Reinterpreting the basic theorem of flagellar hydrodynamics

Lorentz [1] pioneered the representation of flows at very low Reynolds number by a surface distribution of stokeslets - whose strengths, nowadays, are computed by surface-velocity collocations. That method is here compared with a representation widely used in flagellar hydrodynamics, by a curvilinear distribution of stokeslets and dipoles along the flagellar centreline; with the velocity of each cross-section expressed as a centreline value of the combined fields of singularities beyond a certain cutoff distance. The latter is also a good representation, and offers moreover some computational advantages. This paper establishes the equivalence of the two representations, and identifies those properties of Stokes flows which make both the dipoles and the cutoff essential to that equivalence.