Transportational cyclic steps created by flow over an erodible bed. Part 2. Theory and numerical simulation

Experiments on transportational cyclic steps were presented in the preceding companion paper. In the present paper a theoretical explanation of cyclic steps is delineated in terms of upstream-migrating steps of permanent form. The data of the companion paper are used to deduce relations for resistance and entrainment into suspension that apply in the absence of steps. These relations are then used in combination with a quasi-steady shallow-water formulation of the conservation of momentum, flow mass, mass of sediment in suspension and bed sediment in order to develop a complete formulation of steps. The theory is generally successful at explaining most aspects of transportational cyclic steps.