We propose to discuss the relevance of the irrotationality assumption commonly made to obtain reduced water waves models (Shallow Water/Saint-Venant, Korteweg-de Vries, Green-Naghdi, etc.). To do so, we investigate the asymptotic behaviour of two boundary layers associated with oceanic flows: one appearing in the vicinity of the free surface and the other lying near the bottom boundary. This is achieved numerically approximating the solution to the Navier-Stokes equations using the finite-element method on a moving mesh.