  The coarsening of an array of vortex ripples prepared in an unstable state is
discussed within the framework of a simple mass transfer model first introduced
by K.H. Andersen et al. [Phys. Rev. E 63, 066308 (2001)]. Two scenarios for the
selection of the final pattern are identified. When the initial state is
homogeneous with uniform random perturbations, a unique final state is reached
which depends only on the shape of the interaction function $f(\lambda)$. A
potential formulation of the dynamics suggests that the final wavelength is
determined by a Maxwell construction applied to $f(\lambda)$, but comparison
with numerical simulations shows that this yields only an upper bound. In
contrast, the evolution from a perfectly homogeneous state with a localized
perturbation proceeds through the propagation of wavelength doubling fronts.
The front speed can be predicted by standard marginal stability theory. In this
case the final wavelength depends on the initial wavelength in a complicated
manner which involves multiplication by factors of 2 and rational ratios such
as 4/3.
