= Hydrodynamic impulse
{title2=$\mathbf I=\frac12\int\mathbf x\times\boldsymbol\omega\,dV$}
<Hydrodynamic impulse> per unit density is $\mathbf I=\tfrac12\int\mathbf x\times\boldsymbol\omega\,dV$ for localized <vorticity>. In unforced all-space <incompressible flow> its derivative vanishes when far-field fluxes vanish. For a spherical all-space limit, $\mathbf I=(3/2)\lim_R\int_{V_R}\mathbf u\,dV$; a dipolar velocity tail makes the distinction from a bare <momentum> integral important.
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