Induced drag in two dimensions in ideal fluids

Abstract

In this paper we suggest a model for how a significant part of the drag forces on two-dimensional objects can be derived using the circulation that is naturally maintained around the objects. We assume incompressible and inviscid potential flow and that the circulation is already generated. The resulting velocity field complements the one that is known to generate Prandtl's induced drag in three dimensions. We demonstrate how fluid particles in a velocity field are attracted towards an object, and that this, due to conservation of momentum, results not only in lift, but also in drag forces. The magnitude of a disturbance velocity can be derived from the circulation of bound and shed vortices accompanying the object and parameters taken from the von Kármán vortex street description. Another part of the drag is generated by vortices that emerge behind blunt bodies when fluid particles do not follow the surface of the objects. We obtain a mathematical description of the resistance of several types of blunt bodies and rotating cylinders. The model involves no parameters that are derived from empirical data. Still, this inviscid approach corresponds well with experimental data in viscous flow and is close to a mathematical empirical description of rotating cylinders by W. G. Bickley.