A theory of depth averaging in models for coastal dynamics

The present work proposes a general analysis of those models for gravity wave propagation that partially or totally rely on an average procedure over the water depth. The aim is the identification of the intrinsic physical quantities that characterize the wave dynamics, going beyond the usual definition of depth-averaged velocity. In particular, the proposed approach is based on the decomposition of the depth-averaged fields in their gradient- and divergence-free components. This naturally leads to the definition of a generalized velocity field that includes part of the dispersive contributions of the wave dynamics, and to the detection of the intrinsic boundary conditions along the free surface and the seabed. The analysis also proves the existence of generalized velocity potentials that under particular circumstances can include rotational contributions.