Eddy Memory Mode of Low-frequency Ocean Variability

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, psi*, 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 psi* 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 spin-up as a 15% overshoot in isopycnal slope and cannot be explained by the GM-parameterization. We developed an improved parameterization, making psi* proportional to an effective isopycnal slope, s*, that carries a finite memory gamma of past slopes. The memory explains the isopycnal overshoot and a lagged eddy kinetic energy response, bringing to light an oscillation with a period 2pi (Te gamma)^0.5 = 50 years, where the eddy-diffusion time-scale Te = 10 years and γ = 6 years are diagnosed from the eddy-resolving model. The EM-mode increases the Ekman-driven gyre variance by gamma/Te = 50 ± 15% – a fraction that stays relatively constant despite both time-scales decreasing with increasing mean forcing. We expect the eddy memory to be a fundamental property of rotating turbulent flows and highlight the need for better observational constraints on transient eddy-field characteristics.