The mechanism by which tracer is entrained into a spatially decaying gyre from an external source is examined, as well as the homogenization which subsequently occurs. A simple advective-diffusive numerical model is used whose streamlines consist of an elongated gyre situated beside a distinct boundary current, which inputs tracer into the domain. This is meant to represent the deep cyclonic recirculation of the Gulf Stream and adjacent deep western boundary current. A shear flow analysis shows that two parameters dictate the manner in which tracer penetrates across streamlines of the gyre: a peclet number and a parameter which measures the strength of the cross-stream shear. The large values of these parameters cause a plume of tracer to spiral inward toward the center of the gyre. At steady state the tracer which has accumulated in the gyre becomes homogenized. The size of this uniform area is related to the extent to which the spiral penetrated the gyre and decreases with increasing diffusivity, as several examples illustrate. ¿ American Geophysical Union 1988