Appears in collection : 2026 - T2 - WS1 - Vortices and vorticity in geophysical flows

The Lagrangian-Averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) model, a fluid dynamics model based on energy-conserving modifications to nonlinear advection, can produce more energetic simulations than standard models, leading to improved fidelity (e.g., in ocean models). However, comprehensive understanding of the mechanism driving this energetic enhancement has proven elusive. To address this, we derive the fast quasi-geostrophic limit of the three-dimensional, stably-stratified LANS-$\alpha$ equations. This provides both the slow, balanced flow and the leading-order fast wave dynamics. Analysis of these wave dynamics suggests that an explanation for the energetic enhancement lies in the dual role of the alpha parameter: increasing $\alpha$ regularizes the dynamics and simultaneously generates a robustlandscape of wave-wave resonant interactions where $\alpha$ modifies the role of Burger number. We discuss this using simulations and connect our results to numerical stability issues.