The circulation of a homogeneous fluid over an idealized, axisymmetric feature is examined. The motion is forced by a large‐scale background flow that is periodic in time. The focus of the study is the effect of topographic Rossby wave resonance on the mean flow and the movement of passively advected particles. The approach is based on integration of a nonlinear, primitive equation model. Mean flows at fixed locations and particle trajectories are then calculated from the time‐varying model solutions. In agreement with earlier studies the time‐mean flow around the bump (v ) is shown to be approximately proportional to q2 where q is the amplitude of the time‐varying, cross‐isobath flow. Sensitivity studies show that q2 and hence (v ) can decrease as the amplitude of the oscillating background flow increases. This is explained in physical terms by a nonlinear dependence of the effective resonant frequency of the system on the amplitude of the oscillating background flow. To describe the motion of particles passively advected by the flow we present maps showing net particle displacement (?) over one cycle of the background flow. As with (v ) and q it is not possible to parametrize simply the net displacements in terms of the strength and frequency of the background flow: allowance has to be made for the effective resonant frequency of the system and its dependence on the strength of the background flow. An effective diffusivity Ke is estimated from the loss rate of particles from the top of the bump. For small net displacements Ke scales approximately with ?2ω where the overbar denotes an average over the top of the bump and ω is the frequency of the background oscillation. However, even this limited parametrization depends implicitly on the effective resonant frequency of the system through its influence on the net drift of particles.