My latest paper is now published in the Journal of Fluid Mechanics! In this article, we revisit a widely used model for studying baroclinic instability: the quasi-geostrophic two-layer model. A well known instability criterion in this model is that the potential vorticity (PV) gradient must change sign between the layers. In this paper, we show that this criterion only holds in the inviscid case: as soon as bottom friction enters the scene, the instability condition changes. What comes out after many tedious calculations is a rather compact and elegant result. We explore the implications this has for the role of bottom topography. Furthermore, we discuss how instability in the model is impacted by the orientation of the different PV gradients - planetary PV, topographic PV and stretching PV (i.e.\ direction of the mean flow). The result is an overview of the two-layer model in its most general form.
You can read the article here and of course, I am always happy to chat about it.