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# 2.4 Tides and tidal currents

A tide is the flow away (ebb) and flow back or return (flood) of something. The most obvious are those of the oceans and seas, in which there are regular high tides and low tides. The difference in heights is known as the tidal range. These tides are caused chiefly by the gravitational attraction forces of the Moon, and partly by those of the Sun, acting on the Earth. The gravitational pull of the Sun is overall much stronger but, as it is much further away, they are weaker on Earth than those of the relatively nearby Moon. The effects on the Earth are about 70% from the Moon and 30% from the Sun. Tides affect shipping – progress, mooring, loading and departures – and influence the design, build and maintenance of coastal and offshore infrastructure such as estuary bridges, harbour walls, drainage outlets, gas and oil rigs, etc. They also contain and cycle huge amounts of energy, some of which is diverted through turbines to generate useful power.

The tide is a lift and then release of huge bodies of water in the form of a tidal bulge on a regular basis as the Earth rotates beneath the gravitational pulls of the Moon and Sun. When near to a coast, the bulge turns into physical flows of water towards and away from the shoreline as the Earth rotates. When the effects of Moon and Sun occur in phase (together), the flows and heights increase the tidal ranges in what are called spring tides, as in the phrase ‘spring forth’ – nothing to do with the season. About six days later the relative positions of the Sun and Moon mean that they are pulling at right angles to one another and the result is a smaller tidal range called neap tides, from an Anglo-Saxon word meaning ‘without the power’. Figure 16 illustrates the effects of spring and neap tides.

Figure 16 Upper: Earth, Moon and Sun in line – spring tides; lower: Moon and Sun pulling at right angles – neap tides (note: figure not to scale and highly exaggerated)

In the upper part of Figure 16, the Moon is new but is in line with the Sun, and so produces spring tides on Earth. The same thing occurs when the Moon is in its second quarter about two weeks later on the opposite side of the Earth. It is then full but is still in line with the Sun and produces the next spring tides. Meanwhile, in between, the Moon in its first quarter as shown in the lower part of Figure 16 is pulling at right angles to the Sun’s pull, resulting in the lower-range neap tides. The same thing occurs when the moon is in its third quarter. Either way, as the Earth rotates once every 24 hours, it will pass through two tidal bulges; the tides are approximately twelve hours apart. The tidal range takes about a week to go from the largest spring tides to the smallest neap tides, then back again in the next week.

Tidal rise and fall can be predicted as tidal curves. A typical curve (for Hestan Island in the Solway, in October 2019) is shown in Figure 17. The blue peaks represent the twice daily rise and fall of the tides. The graph covers the week that it takes to change from neap to spring tides.

Figure 17 Hestan Island tidal curve

The Earth effectively rotates beneath the tidal bulges and influences the speeds of the tidal flood and ebb streams in an almost sinusoidal way. For many estuaries and other areas subject to high tidal ranges, the 50/90 rule is observed regarding tidal stream speeds, as illustrated in Table 5. From a slack water period (i.e. when the tide changes from ebb to flood and vice versa), the relative speeds of the tidal stream are approximately as in Table 5.

## Table 5 Relative speeds of tidal streams

Hour after slack water | Per cent of maximum speed
--- | ---
0 | 0%
1 | 50%
2 | 90%
3 | 100%
4 | 90%
5 | 50%
6 | 0%

Note that the highest speeds occur at mid-flow, in hours 3 and 4. Local features, however, can create anomalous variations that can catch out the unwary.

This is a useful overlying model as to the causes of ocean and sea tides, but, as might be expected, there are some other issues that affect both the overall and local patterns. Without going into too much detail, these can be summarised as follows:

- Astronomical effects: The gravitational pull of the Moon and Sun vary with the distance from these bodies to Earth; so therefore do the tidal effects they cause. These effects are global, but there are also more local effects depending on how far above or below the equator the Moon and Sun are in the sky at that particular location.
- Physical obstructions: The presence of land masses, coastlines, shallows, etc., in addition to physical obstruction can cause tidal flows to be reflected, interfered with and otherwise modified.
- Reflections and interference: The presence of land masses, coastlines, shallows, etc., can cause tidal flows to reflect and otherwise be modified so as to interfere with the incoming bulge. These can either amplify or detract from a local tidal range.

