The performance of non-eddy-resolving numerical models requires a good understanding, with appropriate representation, of eddy-mean flow feedbacks. To help understand these feedbacks, we propose a diagnostic framework linking eddy geometry with the eddy-mean energy exchange terms from the Lorenz energy diagram. This framework provides explicit mathematical formulas that link eddy-mean energy exchange rates with both mean state structure and the properties of eddy momentum/buoyancy ellipses. Considering that the mean flow has both along- and cross-stream variations, we  decompose eddy-mean  kinetic energy exchange term  into three  components: one associated with cross-stream variation of mean flow (M_C), one associated with along-stream variation of mean flow (M_A), and one associated with the mean flow direction variation (M_R).  Corresponding geometric formulas are provided. The geometric interpretation of M_C is consistent with barotropic instability theories and eddy geometry literature. As to M_A, the weakening (strengthening) of mean flow in the along-stream direction corresponds to eddy kinetic energy generation (decay) through M_A. M_A and part of M_R are interconnected under the quasigeostrophic assumption. From a global integral perspective, both the along-stream and cross-stream variations of the mean flow contribute significantly to eddy-mean kinetic energy exchange.  At the Kuroshio Extension, both mean state and eddy energy level are key for shaping the spatial pattern of eddy-mean energy exchange. This framework offers a tool for geometrically interpreting eddy-mean energy exchange, which may offer guidance for eddy parameterizations. 

eddy geometry, eddy-mean energy exchange, along/cross-stream variation of mean flow