Planetary waves on a hemisphere bounded by meridians of longitude

Abstract
This paper studies the free modes of oscillation in a rotating hemispherical basin bounded by a great-circle passing through the pole of rotation. The radius R of the globe, the rate of rotation iQ, the depth of fluid h and the acceleration of gravity g are assumed to be such that and R£l[fgh) <4 1. The waves can then be treated as non-divergent. The problem is solved by two independent methods, and the results are compared with each other and with the /?-plane approximation. It is found that the eight lowest modes of oscillation correspond quite well to simple modes in the /?-plane, the approximate periods being within 20 %. Higher modes show no clear correspondence. It is suggested that the peak at 0*5 c/d in the spectrum of sea level at Honolulu may correspond to the lowest mode of oscillation in the Pacific Ocean.

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