  Blazars exhibit flares across the electromagnetic spectrum. Many $\gamma$-ray
flares are highly correlated with flares detected at optical wavelengths;
however, a small subset appears to occur in isolation, with little or no
variability detected at longer wavelengths. These "orphan" $\gamma$-ray flares
challenge current models of blazar variability, most of which are unable to
reproduce this type of behavior. We present numerical calculations of the
time-variable emission of a blazar based on a proposal by Marscher et al.
(2010) to explain such events. In this model, a plasmoid ("blob") propagates
relativistically along the spine of a blazar jet and passes through a
synchrotron-emitting ring of electrons representing a shocked portion of the
jet sheath. This ring supplies a source of seed photons that are
inverse-Compton scattered by the electrons in the moving blob. The model
includes the effects of radiative cooling, a spatially varying magnetic field,
and acceleration of the blob's bulk velocity. Synthetic light curves produced
by our model are compared to the observed light curves from an orphan flare
that was coincident with the passage of a superluminal knot through the inner
jet of the blazar PKS 1510$-$089. In addition, we present Very Long Baseline
Array polarimetric observations that point to the existence of a jet sheath in
PKS 1510$-$089, thus providing further observational support for the
plausibility of our model. An estimate of the bolometric luminosity of the
sheath within PKS 1510$-$089 is made, yielding $L_{\rm sh} \sim 3 \times
10^{45} ~ \rm erg ~ \rm s^{-1}$. This indicates that the sheath within PKS
1510$-$089 is potentially a very important source of seed photons.
