How Well Do Simplified Models Capture Complex Ocean Dynamics? A Numerical-Analytical Comparison on the Theory of a Stratified Rotating Fluid

Abstract

Understanding how ocean circulation transitions between stable and oscillatory states under ther- mal, rotational, and wind forcing remains fundamental to climate modelling. This study integrates analytical modelling with numerical simulations to identify stability thresholds where steady cir- culation gives way to self-sustained oscillations. We extend Maas’ low-order moment framework to derive explicit stability criteria in non-dimensional parameter space: buoyancy forcing strength (Ra′), rotation rate (f ′), and diffusion (μ). These predictions are tested in the Miami Isopycnic Coordinate Ocean Model (MICOM) through systematic parameter sweeps. The numerical exper- iments confirm the analytical predictions: increases in Ra′ or f ′ trigger limit cycle oscillations; μ modulates stability; wind torque lowers oscillation thresholds and induces coexistence of steady and oscillatory attractors; and bathymetry shifts but does not eliminate the propensity for oscil- lations. Spectral analysis reveals integer harmonics generated through bilinear coupling between fundamental modes and their higher harmonics. Our results demonstrate that low-order moment models successfully capture the essential stability behaviour of a comprehensive ocean model across different forcings and parameter regimes, including vertical structure response, Hopf bifurcation thresholds, and wind-driven multi-stability.