Tidal Reaches

Tidal reaches of channels generally have a very low bed slope, and the rules of thumb may indicate values of Dx and Dt too large for adequate resolution of the tidal wave. In this case the following methodology should be applied to determine Dx and Dt.

Distance Step (Dx)

Consider for example, a tidal wave propagating up an estuary 3 metres deep. The celerity of the wave will be approximately:

Given a tidal period of 12 hours, the wave will travel in this time a distance of:

A satisfactory resolution would be about 100 points/wave length and this requires sections not further apart than:

If there was a strong 6-hour component in the tide, this distance should be halved.

Practical consideration such as rapid changes in channel section, or detailed requirements for flood levels, may reduce the spacing of sections to as little as 50m at critical sections. The distance step may be varied between sections to suit the data and purposes of the study.

Timestep (Dt)

The relationship between the time and distance steps can have an effect on the stability and accuracy of the solution. A widely used parameter in numerical modelling is the Courant Number:

In so-called explicit computational schemes this is limited to a maximum value of 1.0 which tends to result in very short timesteps, but in the implicit scheme used by Flood Modeller it can be larger.

Thus, for computational economy, CR is preferred large - say up to 5 or 10. From the previous section:

In this example 35 minutes might be too coarse to secure adequate representation of the tidal curve, for which 10 minutes may be more appropriate.