  Context: White dwarf - Brown dwarf short period binaries (P$_{\rm orb}$
$\lesssim$ 2 hours) are some of the most extreme irradiated atmospheric
environments known. These systems offer an opportunity to explore theoretical
and modelling efforts of irradiated atmospheres different to typical hot
Jupiter systems. Aims: We aim to investigate the three dimensional atmospheric
structural and dynamical properties of the Brown dwarf WD0137-349B. Methods: We
use the three dimensional GCM model Exo-FMS, with a dual-band grey
radiative-transfer scheme to model the atmosphere of WD0137-349B. The results
of the GCM model are post-processed using the three dimensional Monte Carlo
radiative-transfer model \textsc{cmcrt}. Results: Our results suggest
inefficient day-night energy transport and a large day-night temperature
contrast for WD0137-349B. Multiple flow patterns are present, shifting energy
asymmetrically eastward or westward depending on their zonal direction and
latitude. Regions of overturning are produced on the western terminator. We are
able to reproduce the start of the system near-IR emission excess at $\gtrsim$
1.95 $\mu$m as observed by the GNIRS instrument. Our model over predicts the IR
phase curve fluxes by factors of $\approx$1-3, but generally fits the shape of
the phase curves well. Chemical kinetic modelling using \textsc{vulcan}
suggests a highly ionised region at high altitudes can form on the dayside of
the Brown dwarf. Conclusions: We present a first attempt at simulating the
atmosphere of a short period White dwarf - Brown dwarf binary in a 3D setting.
Further studies into the radiative and photochemical heating from the UV
irradiation is required to more accurately capture the energy balance inside
the Brown dwarf atmosphere. Cloud formation may also play an important role in
shaping the emission spectra of the Brown dwarf.
