Generation of Internal Tides by Tide-Topography Resonance over Weak Topography: Analytical Calculation

Internal tides generated by the interaction of the barotropic tide with bottom topography are studied by using an analytical solution. Tide-topography resonance takes place when the wavenumber of the truncated sinusoidal topography is equal to that of one baroclinic mode. The minimum amplitude of the resonant mode increases from the center of the domain to both sides of the topography; while the maximum keeps the same. Amplitudes of the internal tides and mode conversion rate are analyzed as a function of the length and wavenumber of the topography. For non-resonant modes, the amplitudes are weak and vary periodically with the extending of the topography, and are exactly zero when the length of topography is integral times of the mode-1 wavelength. For resonant modes, the amplitudes increase with the length of the topography. For each internal tide mode, there is a response zone, where the amplitude for one mode is obviously larger than other baroclinic modes. The response zones for high modes are wider than those for low modes. Mode conversion rate is obviously high when the wavenumber of the topography is equal to that of the baroclinic modes; otherwise it is almost zero. Furthermore, mode conversion rate for small topography wavenumber is more than that for large topography wavenumber with the same number of the sinusoidal topography, and is less with the same topography length.