A family of vortex rings and a variational application to potential flows around three-dimensional bodies

A variational formulation and solution of general three-dimensional potential flows gave rise to the construction of a special family of ‘trial functions’. This family is composed by circular-sector vortex rings, here named α-rings, i.e., rings that are positioned on the border of a circular sector with aperture angle α. An explicit formula for the velocity potential describing the α-rings family is here derived. A particular case is the well-known circular vortex-ring. The formula is given in terms of a uniformly valid series involving trigonometric and Hypergeometric functions. Result...