Reef parameterisation schemes for long wave models

A variety of analytical models is used to investigate the effects on tidal propagation of a barrier reef system. These models specify reef geometry by two parameters. They can accommodate cases where water flows over reefs, as well as through inter-reef gaps, and also incorporate quadratic bottom friction. Although based on a one-dimensional approach, adaptations of a solution by Huthnance are used to account for the additional blockage effects associated with two-dimensional flow patterns near reef barriers. The present work adopts the philosophy that only a numerical approach can cope with the wide variations in reef geometry that are encountered in areas such as the Great Barrier Reef (GBR) region of Australia. Moreover, since typical model grids cannot resolve inter-reef gaps and other features with sufficient accuracy, a parameterised approach is needed to accommodate the conflicting demands of reef geometry and an economically feasible model resolution. The formulation of the analytical models is such that they can be applied immediately to standard numerical algorithms. Numerical experiments for flow in a channel, with a reef barrier across its centre, are used to test the parameterisation schemes. Comparison of the results for parameterised reefs with those obtained using extremely fine grids, shows convincing evidence of the success of the schemes. A separate method for automatically generating reef parameters has simplified the task of applying the methodology to real reefal systems. A tidal model of the Southern GBR, a region which exhibits unusual tidal behaviour, but which also has ample field data available for model testing, is used to demonstrate the accuracy that can be attained with the parameterised approach. Although tides are considered specifically in the present work, the formulation should be applicable with equal ease to the many other significant classes of low frequency motions in the GBR.