ANALYTICAL SOLUTION OF NON-HOMOGENEOUS WAVE EQUATION

Models for shallow water wave processes are routinely applied in coastal, estuarine and river engineering practice, to problems such as flood waves, tidal circulation, tsunami penetration, and storm tides. Evaluation and confirmation of application codes can be facilitated by analytical solutions that may represent this wide range of physical problems, without significantly compromising the contributing flow processes. The appropriate linearized shallow water wave equations are defined, together with quite general initial and boundary conditions that will represent the expected variety of shallow water wave problems. A completely general analytical solution for both water surface elevation and flow is established, in a manner suitable for the evaluation of shallow water wave codes. The contribution of both free and forced modes is identified, together with the role of friction.