The effect of rotation on the natural modes of simple model seas

The effect of rotation on the modes of rectangular seas, closed or open at one extremity, is investigated with the help of the general solution of the equations of hydrodynamics in suitable coordinates. A simple formula is derived which provides an almost exact estimate of the change in the resonant frequency induced by rotation. Since square and circular seas are physically alike, it is shown that using cylindrical or rectangular coordinates leads to similar results, the periodicity of the mode being invariably lengthened by rotation. The influence of rotation is more marked in shallow or broad seas; narrow seas, if not too shallow, are left unaffected. Open seas are more sensitive to rotation than when they are closed, under the same prevailing conditions. Positive modes only are considered since negative modes, moving opposite the direction of rotation, are unlikely to occur in nature. Patterns of vertical displacements are calculated for a square basin when modified by bottom friction. The theoretical results are used to assess the sensitivity to rotation of the modes of some basins on the earth such as the Bay of Fundy, the Great Lakes etc.: such knowledge is essential for the study of resonance or of storm surges.