Semi‐diurnal tides in Cook Strait

Abstract

Abstract The phases and amplitudes of the M2 and S2 constituents of tidal elevation in Coiok Strait may be adequately described as an open mouth reflection of tidal waves advancing from the east and west coasts of New Zealand and reflecting near the latitudes of Titahi Bay and Cape Campbell (a distance of approximately 60 km). Other reflection conditions give amplitude and phase distributions different from those observed. Best fits to the observed phases and amplitudes for the M2 tide elevation arise from non‐rotational one‐dimensional solutions which allow for the bathymetry. If rotation is introduced in the form of Kelvin Wave solutions, the result is a two‐dimensional phase‐distribution pattern qualitatively similar to that observed, with the change in phase more rapid and the tidal amplitude smaller on the eastern than on the western side of Cook Strait. The solution for the S2 tide also fits closest to the observed tidal elevations for the non‐rotational one dimensional solution, but the introduction of rotation leads to a two‐dimensional phase‐distribution pattern qualitatively similar to that observed. The ratio of the amplitude of the wave (£) advancing from the northwest into Cook Strait to that (A) advancing from the southeast is substantially greater for the S2 (B/A = 11) than for the M2 (B/A = 2) tidal constituent and leads to the region of most rapid phase change for S2 being shifted further to the south than that for M2.