Probing the Timescales of Mesoscale Eddy Equilibration

Stratification in the Southern Ocean is determined by a competition primarily between westerly wind driven upwelling and baroclinic eddy transport. The presence of multiple timescales in the wind field calls for a better understanding of the underlying mechanisms of ocean eddy response to variable dynamic forcing. We investigate the timescales of mesoscale eddy equilibration in the SO in response to changing winds through a hierarchy of models. An analytical framework describing the energetic pathways between wind input, available potential energy, eddy kinetic energy, and dissipation, provides a simple theory of the phase and amplitude response to oscillating wind stress. We hypothesize that the transient ocean response to variable winds lies between the two limits of Ekman response (high frequency limit) and “eddy saturation” (low frequency limit). The Ekman response is characterized by the isopycnals adjusting to the wind forcing quickly, while in the eddy saturated limit, all of the wind energy goes into mesoscale eddy kinetic energy. Motivated by an analogy with electric circuits, the system’s frequency response is characterized by a complex transfer function: the "eddy filter”. Both the phase and amplitude response of circumpolar transport, eddy kinetic energy, and potential energy, predicted by the linear analytic framework are verified using multiple ensemble experiments in a high-resolution isopycnal layered coordinate model (GOLD) with different time-periodic wind forcings. The results from the numerical experiments show agreement with the linear theory and is in accord with previous dynamical arguments and modeling studies of eddy saturation. The implications of these results for baroclinic instability, eddy mixing and heat transport in the Southern ocean are discussed.