Forces on a body with a vortex-dominated wake

When a solid body is immersed in fluid moving at a constant speed at Reynolds numbers greater than about 50, a series of alternating vortices forms in its wake, known as the 'von Karman street'. The drag or thrust force on such a body can be predicted using von Karman's drag law. This law relates the characteristics of the vortex street in the wake to the drag (or thrust) coefficient on the body, and was derived by von Karman in 1911 using Newton's second law applied to a rectangular control volume enclosing the body and its wake. In this talk, we will present a generalization of von Karman's drag law to the case of an N-vortex street wake, i.e., to vortex-dominated wakes in which there are an arbitrary number of vortices in the wake. We will show that under a small set of assumptions, it is possible to relate the drag coefficient on a body with an N-vortex wake to the characteristics of the vortex street, including the strengths and positions of the vortices. We will apply this method to wakes with 3 or 4 vortices per period, corresponding to the experimentally observed 'P+S' wakes and 2P wakes.