Tides: A Very Short Introduction by David George Bowers & Emyr Martyn Roberts

Author:David George Bowers & Emyr Martyn Roberts [Bowers, David George & Roberts, Emyr Martyn]
Language: eng
Format: epub
ISBN: 9780192561305
Google: KFS_DwAAQBAJ
Publisher: Oxford University Press
Published: 2019-11-28T00:00:00+00:00

The Gulf of Carpentaria, in northern Australia, is an example of a shallow sea which is close to quarter-wavelength resonance with the diurnal tide. The bay is about 500 kilometres wide and measures between 500 and 600 kilometres from its southern shore to where it joins the Arafura Sea and Torres Strait in the north. The mean depth of the bay is 60 metres and the speed of a progressive tide wave is 87 kilometres per hour. The length of the diurnal tide wave (with period twenty-four lunar hours) is 2,183 kilometres. One quarter of a wavelength is 546 kilometres and the amphidromic point of the diurnal tide is close to the mouth of the gulf. In contrast, the semi-diurnal tide (which has a wavelength half that of the diurnal tide) has an amphidrome located about 250 kilometres from the shore; there is no amplification of the semi-diurnal tide from the mouth to the head of the gulf.

A co-tidal chart of the diurnal tide in the Gulf of Carpentaria is shown in Figure 23(b). The high water travels around the bay in a clockwise direction about an amphidromic point located close to the mouth of the gulf. The tidal range is largest at the shore (particularly at the south-east corner) at points furthest from the amphidrome, and decreases to nothing at the amphidromic point. In the top left of this picture, the tide is behaving as a Kelvin wave. The high tide travels from west to east, and the tidal range is greatest on the northern shore (that is the left hand shore looking down the direction of wave travel).

Not all bays or gulfs exhibit an amphidromic system. First, the gulf needs to stretch, from the mouth to the head, a distance of at least one quarter of a tidal wavelength and, as we have seen, that can be a distance of several hundred kilometres. Only large bays will be big enough to contain an amphidrome. Second, the bay must be wide enough for Earth rotation to matter. In practice that means that the time taken for a tide wave to cross from one side of the bay to another must be a significant fraction of a tidal cycle. On a rotating Earth, a progressive wave will always be converted into a Kelvin wave, but the difference in water level from one side to the other will be small in a narrow channel.

The effect of friction and a poor reflection of the wave at the head of the bay will make the reflected wave smaller than the incoming wave. The two waves will no longer cancel along the centre line of the bay, and the amphidromic point moves to a place where the reflected wave is large enough to cancel the incoming wave. It moves to the left (in the northern hemisphere) and to the right (in the southern hemisphere) looking into the bay. In extreme cases, where the friction is very high, the reflected wave becomes too weak to cancel the incoming wave anywhere.

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