A recently suggested relaxation mechanism which is expected to be dominant in fast flows of polymer melts is combined here with the tube model of Doi and Edwards, and the corresponding constitutive equation is derived. The mechanism consists of the renewal of topology by convective displacement of entanglements. Detailed predictions for the flow curve in steady shear are obtained in order to test the agreement with the Cox-Merz rule. With respect to the basic tube model, significant progress is achieved.