The question of global regularity vs. finite time blow-up remains open for many fluid equations. In this talk, I will discuss an active scalar equation which is an interpolation between the 2D Euler equation and the surface quasi-geostrophic equation. We study the patch dynamics for this equation in the half-plane, and prove that the solutions can develop a finite-time singularity. This is a joint work with A. Kiselev, L. Ryzhik and A. Zlatos.