Friction decoupling and loss of rotational invariance in 2D flooding models

Friction decoupling, i.e. the computation of friction vector components making separate use of the corresponding velocity components, is common in staggered grid models of the SWE simplifications (Zero-Inertia and Local Inertia Approximation), due to the programming simplicity and to the consequent calculations speed-up. In the present paper, the effect of friction decoupling has been studied from the theoretical and numerical point of view. First, it has been found that friction vector decoupling causes the reduction of the computed friction force and the rotation of the friction force vector. Second, it has been demonstrated that decoupled-friction models lack rotational invariance, i.e. model results depend on the alignment of the reference framework. These theoretical results have been confirmed by employing numerical experiments on flat and smoothly variable bed. Since the speed-up obtained with decoupled-friction models is modest, the coupled-friction models, which are more general, should be preferred in every case.