Vertical discretization criteria for barotropic tidal models

Abstract

Although three-dimensional (3D) simulations of tidal flows have become common over the past decade, their high computational cost remains a limiting factor in our ability to model large domains. This cost can be mitigated by appropriate criteria to optimize the vertical placement of the nodes. This paper summarizes and integrates our major results pertaining to the development of criteria for vertical nodal placement in 3D barotropic tidal models.

We first examine the vertical nodal placement within a single vertical. We propose an empirical law for vertical nodal placement that depends on a single parameter, p. the influence of the governing dimensionless number on the optimal value of p is then analized through 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 an order of magnitude relative to a uniform grid, and compares favorably with previously proposed non-uniform grids.

In a practicle 3D application, and for a fixed number f nodes per vertical, the accuracy of the solution is expected to vary horizontaly with the characteristics of the flow. For instance, the bottom boundary layer can occupy the whole water column, or be limited to a small fraction of this column. Since the number of nodes per vertical must remain constant in traditional sigma coordinate grids, we proposed a more flexible method, the localized sigma coordinates(LSC), that allows this number to vary. We take advantage of the added flexibility of the LSC by letting the number of nodes per vertical vary linearly with the amplitude of the depth-averaged velocity. With this linear variation, suggested by observations from the Tagus estuary (Portugal), the maximum and average velocity errors decrease by a factor of two relative to a sigma coordinate grid with the same total number of nodes.

Key words: Vertical discretization. Localized sigma coordinates. Tidal modeling