D’Alembert’s Paradox

Since classical inviscid theory leads to the patently absurd conclusion that the resistance experienced by a rigid body moving through a fluid with uniform velocity is zero, great efforts have been made during the last hundred or so years to propose alternate theories and to explain how a vanishingly small frictional force in the fluid can nevertheless have a significant effect on the flow properties. The methods used are a combination of experimental observation, computation often on a very large scale, and analysis of the structure of the asymptotic form of the solution as the friction tends to zero. This three-pronged attack has achieved considerable success, especially during the last ten years, so that now the paradox may be regarded as largely resolved. The lecture will review these achievements in subsonic and supersonic flow, for bluff bodies, for trailing-edge flows and for internal flows. Most of the work has been on steady two-dimensional problems but the special difficulties in unsteady and th...