We model the propagation of turbulent gravity currents through an array of obstacles which exert a drag force on the flow proportional to the square of the flow speed. A new class of similarity solutions is constructed to describe the flows that develop from a source of strength q0tγ. An analytical solution exists for a finite release, γ = 0, while power series solutions are developed for sources with γ > 0. These are shown to provide an accurate approximation to the numerically calculated similarity solutions. The model is successfully tested against a series of new laboratory experiments which investigate the motion of a turbulent gravity current through a large flume containing an array of obstacles. The model is extended to account for the effects of a sloping boundary. Finally, a series of geophysical and environmental applications of the model are discussed.