On Tidal Resonance in the Global Ocean and the Back-Effect of Coastal Tides upon Open-Ocean Tides

The resonance of semi-diurnal tidal elevations is investigated with a forward numerical forced damped global tide model and an analytical model of forced-damped tides in a deep ocean basin coupled to a shelf. The analytical model contains the classical half-wavelength and quarter-wavelength resonances in the deep ocean and shelf, respectively, as well as a forcing-scale dependence which depends on the ratio of the phase speed of open-ocean gravity waves to that of the astronomical forcing. In the analytical model, when the deep ocean and shelf resonate separately at the same frequency, the resonance in the coupled system shifts to frequencies slightly higher and lower than the original frequency, such that a 'double bump' is seen in plots of elevation amplitude versus frequency. The addition of a shelf to a resonant open ocean tends to reduce open-ocean tides, especially when the shelf is also near resonance. The magnitude of this 'back-effect' is controlled by shelf friction. A weakly damped resonant shelf has a larger back-effect on the open- ocean tide than does a strongly damped shelf. Numerical simulations largely bear out the analytical model predictions, at least qualitatively. Idealized simulations show that continents enhance tides by enabling the half-wavelength resonance. Simulations with realistic geometry and topography but varying longitudinal structure in the astronomical forcing display an influence of the forcing scale on tidal amplitudes somewhat similar to that seen in the analytical model. A frequency sweep in the semi-diurnal band in experiments with realistic geometry and topography reveals weakly resonant peaks in the amplitudes of several shelf regions and in the globally averaged open- ocean amplitudes. Finally, the back-effect of the shelf upon the open ocean is seen in simulations in which locations of resonant coastal tides are blocked out and open-ocean tidal elevations are significantly altered (increased, generally) as a result.