A numerical model of wind-driven surface flow in the Gulf of Mexico is used to examine physical controls on harmful algal bloom formation along the Texas coast. Karenia brevis, which blooms frequently in the Gulf of Mexico, has a relatively slow growth rate (doubling times of 2–3 days). Increases in K. brevis concentration cannot be explained simply in terms of growth. We hypothesize that the primary mechanism responsible for bloom formation in the western Gulf of Mexico is convergence due to downwelling at the coast. Convergence along the Texas coast caused by seasonal downwelling winds can concentrate the plankton up to 1000 times. This is surprising because the modeled cells do not grow; the simulated increase in concentration is due to physical processes alone. The numerical model qualitatively reproduces both the timing and magnitude of bloom initiation along the coast, but does not predict the details of the migration of the bloom along the coast after it has formed, or the destruction of the bloom. The result of this simulation is significant because it implies that K. brevis blooms may be caused primarily by physical processes and that cell division is not an important factor in bloom formation.