Canonical frontal circulation patterns in terms of Green's functions for the Sawyer‐Eliassen equation

Green's function solutions for the Sawyer‐Eliassen equation are derived and compared for quasi‐geostrophic and semi‐geostrophic two‐dimensional frontal dynamics in vertically bounded domains. The semi‐geostrophic Green's functions provide a framework for understanding canonical frontal circulation patterns arising from interactions, or coupling, between upper‐ and lower‐tropospheric jet‐front systems. Previously documented conceptual models for these circulation patterns are reproduced by the solutions. A noteworthy finding is that vertical coupling produces a deep and narrow region of ascent when the upper‐ and lower‐tropospheric point sources for the Green's functions share the same sign and absolute momentum surface.