Motivated by the remarkably large propagation distances observed in turbidity currents near the mouth of the Congo River in Africa, a new model is proposed for their dynamics. It assumes that the erosion of solid particles from the bed underneath the current increases the density of the current such that the vortex rotational rate increases over the case of no erosion. If the rate of increase of vortex rotation is sufficient, the entrainment rate of fluid above the current is inhibited. As a consequence, the turbidity current propagates much farther than would be expected without the dynamic effect of acceleration.