Tidal resonance of eigenmode oscillation in the early Earth's ocean and its acceleration effect on the Moon's orbital evolution

The Earth's ocean tide has affected the Moon's orbital evolution. Recent studies suggest that the ocean would cover almost the entire surface of the early Earth, possibly with larger seawater volume than the present day. It is also suggested that the tidal energy in the present deep ocean is mostly dissipated by internal gravity waves comprising the so-called internal tide. Taking this progress into account, we have made a model of the early ocean and analyzed the tidal response for various parameters of ocean depth and internal tide coefficients. Numerical calculations and semi-analytical eigenmode analyses indicate that tidal resonance of eigenmode oscillation occurs in the early ocean model, yielding a step-like rapid growth of the lunar orbit. If the ocean depth decreases, the outward motion of the Moon is continuously accelerated by the particular tidal response of eigenmode oscillation. These effects of eigenmode oscillations could significantly influence the early evolution of the Earth-Moon system.