Three-dimensional modeling of coastal flows using unstructured grids

Abstract

Although three-dimensional (3D) modeling of coastal and estuarine flows is becoming common, several limitations remain related to our ability both to describe and to numerically simulate the correct physics. Two key limitations concern vertical resolution: the lack of flexibility of current methods for vertical discretization prevents the optimal use of computational resources, and guidelines for vertical nodal placement are not available.

The major contribution of this thesis is the development, analysis and test of an approach that allows for an unprecedented flexibility in the vertical refinement of the domain. This approach, which we refer to as localized sigma coordinates (LSC), is the first to allow the number of nodes per vertical to vary horizontaly, and can therefore be considered a natural extension to the use of unstructured grids in the horizontal.

To take advantege of the LSC, we perform the first systematic study for the vertical discretization in barotropic tidal flow simulations. The resulting optimal grid can reduce the errors relative to a uniform grid by over an order of magnitude and compares favorably with non-uniform grids previously proposed. A criterion to guide the horizontal distribution of the total number of nodes is proposed and discussed in the context of simple one- and two-dimensional models, and is then extended to three dimensions. Accounting for advection in three dimenions forces modifications to the criterion, but the overall concept proved to be useful: using a variable number of nodes per vertical reduces the maximum velocity errors by a factor of two.

As part of our analysis of the LSC, we investigate the evaluation of the horizontal gradients in sigma-coordinate shallow water models. We show that horizontal gradients should be computed in sigma rather than z-coordinates, and that the so-called hydrostatic inconsistency typically associated with sigma coordinates does not correspond to a numerical inconsistency. The large errors associated with the evaluation of horizontal gradients can be by-passed through appropriate horizontal resolution, and a procedure to define this resolution is proposed based on results from a truncation error analysis.

An application to the Tagus estuary demonstrates the enhanced accuracy provided by the LSC, and provides new insights into the estuarys 3D barotropic circulation. Strong residual currents (depth-averaged eulerian residual velocities of up to 0.5 m/s) are generated by advective accelerations and have a major impact on the mixing characteristics at the mouth of the estuary. The assymetry between ebbing and flooding promotes exchanges between marine and estuarine waters, while he interaction between tidal and residual flows leads to strong chaotic stirring.

The good performance of the LSC in a complex application establishes this method as an attractive alternative to the traditional sigma- and z-coordinates.