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Potential vorticity (PV) is seen as one of the important theoretical successes of modern meteorology. It is a simplified approach for understanding fluid motions in a rotating system such as the Earth's atmosphere and ocean.
The potential vorticity is absolute vorticity divided by the vertical spacing between levels of constant (potential) temperature (or entropy). The absolute vorticity of an air mass will change if the air mass is stretched (or compressed) in the vertical direction, but the potential vorticity is conserved in an adiabatic flow.
In Cartesian coordinates, the components of the geostrophic wind are = (1a) = (1b) where is the geopotential.. The geostrophic vorticity = ^ can therefore be expressed in terms of the geopotential as
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
Animation of a Rankine vortex. Free-floating test particles reveal the velocity and vorticity pattern. The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine. The vortices observed in nature are usually modelled with an irrotational (potential or free ...
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:
Fluid elements initially free of vorticity remain free of vorticity. Helmholtz's theorems have application in understanding: Generation of lift on an airfoil; Starting vortex; Horseshoe vortex; Wingtip vortices. Helmholtz's theorems are now generally proven with reference to Kelvin's circulation theorem.
Crocco's theorem is an aerodynamic theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow. Crocco's theorem gives the relation between the thermodynamics and fluid kinematics. The theorem was first enunciated by Alexander Friedmann for the particular case of a perfect gas and published in 1922: [1]