SUMMARYThis paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentumconserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models.

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A spherical coordinate version of the unstructured grid 3‐D FVCOM (finite volume coastal ocean model) has been applied to the Arctic Ocean to simulate tides with a horizontal resolution ranging from 1 km in the near‐coastal areas to 15 km in the deep ocean. By accurately resolving the irregular coastlines and bathymetry in the Arctic Ocean coastal regions, this model reproduces the diurnal (K1 and O1) and semidiurnal (M2 and S2) tidal wave dynamics and captures the complex tidal structure along the coast, particularly in the narrow straits of the Canadian Archipelago. The simulated tidal parameters (harmonic constituents of sea surface elevation and currents) agree well with the available observational data. High‐resolution meshes over the continental shelf and slope capture the detailed spatial structure of topographic trapped shelf waves, which are quite energetic along the Greenland, Siberia, and Spitsbergen continental slope and shelf break areas. Water stratification influences the vertical distribution of tidal currents but not the water transport and thus tidal elevation. The comparison with previous finite difference models suggests that horizontal resolution and geometric fitting are two prerequisites to simulate realistically the tidal energy flux in the Arctic Ocean, particularly in the Canadian Archipelago.

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Eight major tidal constituents in the Sea of Okhotsk have been investigated using a numerical solution of tidal equations on a 5Ј space grid. The tides are dominated by the diurnal constituents. Diurnal tidal currents are enhanced in Shelikhov Bay and Penzhinskaya Guba, at Kashevarov Bank, in proximity to the Kuril Islands and at a few smaller locations. The major energy sink for diurnal tides (over 60% of the total energy) is Shelikhov Bay and Penzhinskaya Guba. The major portion of semidiurnal tide energy is dissipated in the northwestern region of the Sea of Okhotsk and in Shelikhov Bay and Penzhinskaya Guba. Nonlinear interactions of diurnal currents are investigated through K 1 and O 1 constituent behavior over Kashevarov Bank. These interactions generate residual circulation of the order of 10 cm s Ϫ1 , major oscillations at semidiurnal and fortnightly periods (13.66 days), and higher harmonics of basic tidal periods. The M 2 tidal current, caused by the nonlinear interaction of the diurnal constituents over Kashevarov Bank, constitutes approximately a half of the total M 2 tide current there. The fortnightly current, through nonlinear interactions, also influences basic diurnal tidal currents by inducing fortnightly variations in the amplitude of these currents.