  In recent work of Luo and Hou, a new scenario for finite time blow up in
solutions of 3D Euler equation has been proposed. The scenario involves a ring
of hyperbolic points of the flow located at the boundary of a cylinder. In this
paper, we propose a two dimensional model that we call "hyperbolic Boussinesq
system". This model is designed to provide insight into the hyperbolic point
blow up scenario. The model features an incompressible velocity vector field, a
simplified Biot-Savart law, and a simplified term modeling buoyancy. We prove
that finite time blow up happens for a natural class of initial data.
