On the formation of vortices at a solid boundary

A scientific controversy engaged by Kelvin and Stokes a century ago is revisited in the light of a reformulation of the Navier–Stokes equation introduced by Oseledets in 1988; this was identified as an equation of motion for impulse density by Buttke in 1993, who also demonstrated that Lagrangian models of incompressible flow can be based on the impulse density variable. We argue here that the viscous boundary conditions at a solid wall expressed in terms of this variable imply that eddy formation at such a boundary is related (at least in part) to forces normal to the wall. Moreover this formation process can be reconciled with the fact that the circulation of the resulting flow is not advanced by the action of pressure impulse.