Through an idealized modeling study with a depth level coordinate general ocean circulation model (GFDL/MOM), the sensitivity of an eastern boundary current on the horizontal resolution in thermally driven circulations is investigated. In general the circulation patterns do not show significant sensitivity to the resolution except in the northern and the eastern boundaries. When the resolution is low, a notable eastern boundary current is not observed. As the resolution becomes higher, a northward eastern boundary current emerges. A simple scaling analysis based on a linear vorticity equation reveals that such an eastern boundary current is initiated by vortex column stretching due to the downwelling of a zonal flow, which is driven by the sea surface temperature gradient, along the eastern wall. The scaling law predicts that the magnitude of the boundary current is inversely proportional to the horizontal resolution, if the downwelling occurs along the eastern most grid points. The model results follow the scaling law very well when the eastern boundary current, and subsequently the vertical stratification along the eastern wall are weak. In higher resolution cases, when the eastern boundary current becomes strong enough, the vertical stratification along the eastern wall becomes higher due to warm advection by the current, and downwelling is reduced. Therefore a larger part of the zonal flow turns to the north, and the eastern boundary current becomes stronger than predicted by the scaling law, which neglects the effects of the vertical stratification.