The Extended Taylor Method with Application to the Study of M2 Tidal Waves in the Taiwan Strait

Abstract

Large semidiurnal lunar (M2) amplitudes are present in the Taiwan Strait. In this paper, an analytical model for the M2 tide in the Taiwan Strait is provided using an extension of the Taylor technique. The Taylor problem is a classical tidal dynamic problem. In this study, the classical Taylor method is extended such that the Coriolis force and bottom friction are kept in the governing equations. The Taiwan Strait is idealised as a rectangular basin with a uniform depth. As open boundary conditions, the tides at the northern and southern openings are observed. The resulting analytical solution, which includes a stronger southward propagating Kelvin wave, a weaker northward propagating Kelvin wave, and two families of Poincaré modes trapped at the northern and southern entrances corresponds well with the data in the strait. The observed tidal pattern can be essentially represented by the superposition of two Kelvin waves, which includes an anti-nodal band in the central strait and the anti-nodal band's cross-strait asymmetry (larger amplitudes in the west and smaller in the east). The inclusion of Poincaré modes enhances the model outcome by better reproducing the cross-strait asymmetry. Three experiments are carried out to investigate the mechanism of the northward propagating wave in the Taiwan Strait, including the deep basin south of the strait. The findings indicate that the abruptly deepened topography south of the strait reflects the southward incident wave to form a northward wave, though the reflected wave is slightly weaker than the northward wave derived from the aforementioned analytical solution, in which the southern open boundary condition is specified through observations. One of these experiments further indicates that forcing at the Luzon Strait strengthens the northward M2 Kelvin wave in the Taiwan Strait to a certain degree.