Drag and lift predictions for vortex-dominated bluff body wakes*

The forces on a wake-producing body in an otherwise uniform flow can be calculated by applying linear momentum conservation to a control volume that encompasses the body and passes through the mid-wake region. With some simplifying assumptions regarding the mid-wake flow structure, the result can be a mathematical prediction of lift and drag. This approach was used famously by von Kármán (1912) to predict the time-averaged drag on a cylinder when the wake is modeled as a singly-periodic array of two point vortices; various formulations can be found in the textbooks by Goldstein (1938), Milne-Thompson (1968), et al. We generalize this approach to consider a variety of flows for which the wake can be approximated by coherent vortices embedded in potential flow. In particular, we present a closed-form estimation of drag and lift forces when the wake is approximated as periodic collections of N point vortices, with von Kármán's "drag law" being a special case for N=2.