  Inspired by recent developments in Berdina-like models for turbulence, we
propose an inviscid regularization for the surface quasi-geostrophic (SQG)
equations. We are particularly interested in the celebrated question of blowup
in finite time of the solution gradient of the SQG equations. The new
regularization yields a necessary and sufficient condition, satisfied by the
regularized solution, when a regularization parameter $\alpha$ tends to zero,
for the solution of the original SQG equations to develop a singularity in
finite time. As opposed to the commonly used viscous regularization, the
inviscid equations derived here conserve a modified energy. Therefore, the new
regularization provides an attractive numerical procedure for finite time blow
up testing. In particular, we prove that, if the initial condition is smooth,
then the regularized solution remains as smooth as the initial data for all
times. Moreover, much like the original problem, the inviscid regularization
admits a maximum principle.
