  A uniform dilute Bose gas of known density has a universal behavior as the
atomic scattering length tends to infinity at unitarity while most of its
properties are determined by a universal parameter $\xi$ relating the energies
of the noninteracting and unitary gases. The usual mean-field equation is not
valid in this limit and beyond mean-field corrections become important. We use
a dynamical model including such corrections to investigate a trapped
disk-shaped dipolar Bose-Einstein condensate (BEC) and a dipolar BEC vortex for
large scattering length. We study the sensitivity of our results on the
parameter $\xi$ and discuss the possibility of extracting the value of this
parameter from experimental observables.
