Numerical simulations of transportational cyclic steps

Abstract

A numerical model that couples water flow and sediment transport over a non-cohesive bed is developed to simulate the initiation and evolution of transportational cyclic steps. Transportational cyclic steps are periodic bedforms characterized by corresponding hydraulic jumps that form when a supercritical flow erodes and deposits bottom sediments on a steep bed. The flow transition at the hydraulic jump leads to bed erosion on the supercritical part and deposition on the subcritical part of the step, with consequent upstream migration while the form is preserved. The numerical scheme developed to study transportational cyclic steps utilizes an approximate Riemann solver to capture the exact location of the hydraulic jumps present in the domain. Simulations of step growth from small perturbations on an initially flat bed are carried out and partly answer the question of how transportational steps form. Results show that both an initial infinitesimal bottom perturbation and a random distribution of bottom elevations evolve in a series of steps migrating upstream. Moreover, numerical simulations clearly show that the final configuration strongly depends on initial conditions.