## Amphidromic Point North

Although the behaviour of tides is very complex, the underlying cause of their motion has been understood since Newton (1647-1727) accounted for tides as due to the gravitational attraction of the moon and the sun upon the oceans. A brief description is given here but fuller explanations can be found in the Admiralty Manual of Tides (Doodson and Warburg, 1941, reprinted 1973). Other useful and practical material on tides and tidal streams can be found in the RYA Manual of Navigation (RYA, 1981). Most general texts on oceanography will also carry explanations and references concerning tides.

Considering the lunar effect alone, the tide-generating force is the resultant of the centrifugal force due to the revolution of the earth-moon system acting in one direction, and the moon's gravitational pull on the water acting in another. The centrifugal force on any small mass of water is the same at any point on the earth, and is equal to the moon's pull on an equal small mass at the earth's centre of gravity. Gravitational force varies inversely with the square of the distance at which it acts, and is therefore greater than the centrifugal force on the side of the earth facing the moon, and less than the centrifugal force on the side away from the moon. The horizontal components of the tide-generating forces therefore tend to move the water towards two points, one immediately below the moon and one in the same line on the opposite side of the earth (Figure 8.1). If the earth were

Earth N

Earth N

F3, moon's attraction at Q =

F3, moon's attraction at Q =

Figure 8.1 Tide-generating forces at P and Q are F4 and F5, the resultants of F^ F2 and F^ F3; M = mass of moon, m = point mass of water at P or Q; G = gravitational constant; E = earth's centre of gravity; L = moon's centre of gravity; x = distance PL; y = distance EL, z = distance QL.

covered with water, this would distort the water layer to produce two tidal bulges at A and B, where the tide would be high. Low tide would be at positions half-way between A and B, such as C and D, where the moon would be on the horizon. During the earth's rotation the tidal bulges would remain stationary relative to the moon, and at any point on the earth's surface there would be a diurnal cycle of alternate high tide, low tide, high tide and low tide within the period of the lunar day, i.e. 24 h 50 min.

Tidal bulges of such simple form cannot occur because the land surface divides the oceans into a number of more or less separate bodies of water. Nevertheless, in most parts of the sea there are tidal movements of this semi-diurnal pattern corresponding closely with the lunar period. The lunar effect on the tide varies slightly from day to day with changes in the declination of the moon and its position in its elliptical orbit.

The sun's effect on the tides is less than the moon's because of its greater distance from the earth, but is sufficient to exert an appreciable modifying influence. When the moon is new or full, the pull of the sun on the water is in nearly the same line as that of the moon. The combined pull of sun and moon then causes the specially high and low tides known as spring tides. At the moon's first and last quarters the sun pulls at right-angles to the moon, reducing the lunar effect. There is then less difference in the levels of high and low water, and these tides of reduced range are termed neap tides. The height of the tides therefore varies daily with the phases of the moon, spring and neap tides each recurring

Figure 8.2 Tidal movements around the British Isles. Continuous lines are co-tidal lines joining points where high water occurs at approximately the same time. The figures against these lines give the difference of time of high water from the standard port. The standard port for the North Sea is Tynemouth, Devonport for the English Channel and Holyhead for the Bristol Channel and Irish Sea. Co-tidal lines converge on amphidromic points (three in the North Sea). Degenerate amphidromic points lie inland of Bournemouth and Wexford. Pecked lines are co-range lines joining points of the same tidal range, and the figures against them give mean range in feet.

(Reproduced from BA chart no. 5058 with the sanction of the Controller, HM Stationery Office and of the Hydrographer of the Navy.)

Figure 8.2 Tidal movements around the British Isles. Continuous lines are co-tidal lines joining points where high water occurs at approximately the same time. The figures against these lines give the difference of time of high water from the standard port. The standard port for the North Sea is Tynemouth, Devonport for the English Channel and Holyhead for the Bristol Channel and Irish Sea. Co-tidal lines converge on amphidromic points (three in the North Sea). Degenerate amphidromic points lie inland of Bournemouth and Wexford. Pecked lines are co-range lines joining points of the same tidal range, and the figures against them give mean range in feet.

(Reproduced from BA chart no. 5058 with the sanction of the Controller, HM Stationery Office and of the Hydrographer of the Navy.)

twice in every 28-day lunar cycle. The solar effect on the tides also varies with the sun's declination, being greatest at the equinoxes. The spring tides then have their maximum range and the neaps their minimum.

Many of the complexities of tidal behaviour arise because the oceans do not completely cover the earth, but are broken up by land. The oceans comprise many interconnected bodies of water, each with a natural period of oscillation. The tide-generating forces apply a continually varying to-and-fro pull on the water, making two complete alternations of direction within each period of complete rotation of the earth relative to the moon. The effect is to set up various complex oscillations in different parts of the sea. The number, extent and motion of these oscillating tidal systems are not completely known because of difficulties of measurement in the open ocean. In some areas the oscillation resembles a standing wave, but within each system the oscillations are to some degree deflected by the earth's rotation. This generally causes the oscillation to take the form of a progressive wave swinging around a centre, anticlockwise in the northern hemisphere, clockwise in the southern. Where the wave motion makes a complete rotation within a tidal cycle, the oscillation is termed an amphidromic system centred on an amphidromic point (see Figure 8.2). The change of water level is minimal at the amphidromic point and increases towards the periphery of the system.

Throughout the oceans the tidal movements comprise a number of interacting oscillations, the position and extent of each system being determined by the dimensions and location of particular sea areas. The range of tidal movement depends on the natural oscillation period of each basin, being strongest where this is in rhythm with the period of the tide-generating force. Areas of little tidal movement, for example the Mediterranean, are out of phase with the tidal period.

The coastal waters of the British Isles are set in oscillation by the rise and fall of the Atlantic tides. In the North Sea the tidal movements comprise three amphidromic systems as shown in Figure 8.2. The displacement of the amphidromic points to the east is the consequence of frictional loss of energy by the tides as they move anticlockwise over a shallow bottom. In the English Channel and the Irish Sea the shallow water distortion of the amphidromic systems is so great that the amphidromic points appear to lie inland, north of Bournemouth and north-west of Wexford. These are termed degenerate amphidromic systems (Doodson and Warburg, 1941).

Along the shore the extent of tidal movement is determined partly by the shape of the coastline. In tapering channels, where the tide enters a wide mouth and moves forwards between converging coastlines, the height of the tide is increased by the constriction of the water between opposite shores. An example is the Bristol Channel, where the tidal range sometimes exceeds 12 m at Chepstow. The average range of tides around the British Isles is about 4 m.

Tidal movements throughout each complete tidal cycle involve approximately equal ebbing and flowing of water as the tidal currents reverse their direction. Nevertheless there is usually some net transport of water in a particular direction. This resultant flow is termed a residual current.

Wind and atmospheric pressure have some influence on sea level, and can produce unexpected tidal anomalies. Of special importance are storm surges which occur when strong on-shore winds pile up the water along the coast and cause the tide to rise to abnormal heights. A striking instance occurred in 1953 along the east coast of England, when a great storm surge in the North Sea during the night of 31 January resulted in remarkably high tides, up to 3 m above predicted levels, overwhelming the coastal defences in many areas and causing widespread devastation and flooding.