Finite Wings

Kelvin’s Theorem

The total circulation of a given fluid element cannot change unless work is done on it.

The total vorticity in a potential flow must be zero.

This leads to several conclusions.

The “fluid element” can include all the fluid in the whole flowfield of interest to us. So, we can say that if

positive vorticity is generated somewhere in the flow, there must be negative vorticity generated

somewhere else to compensate for it. This is seen in the case of the “starting vortex”

Note the fact that vorticity can indeeed be generated (or absorbed) at boundaries of the potential flow.

Such boundaries may be the rotational core of a vortex, a sink, or a solid wall, or a boundary between

two layers of fluid of different properties. Thus, vorticity can be generated at density gradients in a fluid:

for example, at the interface between a “cold front” and a “warm front”, or at the edge of a plume of hot

air rising

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