On the evolution of global ocean tides

Abstract: We apply Laplace's tidal theory to the evolution of lunar and solar tides on the geologic timescale of Earth's rotation and focus on the tidal resonance. We study the global tide in the mid-ocean far away from continents. On the short timescale, a linear relationship of tidal height and Earth's rotation is obtained. On the long timescale, the tide is less than 1 metre at present but it was 5 metres in the past and will reach 8 metres in the future because of resonances of tidal wave and Earth's rotation. We conclude that the Earth-Moon orbital separation and the slowdown of Earth's rotation are faster than expected before.