The tides in Oceans on a Rotating Globe.—Part IV

Abstract

In previous papers of this series approximate solutions of the tidal equations have been given which represent the semi-diurnal tide in an ocean bounded by two meridians of longitude 60° apart. The present investigation is to find the nature and periods of the free oscillations in such an ocean, particularly of that mode which has a period near to the period of the semi-diurnal tide. The principal conclusion is that in an ocean of uniform depth 12,880 feet and bounded by two meridians of longitude 60° apart there is a normal mode of vibration having a period of 12 hours 33 minutes of mean solar time. In the course of the work it is shown that the normal frequencies appear in groups of three: one giving a wave travelling in a positive direction, the second giving a wave travelling in a negative direction, and both of them remaining finite as the speed of rotation diminishes. The third is an oscillation of “the second class,” corresponding to a wave travelling in the positive direction and reducing to a steady motion as the speed of rotation diminishes.