Ocean Tides. Part 1. Global Ocean Tidal Equations
NAVAL SURFACE WEAPONS CENTER DAHLGREN VA
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A detailed derivation of improved ocean tidal equations in continuous COTEs and discrete DOTEs forms is presented. These equations feature the Boussinesq linear eddy dissipation law with a novel eddy viscosity that depends on the lateral mesh area, i.e., on mesh size and ocean depth. Analogously, the linear law of bottom friction is used with a new bottom friction coefficient depending on the bottom mesh area. The primary astronomical tide-generating potential is modified by secondary effects due to the oceanic and terrestrial tides. The fully linearized equations are defined in a single-layer ocean basin of realistic bathymetry varying from 50 m to 7000 m. The DOTEs are set up on a 1 by 1 deg spherically graded grid system, using central finite differences in connection with Richardsons staggered computation scheme. Mixed single-step finite differences in time are introduced, which enhance decay, dispersion, and stability properties of the DOTEs and facilitate--in Part 2 of this paper--a unique hydrodynamical interpolation of empirical tide data. The purely hydrodynamical modeling is completed by imposing boundary conditions consisting of now-flow across and free-slip along the mathematical ocean shorelines. Shortcomings of the constructed preliminary M2 ocean tide charts are briefly discussed. Needed improvements of the model are left to Part 2.
- Physical and Dynamic Oceanography
- Numerical Mathematics