Eddy Memory Mode of Multidecadal Variability in Residual-Mean Ocean Circulations with Application to the Beaufort Gyre

Mesoscale eddies shape the Beaufort Gyre response to Ekman pumping, but their transient dynamics are poorly understood. Climate models commonly use the Gent–McWilliams (GM) parameterization, taking the eddy streamfunction Ψ* to be proportional to an isopycnal slope s and an eddy diffusivity K. This local-in-time parameterization leads to exponential equilibration of currents. Here, an idealized, eddy-resolving Beaufort Gyre model is used to demonstrate that Ψ* carries a finite memory of past ocean states, violating a key GM assumption. As a consequence, an equilibrating gyre follows a spiral sink trajectory implying the existence of a damped mode of variability—the eddy memory (EM) mode. The EM mode manifests during the spinup as a 15% overshoot in isopycnal slope (2000 km3 freshwater content overshoot) and cannot be explained by the GM parameterization. An improved parameterization is developed, such that Ψ* is proportional to an effective isopycnal slope s*, carrying a finite memory γof past slopes. Introducing eddy memory explains the model results and brings to light an oscillation with a period 2π√T_Eγ ≈ 50 yr, where the eddy diffusion time scale T_E ~ 10 yr and γ ≈ 6 yr are diagnosed from the eddy-resolving model. The EM mode increases the Ekman-driven gyre variance by γ/T_E ≈ 50% ± 15%, a fraction that stays relatively constant despite both time scales decreasing with increased mean forcing. This study suggests that the EM mode is a general property of rotating turbulent flows and highlights the need for better observational constraints on transient eddy field characteristics