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Abstract The existence of multiple equilibria (ice-covered and ice-free states) is explored using a set of coupled, nondimensional equations that describe the heat and salt balances in basins, such as the Arctic Ocean, that are subject to atmospheric forcing and two distinct water mass sources. Six nondimensional numbers describe the influences of atmospheric cooling, evaporation minus precipitation, solar radiation, atmospheric temperature, diapycnal mixing, and the temperature contrast between the two water masses. It is shown that multiple equilibria resulting from the dependence of albedo on ice cover exist over a wide range of parameter space, especially so in the weak mixing limit. Multiple equilibria can also occur if diapycnal mixing increases toO(10⁻⁴) m²s⁻¹or larger under ice-free conditions due to enhanced upward mixing of warm, salty water from below. Sensitivities to various forcing parameters are discussed. Significance StatementThe purpose of this study is to better understand under what circumstances high-latitude seas, such as the Arctic Ocean, can exist in either an ice-covered or an ice-free state. The temperature and salinity of the ocean, as well as the heat exchange with the atmosphere, are drastically different depending on which state the ocean is in. The theory presented here identifies how forcing from the atmosphere and ocean dynamics determines whether the ocean is ice covered, ice free, or possibly either one. 

Abstract Upwelling along the western boundary of the major ocean basin subtropical gyres has been diagnosed in a wide range of ocean models and state estimates. This vertical transport isO(5 × 10⁶) m³s⁻¹, which is on the same order of magnitude as the downward Ekman pumping across the subtropical gyres and zonally integrated meridional overturning circulation. Two approaches are used here to understand the reason for this upwelling and how it depends on oceanic parameters. First, a kinematic model that imposes a density gradient along the western boundary demonstrates that there must be upwelling with a maximum vertical transport at middepths in order to maintain geostrophic balance in the western boundary current. The second approach considers the vorticity budget near the western boundary in an idealized primitive equation model of the wind- and buoyancy-forced subtropical and subpolar gyres. It is shown that a pressure gradient along the western boundary results in bottom pressure torque that injects vorticity into the fluid. This is balanced on the boundary by lateral viscous fluxes that redistribute this vorticity across the boundary current. The viscous fluxes in the interior are balanced primarily by the vertical stretching of planetary vorticity, giving rise to upwelling within the boundary current. This process is found to be nearly adiabatic. Nonlinear terms and advection of planetary vorticity are also important locally but are not the ultimate drivers of the upwelling. Additional numerical model calculations demonstrate that the upwelling is a nonlocal consequence of buoyancy loss at high latitudes and thus represents an integral component of the meridional overturning circulation in depth space but not in density space. Significance StatementThe purpose of this study is to better understand what is forcing water to upwell along the western boundary at midlatitudes of the major ocean basins. This is a potentially important process since upwelling can bring heat and nutrients closer to the surface, where they can be exchanged with the atmosphere. Also, since ocean currents vary with depth, pathways followed in the upper ocean are different from those found for the deeper ocean, so the amount and location of upwelling influence where these waters go. Idealized numerical models and theory are used to demonstrate that the upwelling is ultimately driven by density changes along the western boundary of the basin that result from heat loss at high latitudes.