On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

• We propose a modified general definition for bedload transport.
• It takes into account the thickness of the sediment layer.
• It coincides with a classical bedload transport formula in the case of uniform flows.
• Mathematical properties (hyperbolicity) are preserved but eigenvalues can differ.
• Numerical simulations show a more realistic behavior in the case of an advancing dune.

In this paper we study Exner system and introduce a modified general definition for bedload transport flux. The new formulation has the advantage of taking into account the thickness of the sediment layer which avoids mass conservation problems in certain situations. Moreover, it reduces to a classical solid transport discharge formula in the case of quasi-uniform regime. We also present several numerical tests where we compare the proposed sediment transport formula with the classical formulation and we show the behavior of the new model in different configurations.