Precession of spherical spin-1 vortices

A spin-1 vortex consists of the three time-dependent multipolar spherical modes associated with the three spherical harmonic functions of degree ℓ=1. The spin-1 vortex is basically the spherical Hicks–Moffatt vortex with an arbitrary orientation in the three-dimensional space. It is shown that, in the presence of a background flow with cylindrical swirl of arbitrary orientation and a background time-dependent radial expansion/contraction flow, the orientation of the spin-1 vortex precesses about an axis and with a frequency both prescribed by the background cylindrical flow. The time dependence of the precession frequency is prescribed by a background radial divergent flow. It is shown that this vortex precession in the presence of a constant background vorticity is analogous to the precession of the magnetic moment of a body in the presence of an external constant magnetic field, or Larmor precession.