On calculation of hydrodynamic forces for steady flows in unbounded domains

This note addresses the question why the “impulse formula”, often employed to compute hydrodynamic forces in vortex-dominated time-dependent flows, is not applicable to steady flows in unbounded domains. By analyzing the asymptotic structure of steady and unsteady flow solutions in unbounded domains, it is demonstrated that one assumption made in the derivation of the impulse formula is in fact not satisfied in the steady case. This result also highlights the special character of steady flows in unbounded domains.