A recent study led by former post-doctoral fellow Dr. Suraj Singh, in collaboration with Dr. Amit Tandon and former research professor Dr. Christian E. Buckingham, titled ‘On baroclinic instability of curved fronts’, explores how introducing slight curvature to oceanic fronts impacts baroclinic instabilities.
The research extends the classic Eady and Charney models on a cylindrical polar coordinate system by adding a slight curvature to a predominantly zonal flow. Under quasi-geostrophic scaling, the team analyzed the structure and growth rates of the pressure perturbations.
A key finding reveals that while unstable Eady modes remain largely unaffected by curvature, unstable Charney modes deepen owing to the introduction of a depth scale, enhancing vertical buoyancy flux—a phenomenon highlighted in their results (figure below).
The study also acknowledges certain limitations and suggests that understanding curved fronts could improve future parametrization of baroclinic instabilities in ocean models, and eddies which are deeper than the mixed layers. (here)

Fig: Vertical structure of the along-front averaged buoyancy flux for several values of the radius of curvature (Fig 8 of the paper)