A proposal concerning laminar wakes behind bluff bodies at large Reynolds number

Abstract

This note advocates a model of the steady flow about a bluff body at large Reynolds number which is different from the classical free-streamline model of Helmholtz and Kirchhoff. It is suggested that, although the free-streamline model may be a proper solution of the Navier-Stokes equation with μ = 0, it is unlikely to be the limit, as μ → 0, of the solution describing the steady flow due to the presence of a bluff body in an otherwise uniform stream. The limit solution proposed here is one which gives a closed wake.

A closed wake contains a standing eddy, or eddies, whose general features can be inferred from the results of an earlier investigation of steady flow in a closed region at large Reynolds number. In all cases, the drag (coefficient) on the body tends to zero as the Reynolds number tends to infinity. The proccedure for finding the details of the closed wake behind two-dimensional and axisymmetrical bodies is described, although no particular case has yet been worked out.