Understanding the Mesoscale Eddy Vertical Tilt Based on Mode Decomposition

Abstract The vertical tilt of mesoscale eddy is widely observed in the world ocean. Based on observations, idealized numerical simulations, and analytical theory, we demonstrate that such tilt arises fundamentally from differences in propagation speeds between the first and second baroclinic modes. We construct an initial idealized Gaussian eddy without vertical tilt and isolate its first mode, second mode, and the combined mode 1 + 2 components. Simulations demonstrate that while the individual mode 1 and mode 2 eddies remain vertically aligned, the real eddy and the combined mode 1 + 2 eddy develop significant vertical tilt during evolution. Crucially, superimposing the independently evolved mode 1 and mode 2 eddies replicates this tilt pattern, confirming that the speed difference between the two modes drives tilting. Additional experiments including higher modes confirm their secondary role. Furthermore, sensitivity experiments and analytical derivations using the WKB and the long‐wave Rossby approximations establish that a larger inverse square of Prandtl ratio, Pr −2 ( N 2 / f 2 ), arising from stronger stratification or weaker rotation, increases the propagation speed difference between modes, leading to greater vertical tilt. The nonlinear energy transfer from mode 2 to mode 1 is shown to suppress the tilting by reducing the influence of the slower mode. This work provides a mechanistic understanding of mesoscale eddy vertical tilting, linking it directly to modal dynamics and environmental parameters.