Multipole expansions in Stokes flow

Maxwell's theory of multipoles is extended from potential theory to Stokes flow field, and from spherical to spheroidal geometry. The expansion is bas ed on an exterior integral representation of the velocity and the pressure field of Stokes flow as well as the appropriate fundamental solution. It is shown that the velocity field is expandable in terms of five different mul tipoles, four of which are weighted multipoles. On the other hand, the pres sure as well as the vorticity field, have multipole expansions that involve only the non-weighted multipoles. In fact, a more general result is demons trated according to which the pressure and the vorticity are given as the s calar and the vector invariants of the same harmonic dyadic field. The impo rtance of the multipole expansion for the velocity and the pressure field i s well known, and it refers both to the theoretical understanding of the fl ow, as well as to practical applications and numerical implementations. (C) 2001 Elsevier Science Ltd. All rights reserved.