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The Beaufort Gyre (BG) is a large anticyclonic circulation in the Arctic Ocean. Its strength is directly related to the halocline depth, and therefore also to the storage of freshwater. It has recently been proposed that the equilibrium state of the BG is set by the Ice‐Ocean Governor, a negative feedback between surface currents and ice‐ocean stress, rather than a balance between lateral mesoscale eddy fluxes and surface Ekman pumping. However, mesoscale eddies are present in the Arctic Ocean; it is therefore important to extend the Ice‐Ocean Governor theory to include lateral fluxes due to mesoscale eddies. Here, a nonlinear ordinary differential equation is derived that represents the effects of wind stress, the Ice‐Ocean Governor, and eddy fluxes. Equilibrium and time‐varying solutions to this three‐way balance equation are obtained and shown to closely match the output from a hierarchy of numerical simulations, indicating that the analytical model represents the processes controlling BG equilibration. The equilibration timescale derived from this three‐way balance is faster than the eddy equilibration timescale and slower than the Ice‐Ocean Governor equilibration timescales for most values of eddy diffusivity. The sensitivity of the BG equilibrium depth to changes in eddy diffusivity and the presence of the Ice‐Ocean Governor is also explored. These results show that predicting the response of the BG to changing surface forcing and sea ice conditions requires faithfully capturing the three‐way balance between the Ice‐Ocean Governor, wind stress, and eddy fluxes.

Anthropogenic influences have led to a strengthening and poleward shift of westerly winds over the Southern Ocean, especially during austral summer. We use observations, an idealized eddy‐resolving ocean sea ice channel model, and a global coupled model to explore the Southern Ocean response to a step change in westerly winds. Previous work hypothesized a two time scale response for sea surface temperature. Initially, Ekman transport cools the surface before sustained upwelling causes warming on decadal time scales. The fast response is robust across our models and the observations: We find Ekman‐driven cooling in the mixed layer, mixing‐driven warming below the mixed layer, and a small upwelling‐driven warming at the temperature inversion. The long‐term response is inaccessible from observations. Neither of our models shows a persistent upwelling anomaly, or long‐term, upwelling‐driven subsurface warming. Mesoscale eddies act to oppose the anomalous wind‐driven upwelling, through a process known as eddy compensation, thereby preventing long‐term warming.