  Spiral surface growth is well understood in the limit where the step motion
is controlled by the local supersaturation of adatoms near the spiral ridge. In
epitaxial thin-film growth, however, spirals can form in a step-flow regime
where desorption of adatoms is negligible and the ridge dynamics is governed by
the non-local diffusion field of adatoms on the whole surface. We investigate
this limit numerically using a phase-field formulation of the
Burton-Cabrera-Frank model, as well as analytically. Quantitative predictions,
which differ strikingly from those of the local limit, are made for the
selected step spacing as a function of the deposition flux, as well as for the
dependence of the relaxation time to steady-state growth on the screw
dislocation density.
