow with no-slip boundary condition must be orthogonal to the obtained ...