Representation of balanced state in models of geophysical flows

Balanced motions, such as mesoscale eddies, dictate the atmospheric and oceanic dynamics. However, determining a precise balanced state in models remains challenging, primarily due to their nonlinear coupling with the unbalanced flows, such as internal gravity waves. The spontaneous loss of balance, resulting in nonlinear internal wave generation, challenges the existence of an invariant balanced state from a mathematical perspective, and at the same time has physical implications for the energy cycle of the atmosphere and ocean.

In this talk, I will discuss the recent progress in deriving and quantifying the balanced state in geophysical flows from nonlinear flow decomposition as well as the comparison of balanced states from different mathematical approaches. This is applied to varied oceanic regimes in a suite of idealized models to quantify spontaneous wave generation and assess its role in the energy cycle relative to other mechanisms. To diagnose these processes in complex flows, a new flow decomposition approach is presented for realistic applications, such as flows with boundaries. These developments provide new avenues to determine the balanced state and offer fresh insights into the energetics and dynamics of the atmosphere and ocean.