On Oseen's approximation

Abstract

An investigation is made into the validity of the Oseen equations, for incom-pressible, viscous flow past a body, as an approximation to the Navier-Stokes equations. It is shown that, when the body is such that a reversal of the uniform flow at infinity merely reverses any component of the force on the body without changing its absolute magnitude, that component can be determined correctly to the first order in the Reynolds number, though the detailed velocity field is not correct to this order. Moreover, this force can be deduced simply from a knowledge of the force on the body according to Stokes's approximation. The analysis is also generalized to include the magneto-hydrodynamic effects when the fluid is conducting and the flow takes place in the presence of a magnetic field.