The Lift and Drag on a Flat Plate at Low Reynolds Number via Variational Methods* By

The problem of determining the low Reynolds number lift and drag on a flat plate in Oseen flow is treated by the application of a variational principle due to Levine and Schwinger. This approach circumvents the difficulty which has limited previous results to drastically low values of the Reynolds number. In particular, an asymptotic form for the drag coefficient is derived, and found to be suitable for a much larger range of this parameter. The ease with which the variational principle can be applied rests heavily on the ability to reduce the pair of coupled integral equations which govern this problem to one integral equation. This equation and its adjoint are shown to have solutions which are quite simply related, which further facilitates the treatment of the variational problem.