  This work examines the dynamics of density patches in the 2D zero-diffusivity
Boussinesq system modified such that momentum is in a large Prandtl number
balance. We establish the global well-posedness of this system for compactly
supported and bounded initial densities, and then examine the regularity of the
evolving boundary of patch solutions. For $k \in \{0,1,2\}$, we prove the
global in time persistence of $C^{k+\mu}$-regularity, where $\mu \in (0,1)$,
for the density patch boundary via estimates of singular integrals. We conclude
with a simulation of an initially circular density patch via a level-set
method. The simulated patch boundary forms corner-like structures with growing
curvature, and yet our analysis shows the curvature will be bounded for all
finite times.
