On using Boussinesq-type equations near the shoreline: a note of caution

We briefly analyze some characteristics of the behavior in very shallow waters i.e. near the shoreline of high-order (dispersive-nonlinear) Boussinesq-type equations. By using the Carrier and Greenspan (1958) solution as test flow conditions we illustrate the behavior of both purely dispersive and dispersive-nonlinear contributions near the shoreline. It is also shown that Boussinesq-type equations can be more usefully handled in the swash zone if written in terms of the total water depth.