Wetting and drying in coastal flows

A complete description is presented of the physics of the wetting and drying or long wave runup of free surface coastal flows. A careful analysis of the front kinematics recognises the front as a material surface for which exact descriptions are provided. The limiting calculus at the front leads to a similarly exact description of the characteristic path of the wetting and drying front. The utility of this complete specification of the front kinematics is demonstrated in a method of lines algorithm. Visually perfect agreement is shown with two nonlinear analytical solutions.