Abstract Many test problems have been posed in which the behavior of schemes may be examined within the simplified context of passive tracer transport. Most often these tests involve transport of a tracer containing sharp or discontinuous gradients within a smooth advecting field. Hecht et al. [J. Geophys. Res. 100 (1995) 20763–20778] presented a test problem, using the simple analytical gyre of Stommel [Trans. Am. Geophys. Union 29 (1948) 202–206], in which an initially smooth tracer field is transported through a highly sheared circulation, representing another scenario of relevance to ocean modeling. We present a modification of that test in which the underlying grid is rotated relative to the gyre, such that the western boundary falls at 45° to the principal grid axes. The advection schemes used by most ocean modelers to date are examined within this test problem. We find, in two cases, that methods which performed acceptably under the original formulation of the problem, and which have seen extensive application to geophysical fluid dynamics, fail to perform acceptably within the reformulated problem. The important qualities of this more discriminating test include the skewing of the fast boundary current flow relative to the underlying grid axes and the high shear in that boundary current.