The spin‐up from rest to a state of solid‐body rotation in a tank with one or more stepwise changes in depth is studied experimentally. Since flow across the steps is counteracted by the rotation acquired by the fluid in the course of the spin‐up process, eventually the flow is forced into a cellular pattern determined by the position of the steps. However, if the initial flow field has little resemblance with the quasisteady pattern imposed by the topography, most of the energy of the flow may be dissipated before the organization into the preferred pattern is complete. ©1996 American Institute of Physics.