Impulse and conformal mapping of vortex flows

Abstract

The concept of impulse is employed with conformal mapping to yield relatively simple relations for the force exerted on a two-dimensional stationary object by an incompressible irrotational and unsteady flow with moving vortices. An explicit relation for symmetric vortex flows is found, involving the vortex strength and the first and second derivatives of the mapping function evaluated at the vortex position. Furthermore an expression for not-necessarily symmetric vortex flows is derived, containing vortex strength, the first derivative of the mapping function evaluated at the vortex position, and the vortex velocity.