Long water waves and electromagnetic waves--An analogy

lt is shown that Maxwell's equations which describe the propagation of electromagnetic radiation are analogous to the kinematic relationships which govern the propagation of long water waves, if the latter equations are described in terms of a vector potential. The analogy between the two phenomena may be used to study, for example, seiching, or long wave resonance, in harbors by means of an equivalent microwave cavity. The plan geometry of the cavity would be geometrically similar to that of the harbor basin so that wave reflections were correctly reproduced, and the refraction caused by depth variations in the harbor would be modeled by varying the dielectric properties of the cavity interior. When supplied with an appropriate source of microwaves, the intensity of the electric field at a given point can be related to wave induced currents at a similar location in the harbor. Such information is an important factor in the siting of berthing and mooring facilties for shipping. It is also shown how the impedance concept can be used to study the transformation of long waves as they traverse a step change in water depth.