ON A VARIATIONAL PRINCIPLE FOR THE DRAG IN LINEAR HYDRODYNAMICS

It has been demonstrated several times that the method of induced forc es is a suitable tool to calculate the drag on a submerged body in var ious linear approximations of the Navier-Stokes equation. In this pape r we show that this method may be derived from a variational principle . The stationary value of the appropriate functional is the drag. The derivation of the set of equations for the induced force moments is gi ven explicitly for two hydrodynamically relevant problems, namely a sp here moving slowly along the axis of a rotating viscous fluid and a sp here in Oseen flow. Moreover, the variational scheme is employed to st udy the influence of momentum convection on the drag on a sphere for s mall Reynolds and Taylor numbers. Already with a simple approximation for the induced force density, the results are in reasonably good agre ement with experimental data.