Open AccessThe tidal oscillations in an elliptic basin of variable depth
Publication year - 1930
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1930.0197
Subject(s) - simple (philosophy) , bessel function , mathematics , variable (mathematics) , elliptic function , algebraic number , function (biology) , mathematical analysis , oscillation (cell signaling) , transcendental function , cylinder , transcendental equation , structural basin , transcendental number , geometry , numerical analysis , geology , paleontology , philosophy , genetics , epistemology , evolutionary biology , biology
The problem of the "long" waves in a circular basin of uniform depth involves in its solution a transcendental function–the Bessel function, and the determination of the free periods requires a knowledge of the zeros of this function or an allied function. On the other hand, when the basin, still circular, has a certain variable depth, it was shown by Lamb that the solution is expressed in terms of simple algebraic polynomials and the free periods of oscillation are expressed by an extremely simple formula. In similar fashion, the solution of the problem of the "long" waves in an elliptic basin of uniform depth involves the use of elliptic cylinder functions, and the free periods are only obtained as the result of lengthy numerical approximations.