Vicki Billings began by looking at tidal theory, went on to investigate the Coriolis effect and finally put the two together to explain the existence and formation of amphidromic systems.
In the UK we are generally accustomed to semi-diurnal tides: 2 high and 2 low tides each day, and a fortnightly cycle of spring to neap tides. High tide occurs about 50 mins later each day because as the earth rotates, the moon moves on in its orbit around the earth. It takes the moon a month to orbit the earth during which time there are 2 spring/neap tidal cycles. When the earth, moon and sun are aligned they are said to be in syzygy, and spring tides (large tidal range) result. When the moon is in quadrature, neap tides (small tidal range) occur. When syzygy occurs, alignment may be earth-moon-sun when the moon is in conjunction, or moon-earth-sun when the moon is in opposition. Either way, there are 2 tidal bulges because the centre of mass of the earth-moon system is within the earth’s sphere and there are 2 tide producing forces: gravitational pull of the moon and centrifugal force of rotation of the earth-moon system. Any point on the earth’s surface will be subjected to both to varying degrees depending on proximity to the moon.
The moon’s orbit is elliptical and eccentric. When the moon is closest to the earth it is at perigee, and when it is furthest away it is at apogee. The tide producing force of the moon varies by 40% between perigee and apogee. Another variable occurs because the plane of the moon’s orbit is at an angle of 28ᵒ to the equatorial plane, so over the course of a month, the moon tracks across the sky through an angle of 56ᵒ. When the moon is over the equator, tides are said to be ‘equatorial’ and when the moon is at maximum declination tides are called ‘tropic’ tides and there may be inequalities in the two high tides during the day. The moon’s orbit gradually precesses and it takes about 18 years for it to complete a cycle.
The sun’s tide-producing force is 46% of that of the moon, so it has a significant effect on the tides. The spring/neap cycle results from the combined forces of the sun and moon. The tilt of the earth’s axis results in the sun being directly over the equator at the equinoxes in March and September and high spring tides can be expected at these times of year.
Tides are predicted using the harmonic method. The main semi-diurnal partial tides are M₂ (for the moon) and S₂ (for the sun). There are also diurnal partial tides, in fact 9 main components are used in tidal prediction, however about 390 have been identified all together. Tides can be accurately predicted into the future and looking back into the past.
This affects fluids moving on the surface of the earth: oceans and atmosphere. It arises because, as the earth rotates, the maximum speed of rotation is at the equator, decreasing with increasing latitude to N and S. Momentum is linear at the equator, whereas angular momentum increases with latitude due to the curvature of the earth, with the result that fluids in motion in the N hemisphere are deflected to the right, and in the S hemisphere they are deflected to the left. This creates anticlockwise circulation in the oceans of the N hemisphere and clockwise circulation in the S. This can be seen in the major gyres that circulate in the N and S Atlantic.
These are created by the influence of Coriolis effect on the tides as they approach a coastline. Taking a hypothetical semi-circular bay, as the tidal wave approaches the bay it becomes deflected to the right in the N hemisphere and proceeds to circulate in a clockwise direction around the bay for the duration of the 12 hour tidal cycle. At the centre of this system, the amphidromic point, there is no tide and it acts like a hub around which the tide circulates. With increasing distance from the amphidromic point, the tidal range increases. Thus there are concentric co-range lines around which the tides are of the same height, and co-tide lines like spokes on a wheel along which high tide occurs at the same time. The North Sea is a large bay and as the tidal wave approaches from the N, it is deflected to the right, causing clockwise circulation of the tides. In fact there are 3 amphidromic systems in the N Sea. The English Channel is a special case. It is not wide enough for a full amphidromic system to develop, so there is a ‘virtual’ amphidromic point somewhere in Hampshire! Co-tide lines fan out across the Channel and co-range lines indicate tides of about 2m along the S coast, increasing to 8m or more in the Channel Islands. Double tides along the S coast are caused by harmonics of M₂ so that at Southampton there are double high tides, at Kimmeridge there are double low tides, and somewhere in between there are 4 high and 4 low tides each day!
The major amphidromic systems are based on tidal component M₂, but each of the tidal components has its own amphidromic systems. Tides are classified using the ratio of the 2 main diurnal components to the 2 main semi-diurnal components. At locations which happen to be close to the centres of semi-diurnal amphidromic systems, diurnal components take precedence and there may only be one high and one low tide each day.