Mathematical modelling for the evolution of aeolian dunes formed by a mixture of sands: entrainment-deposition formulation
In this work we present a mathematical model of the evolution of aeolian sand dunes, in particular we consider the case of dunes formed by a mixture of sands with different characteristics. We first recall a basic model for the evolution of two dimensional sand dunes that has been proposed in the literature. Then, we propose a novel type of mathematical formulation for the evolution of sand dunes formed by a mixture of two (or more) sands, which expresses the temporal variation of sand surface elevation and concentration of each sand type in terms of the balance between entrainment and deposition rates of sand. We provide some simple but physically based constitutive relationship for the new variables and we present some numerical simulations that clearly demonstrate that our model can be protably adopted for the study of interesting physical problems such as sand tracking and dunes collision.