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Happily spending my holidays in the Fiji Islands, I noticed a couple of days ago that when the moon was very high in the sky (my shadow was maybe 0.5-1m long) the tide was low. That really puzzled me. How does this happen?

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  • $\begingroup$ I used to think it was when the moon was on the beachside horizon that it would be highest, "pulling the water" that way. But I believe it's much more complex than just where the moon is, with interactions between different areas. I hope someone will chime in with a much more detailed explanation :-) $\endgroup$ – JeopardyTempest Nov 1 '17 at 18:08
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    $\begingroup$ Related: Definitions of tidal harmonic constituents…? $\endgroup$ – David Hammen Nov 2 '17 at 13:56
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This is based on the overly-simplified model of tides being the result of tidal bulges. As I explained in my answer to a related question on the physics.SE sister site, those tidal bulges do not and cannot exist.

Instead, the tides are dynamic responses to the tidal forcing functions from the Moon and the Sun, with the orbits of the three bodies about one another, the Earth's rotation rate, and the geometry of the oceanic basins all playing roles in the dynamic response. For any point on the surface of the Earth's oceans, the tides can be described in terms of a composition of frequency responses to those cyclic forcing functions. See the related question Definitions of tidal harmonic constituents…? for details.

At many places, Fiji included, the key component of the tides is the $M2$ tidal constituent, with a period of 12.42 hours. This is the principal response to the tides induced by the Moon. If Newton's equilibrium (tidal bulge) theory of tides was correct, every oceanic place on the Earth's surface would see high tide when the Moon is at zenith and nadir, and low tides when the Moon is at the horizon. Except for a few places, this is not what is observed. In Fiji, the situation is nearly reversed, as depicted by the tide chart below for Nadi on the west coast of Viti Levu, where high tides are more or less in sync with moonrise and moonset.

Graph of predicted tide heights at Nadi Waters, Viti Levu, Fiji Islands from 1 Nov to 9 Nov, 2017
Source: https://www.tide-forecast.com/locations/Nandi-Waters-Viti-Levu-Fiji-Islands/tides/latest, accessed 2 November, 2017.

Laplace's dynamic theory of the tides says that the oceans' response to each of the tidal constituents comprises a set of amphidromic systems. Each such system is centered about an amphidromic point, a place with a null response to the component in question. A wave whose amplitude increases with distance from the the amphidromic point rotates about the amphidromic point at the constituent frequency. The $M2$ tidal response is depicted below. The $M2$ amphidromic points are at the centers of the dark blue areas. The white lines emanating from the amphidromic points are cotidal lines, curves along which high tide occurs at the same time. The different colors indicate height, which again increase with distance from the governing amphidromic point.

The response to the tidal forcing function comprise a number of different frequencies. The component with the largest response, by more than a factor of two, is the semidiurnal lunar tide, designated as "M2" by George Darwin. This image uses colors to depict the amplitude of the M2 tidal response around the globe. Key features are the amphidromic points, places where the M2 component is zero, the cotidal lines that emanate from these amphidromic points, and the directions in which these cotidal lines rotate about the amphidromic points.
Source: http://en.wikipedia.org/wiki/File:M2_tidal_constituent.jpg.

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  • $\begingroup$ Very clear and thorough explanation, thank you $\endgroup$ – Nodjo Nov 2 '17 at 21:22

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