On a Variational Principle for the Drag in Linear Hydrodynamics

It has been demonstrated several times that the method of induced forces is a suitable tool to calculate the drag on a submerged body in various linear approximations of the Navier-Stokes equation. In this paper 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 given explicitly for two hydrodynamically relevant problems, namely a sphere moving slowly along the axis of a rotating viscous fluid and a sphere in Oseen flow. Moreover, the variational scheme is employed to study the influence of momentum convection on the drag on a sphere for small Reynolds and Taylor numbers. Already with a simple approximation for the induced force density, the results are in reasonably good agreement with experimental data.