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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.

Here the process of internal tide generation over idealized (sinusoidal) topography was investigated using numerical techniques, in which the barotropic-to-baroclinic energy conversion was discussed. The result shows that when the wavenumber of the sinusoidal topography, ktopo, is equal to the horizontal wavenumber of the m-th baroclinic mode km, the conversion from the barotropic tide to the m-th baroclinic mode is enhanced with the increase of topography length; When the wavenumber of the sinusoidal topography is not equal to horizontal wavenumbers of any baroclinic modes, ktopo≠km(m=1,2,...), conversion from the barotropic energy to baroclinic modes is decreased with the increase of topography length. Furthermore, it shows that in resonance case, the phase of the perturbation pressure gradually agrees with the phase of the truncated sinusoidal topography, and the conversion rate is always positive over the topography, thus the baroclinic mode which matches with the wavenumber of the sinusoidal topography persists in absorbing energy from the barotropic tide, and the conversion rate is increased.