The tidal bulge in the open ocean is at most still less than a metre above stationary sea level, and the direct effect of the tidal forces on smaller seas and inland lakes is much smaller than this. Nevertheless, an ocean tidal bulge is a huge quantity of water when it encounters a shoreline (or, strictly speaking, when the rotating Earth shoreline encounters the bulge). The effects of the depth and shape of the sea bed, the orientation and shapes of the shoreline, etc., can create substantial changes in the local sea level. On the other hand, in some areas these features in conjunction with the Coriolis effect can create a tidal node region or system in which all effects cancel each other out such that there is no regular change in sea level. This is also known as an amphidromic point around which there may be strong currents in the amphidromic system but no net change in the sea level.

Figure 18 Sample of amphidromic points. There are 140 known such points

Figure 18 shows some of the 140 known amphidromic points distributed around the world’s oceans. By definition, the tidal range at amphidromic points is zero, but it increases with distance away from the point. Due to the Coriolis effect, lifting or incoming tides tend to circulate around amphidromic points, anticlockwise in the northern hemisphere and clockwise in the southern hemisphere. This has the effect of creating high tides at the same time in different locations, shown by cotidal lines or contours; some examples of these are shown in Figure 19.

Figure 19 Co-tidal lines indicating high tides occurring at the same times

Tides can be funnelled to stream around islands, promontories and other features both large and small to create regular surges, currents and amplified sea-level changes. The effect of shallow water and projecting spits of land create the aforementioned wave reflections and interferences, setting up tidal currents which appear to have little direct relationship with the oncoming open ocean tidal bulge. Such currents can give rise to double tides like those around Southampton, where the ebb tide of the English Channel running through Spithead creates a local high tide in addition to the ‘normal’ flood tide up the river Solent.

For the British Isles, the main stream of the Atlantic bulge flood tide approaches from the west, and on approaching the southern part of Ireland it splits into three main current streams. One follows the west coast of Ireland travelling north. Another enters and travels northwards up the Irish Sea, meeting up with the first one to the north of Ireland; both of these combine to continue flowing around the north of Scotland and back down the east coast of Britain and the North Sea towards Dover. Meanwhile, the third current stream flows into the English Channel, meeting the North Sea stream off Dover. In other words, the currents swirl both clockwise and anticlockwise around the island of Great Britain. These North Sea currents and surges can cause large tidal ranges, particularly when accompanied by strong winds, but there is an amphidromic point on the eastern side of the North Sea, off Denmark, and another midway between Norfolk and the Netherlands.

## Coriolis effect on a tidal current stream

A tidal current stream is flowing due north at a speed of 10.0 km h−1. What would be the Coriolis acceleration forces on a body of 100.0 tonnes of seawater at latitudes 30 and 75 degrees respectively? Give your answers to 3 significant figures.

### Solution

The reference frame angular velocity is that of the Earth, i.e.

The effective radial velocity from the axis of rotation is given by

So at latitude 30 degrees

and at latitude 75 degrees

The velocity itself is

The Coriolis accelerations are: for 30 degrees so

and for 75 degrees so

The Coriolis forces are given by . So for 30 degrees

and for 75 degrees

Thus at latitude 30 degrees the Coriolis force is 20.2 N and at latitude 75 degrees it is 39.0 N (both to 3 s.f.). Note how the force nearly doubles with the 45 degree increase in latitude. Also, although these are relatively small forces, 100 tonnes of water represents the mass of a cube of water with sides of only about 4.6 m, which is tiny compared with a sizeable chunk of ocean.

## Activity 2

A tidal current stream is flowing north to south at a speed of 8.0 km h−1. Referring to the approach presented in Figure 19, estimate the lateral Coriolis acceleration force on a cubic metre of seawater of density 1025.0 kg m−3 at latitude 60 degrees. What would be the lateral speed due to the Coriolis acceleration of the same volume of water after 3 hours, neglecting the change in latitude? Give your answer to 2 significant figures.

### Answer

The angular velocity of the Earth is

and the wind speed is

At 60 degrees the effective radial velocity north to south is

So the Coriolis acceleration is

The lateral Coriolis force is

and after three hours the lateral speed will be

or (to 2 s.f.).

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