  We explore vortex solutions for a class of dual $SU(N)$ Yang-Mills models
with $N^2-1$ Higgs fields in the adjoint representation. Initially, we show
that there is a collective behavior that can be expressed in terms of a small
$N$-independent number of field profiles. Then, we find a region in parameter
space where the nontrivial profiles coincide with those of the Nielsen-Olesen
vortex, and the energy scales exactly with the quadratic Casimir. Out of this
region, we solve the ansatz equations numerically and find very small
deviations from the Casimir law. The coexistence of Abelian-like string
profiles and non-Abelian scaling features is welcome, as these properties have
been approximately observed in pure YM lattice simulations.
