In order to understand better the dynamics of hot spots such as Hawaii, we present a three-dimensional numerical model for the interaction of a thermal plume with a moving lithosphere. The model domain is a rectangular box filled with fluid whose viscosity depends upon temperature and pressure. The lithosphere is represented by a layer of cold, highly viscous fluid moving with an imposed horizontal velocity U in the x direction, and a thermal plume is generated by a circular temperature anomaly on the bottom of the box. The steady flow is determined numerically using a hybrid spectral/finite difference technique. The flow is characterized by a ''stagnation streamline'' of width y~x1/5 that represents the edge of the spreading plume material. We illustrate the detailed behavior of the model using the example of the Hawaiian plume. Our best fitting Hawaiian model is obtained by adjusting the plume buoyancy flux B until the predicted topography anomaly matches the observed Hawaiian swell topography; we find B=4100 kg s-1, which implies a plume radius of 90 km for an assumed plume/mantle temperatures contrast of 300¿C.

The predicted topography is supported primarily by density anomalies beneath the lithosphere and cannot be explained by lithospheric erosion. We therefore conclude that the classical ''lithospheric reheating'' model is unable to account for hotspot swells. The horizontal flux of buoyancy assoicated with the swell exceeds B by up to 80%, suggesting that current estimates of B for mantle plumes are too high. Empirically derived scaling laws for the width of the stagnation streamline and for topography anomaly exhibit power law dependencies on B and U that agree well with those predicted by the ''refracted plume'' model of Olson (1990). The principal weakness of the model is that the predicted geoid/topography ratio of 0.010 for the Hawaiian swell is about twice the observed value of 0.004--0.006.