The wind‐ and buoyancy‐forced upper ocean circulation in a marginal sea connected to the open ocean through two straits is investigated using idealized numerical and analytical models. The study is motivated by the Japan/East Sea (JES) and other marginal seas found along the western North Pacific. It is shown that for anticyclonic wind stress curl and atmospheric cooling in the marginal sea, the inflow transport branches into eastern and western boundary currents, in qualitative agreement with observed branching of the Tsushima Current in the southern JES. The eastern boundary current arises because wind forcing in the open ocean, and a circulation integral around the island that separates the marginal sea from the open ocean, maintains the temperature on the island to be warmer than that found in the interior of the marginal sea. Buoyancy forcing in the marginal sea plays a key role in maintaining the eastern boundary current. The dynamics that control the water mass transformation and downwelling are described and related to the model parameters. The largest heat loss to the atmosphere is found in the eastern boundary current. The exchange rates with the open ocean, downwelling within the marginal sea, and current structure within the marginal sea predicted by a linear analytic theory compare closely with results from a shallow water numerical mo