A two-dimensional vorticity model of internal tides generated on the continental shelf/slope

Abstract

A two-dimensional spectral-difference model (with vorticity and density equations) of internal tides is developed for studying the generation and propagation of internal tides generated at the continental shelf/slope. In general, internal tides propagate seaward in deep sea regions and shoreward on the shelf, and are dissipated rapidly. When the Vaisala frequency decreases vertically, waves may be mostly limited to the continental slope region. In deep sea region, motions may have either beam-like structure or modal structure, depending on the stratification strength and structure, whereas a modal structure may always exist on the shelf. Waves show strong bottom intensification on the slope when strong stratification exists on the bottom. The barotropic tidal advection may affect the temporal character of internal tides at the continental slope, shelf break and shelf regions, but may have little influence on the energy density and energy flux of internal tides. In the case of strong stratification, waveforms of internal tides on the continental slope, shelf break and shelf may be deformed by the barotropic tidal advection, and sometimes intermittency appears. Waves depend considerably on the relative slope δ=α/C (where α denotes topography slope andC is the characteristic slope) and the e-fold scaleb of the Vaisala frequency. As in Craig (1987a), the deep sea energy fluxF1 and on-shelf fluxF2 also vary exponentially, but our exponents are different from his in the subcritical case, and may have complicated dependence on δ in the supercritical case. For subcritical topography,F2 increases linearly withb butF1 remains nearly constant. For supercritical topography,F1 increases linearly withb andF2 varies complicatedly. For special values ofb, waves may have strong bottom intensification because of the self-closing of ray on the bottom of the slope.