The Dynamical Theory of the Tides in a Polar Basin

G. R. Goldsbrough
1915 Proceedings of the London Mathematical Society  
Int'roductory. THE problem here attacked is that of finding the tidal oscillations on a rotating globe in an ocean which is bounded by parallels of latitude. In this paper the case examined is that of a polar basin, so that only one boundary is to be considered. A similar analysis, however, can be applied to the double boundary problem-the zonal sea. In a further paper I intend to give the results of the latter case. The only complete solution of a tidal problem hitherto found is that of Hongh
more » ... d is that of Hongh * for the case of an ocean wholly covering a rotating globe. His results are in the form of series of spherical surfaceharmonics, and, in consequence, it is possible to include the effects of the self-attraction of the water particles. Poincare t and Love t have suggested the use of the method of Ritz for the determination of tides in restricted basins; and Poincare § has also mentioned the possible application of Fredholm'8 integral equation method to these problems. Previously Kelvin Ii had indicated a direct method of 따tacking the simpler problem of the tides in a zonal sea. Upon his method the following analysis is based. The form in which his results were left was such that it was almost impossible to make a numerical discussion of them; so that several alterations, suggested by Hough's work , have been made in the following paper. Since series of powers of cosines of the latitude are used, it is not possible to include the self-attraction. But the effects of the latter appear to be small, except in the vicinity of a coincidence of free and forced oscillations. The final results show that such an event cannot occur .
doi:10.1112/plms/s2_14.1.31 fatcat:5kzdcbsih5aubfbsmmywz7e2dq