Vertical discretization in tidal flow simulations

We propose an empirical law for vertical nodal placement in tidal simulations that depends on a single parameter p. The influence of dimensionless numbers on the optimal value of p is analysed through a series of numerical experiments for an individual vertical and a single value of p is found to be adequate for all cases. The proposed law can lead to gains in accuracy of over two orders of magnitude relative to a uniform grid and compares favourably with non-uniform grids previously used in the literature. In practical applications the most effective use of this law may require each vertical to have a different number of nodes. Criteria for the distribution of the total number of nodes among different verticals are also proposed, based on the concept of equalizing errors across the domain. The usefulness of the overall approach is demonstrated through a two-dimensional laterally averaged application to a synthetic estuary.