The Dynamics of Nonlinear Triads of Rossby-Haurwitz and Gravity Shallow Water Waves on the Sphere

Breno Raphaldini , Pedro S. Peixoto, Marco Antonio Dourado, Andre Seiji Wakate Teruya

Understanding the interplay between nonlinearity and multiple scales is one of the cornerstones of geophysical fluids and climate modelling. Nonlinear interactions between atmospheric waves of disparate scales, from fast inertia-gravity waves to slow planetary-scale Rossby-Haurwitz waves, are central to energy cascades and to low-frequency phenomena. Yet, they remain poorly understood beyond simplified f-plane and beta-plane settings, and are often left only partially represented once gravity waves are filtered out of forecast models. Here, we study these couplings directly in the rotating shallow-water equations on the sphere with realistic atmospheric parameters for a single layer representing the troposphere. We derive reduced models of three, four and five nonlinearly interacting Hough harmonics to quantify the efficiency and timescale of energy exchange between wave families including both slow (Rossby-Haurwitz) and fast (inertia-gravity) modes. We show, in several configurations, that inertia-gravity modes can influence the slow Rossby-Haurwitz modes both through exchange of energy and by generating new low-frequency oscillations.