### Utility to calculate and graph co-oscillation tides

**The numerical scheme for the utility to calculate and plot the amplitude and phase of a co-oscillation tide in a narrow gulf.**

The model is based on the linearised vertically integrated Equations of Motion and the continuity equation in the form derived in the theory page:

A co-oscillation tide is a standing wave generated by tidal movement at the open end of the basin or gulf. The two unknowns **ζ** and **q** can therefore be written as

where **ω**< is the frequency of a tidal constituent. Introducing these forms for the unknowns into the equations gives a set of coupled equations for **Z** and **Q**:

These equations can be solved numerically if the width **B** and the cross-sectional area **S** vary only slowly in x. The gulf or basin is divided into sections of length Δ**x**, and the equations are written in finite difference form:

The computation begins at the head of the gulf with Q_{0}= 0 and Z_{1} = 1, and Q and Z are evaluated at alternate sections.

The effect of bottom friction on the tidal wave can be incorporated through a linear damping term. If friction is assumed to be proportional to the bottom velocity, which is proportional to the transport **q**, the vertically integrated equations become

where **r** is a friction parameter; 1/**r** corresponds to the time over which the tidal amplitude would decrease to 1/e of its original value if the tidal forcing would be switched off. The finite difference equations are then

This utility is based on A. K. Easton (1978) A reappraisal of the tides in Spencer Gulf, South Australia. *Australian Journal of Marine and Freshwater Research* **29**, 467 - 477.

© 2000 M. Tomczak

Last updated 23 August 2000.