On the differential equation for the conventional tide-well system

1 October 1972

journal article
research article
Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society

Vol. 7 (2) , 251-267
https://doi.org/10.1017/s0004972700045007

Abstract

This paper discusses solutions to the differential equation which governs the height of the non-dimensional water level inside a conventional tide-well when the corresponding height of the sea-level outside is X(τ). A perturbation solution correct to O(β⁴), for small β, for the particular case X = sinτ described previously has been extended to O(β⁶) for any function X(τ) differentiable at least three times. Two special cases, where X(τ) is a single sinusoid and the sum of two sinusoids, are treated in detail.

Keywords

This publication has 3 references indexed in Scilit:

On the differential equations for tide-well systems
Bulletin of the Australian Mathematical Society, 1971
On a class of differential equations which model tide-well systems
Bulletin of the Australian Mathematical Society, 1970
An Intensive Analysis of Shallow Water Tides
Geophysical Journal International, 1968