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On a class of differential equations which model tide-well systems

Published online by Cambridge University Press:  17 April 2009

B. J. Noye
B. J. Noye
Affiliation:
University of Adelaide, Adelaide, South Australia.
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Abstract

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For three possible types of tide-well systems the non-dimensional head response, Y(τ), to a sinusoidal fluctuation of the sea-level is given by the differential equation Estimates of the non-dimensional well response Z(τ) = sinτ - Y(τ) are found by considering the steady state solutions of the above equation. With n = 2 the equation is linear and an exact solution can be found; for n ≠ 2 the equation is non-linear and several methods which give approximate solutions are described. The methods used can be extended to cover other values of n; for example, with n = 4 the equation corresponds to one governing oscillations near resonance in open pipes.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 3 , December 1970 , pp. 391 - 411
Copyright
Copyright © Australian Mathematical Society 1970

References

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