  The detection of disk-integrated polarization from Luhman 16A and B in
H-band, and subsequent modeling, has been interpreted in the framework of zonal
cloud bands on these bodies. Recently, Tan and Showman (2021) investigated
three-dimensional atmospheric circulation and cloud structures of brown dwarfs
with general circulation models (GCMs), and their simulations yield complex
cloud distributions showing some aspects of zonal jets, but also complex
vortices that cannot be captured by a simple model. Here we use these 3D GCMs
specific to Luhman 16A and B, along with the three-dimensional Monte Carlo
radiative transfer code ARTES, to calculate their polarization signals. We
adopt the 3D temperature-pressure and cloud profiles from the GCMs as our input
atmospheric structures. Our polarization calculations at 1.6 $\mu$m agree well
with the measured degree of linear polarization from both Luhman 16 A and B.
Our calculations reproduce the measured polarization for both the objects with
cloud particle sizes between 0.5-1 \,$\mu$m for Luhman 16 A and 5 \,$\mu$m for
Luhman 16 B. We find that the degree of linear polarization can vary on
hour-long timescales over the course of a rotation period. We also show that
models with azimuthally symmetric band-like cloud geometries, typically used
for interpreting polarimetry observations of brown dwarfs, over-predict the
polarization signal if the cloud patterns do not include complex vortices
within these bands. This exploratory work shows that GCMs are promising for
modeling and interpreting polarization signals of brown dwarfs.
