#### Date

January 1996

#### Document Type

Dissertation

#### Degree Name

Ph.D.

#### Department

Dept. of Environmental Science and Engineering

#### Institution

Oregon Graduate Institute of Science & Technology

#### 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 horizontally, and can therefore be considered a natural extension to the use of unstructured grids in the horizontal. To take advantage 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 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 dimensions 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 estuary's 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 asymmetry between ebbing and flooding promotes exchanges between marine and estuarine waters, while the 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.

#### Identifier

doi:10.6083/M4736NVC

#### Recommended Citation

Fortunato, AndrÃ© Bustorff, "Three-dimensional modeling of coastal flows using unstructured grids" (1996). *Scholar Archive*. 300.

http://digitalcommons.ohsu.edu/etd/300