TIDES AND TIDAL CURRENTS IN SHALLOW SEAS

75 It is worth mentioning here that, at any particular location, the highest and lowest spring tides will occur at the same times of day (~6 hr 25 min. apart).

That is because the alternation of spring and neap tides is determined by the Sun (Figure 2.12) and the period of the $2 constituent is 24 hr (Table 2.1).

As you might expect, a similar relationship applies to neap tides. The feeding and reproductive behaviour of many marine animals, especially those living in nearshore and shallow shelf waters, is 'tuned' to tidal cycles, notably the 29.5-day lunar or synodic month (the spring-neap period, Section 2 . 2 . 1 ) - see also Section 2.4.1.

In shallow water, local effects can modify tidal constituents such as Me, particularly by producing harmonics whose frequencies are simple multiples of the frequency of the constituent concemed. These harmonics result from frictional interactions between the sea-bed and the ebb and flow of the tide - especially in shallow waters. For example, the quarter-diurnal constituent M4 (twice the frequency of M2) and the one-sixth-diurnal constituent M 6 (three times the frequency of M2) are generated in addition to the semi-diurnal constituents. In most locations, the effect of these two harmonics is

insignificant compared with the principal constituents, but along the Dorset and Hampshire coasts of the English Channel each has a larger amplitude than usual. Moreover, the two harmonics are in phase, and their combined amplitude is significant when compared to that of M2. (Just west of the Isle of Wight, M2 is about 0.5 m, M4 about 0.15 m, and M6 about 0.2 m.) The additive effect of all three constituents causes the double high waters at Southampton and the double low waters at Portland. However, there is no truth in the popular myth that double high water at Southampton is caused by the tide flooding at different times around either end of the Isle of Wight.

The Mediterranean and other enclosed seas (e.g. Black Sea, Baltic Sea) have small tidal ranges of about 0.5 m or less, because they are connected to the ocean basins only by narrow straits. The tidal waves of the major amphidromic systems (Figure 2.15) cannot themselves freely propagate through these restricted openings. However, interaction between Atlantic tides and the shallow-water shelf region near Gibraltar for example, results in the generation of internal waves, which do propagate into the

Mediterranean (Figure 1.23(b)) - and the internal waves seen in Figure 1.23(a) in the South China Sea may have a similar cause. By contrast, it is unlikely that similar packets of internal waves would occur where the Bosphorus connects to the Black Sea because the tidal range in the adjacent Mediterranean is negligible.

Figure 2.19 A variety of tidal ellipses. Each shows the change in direction and speed of current at one location (i.e. notthe path of a water particle).

(a) Representation of a linear ebb-flow-ebb tidal current system.

(b) A more typical tidal ellipse, showing changing directions of tidal current during a cq tidal cycle. In both (a) and (b), arrows represent current speed and direction, and length is proportional to current velocity at the relevant time. Numbers refer to lunar hours (62 measured after an arbitrary starting time in the cycle.

(c) Three irregular and asymmetrical tidal ellipses in Lyme Bay, from current meter meas averaged over a lunar month in summer. Arrows represent current speed and direction, ar numbers show time in hours either side (+/-) of predicted high water (HW) at Devonport, I

Tidal current patterns can be conveniently represented by diagrams in the direction and speed of current flows, measured at specific locations intervals throughout the tidal cycle, are recorded by arrows of appropria length plotted from a common origin, i.e. vector arrows. Figure 2.19(a) a simple to-and-fro motion, with tidal currents flowing NNW througho~

of the tidal cycle, and SSE during the other half. The arrows at each into are of different lengths because the currents wax and wane with the tida and flow. In Figure 2.19(b), the currents display the more usual elliptica pattern, increasing in speed as they swing from WNW to NNW, decrea, again as they swing back to ESE, and then speeding up again in southe~

directions, before completing the cycle. The sense of rotation of tidal e]

may be either clockwise or anficlockwise, but rotations cure sole tend t~

favoured if there are no constraining land masses.

Figure 2.19(c) shows three typically irregular asymmetrical tidal ellips~

drawn from current meter measurements made in Lyme Bay, off south-'

Figure 2.20 The combination of the semi- diurnal M2 and quarter-diurnal M4 tidal constituents. When the semi-diurnal M2 (blue) and the quarter-diurnal M4 (red) tidal constituents are in phase, the flood tide is strengthened and the ebb tide is weakened (purple curve, lower picture).

Figure 2.21 A series of tidal current velocity profiles, showing vertical current shear due to retardation of the flow close to the sea-bed. The numbers refer to time in lunar hours after an arbitrary starting time, and only half a tidal cycle is shown. Note that at hour 3 water at the surface is moving in one direction while water near the bed is moving in the other.

77 England. The dominant tidal flows are generally between north-east and south-west, modified off the mouth of the Teign estuary by an easterly component resulting from the flow of the fiver (see also Chapter 6).

On continental shelves and in shallow seas generally, it is usual for the tidal ellipses (Figure 2.19) to be asymmetrical, because the peak ebb and flow tidal currents tend to be unequal, i.e. complete reversals of tidal current flow are rare. Part of the reason for this is the interaction between tidal constituents of different periods. Figure 2.20 shows such an interaction, between the larger semi-diurnal M2 constituent and the smaller quarter-diurnal M 4 constituent (Section 2.4). In this example, the two constituents are in phase such that the flood tidal current is strengthened because the two 'crests' coincide, while the ebb tidal current is weakened because the 'trough' of M2 coincides with the 'crest' of M4. Asymmetry and/or distortion of the tidal ellipse also occurs if a persistent current is superimposed on the tidal flow, for example the ellipse off the Teign estuary in Figure 2.19(c).

The patterns of tidal current flow in shelf seas are additionally modified by factors such as the shape of coastlines, bottom topography, and local weather conditions, as well as fronts (see Figure 2.22). All of these can reinforce the effect illustrated in Figure 2.20 and further contribute to distortion and asymmetry of the idealized tidal ellipses (Figure 2.19). The result is that there are residual currents, long-term net movements of water in fairly well-defined directions. Residual currents can be of considerable significance for the movement of sediments (see Chapter 4), though their speeds are typically only a few cm s -1.

The effect of the sea-bed upon tidal current velocity in shallow water is illustrated in Figure 2.21, which shows a series of current velocity profiles during a tidal cycle. Retardation of the flow towards the bottom of the profile is a consequence of friction with the sea-bed which produces vertical c u r r e n t shear, i.e. change of current velocity with height above the bed.

Tidal ellipses at the surface and near the bed are often out of phase, so that the surface and near-bed currents turn (from flood to ebb or vice versa) at different times. The result of such a 'phase difference' is particularly clear in the velocity profile for hour 3 in Figure 2.21.

The turbulence resulting from friction with the sea-bed causes vertical mixing of the water column, which can extend to the surface in areas where the water is shallow and/or where the tidal current is strong enough. In other areas, where tidal currents are weaker and/or the water is deeper, less mixing occurs, and stratification, with layers of different densities, can develop when surface waters are warmed in summer. The inclined boundaries or fronts between contrasting areas of mixed and of stratified waters typically have gradients of between 1 in 100 and 1 in 1000 and are often sharply defined, with rnarked differences in water density on either side of the front (Figure 2.22). Density must increase downwards in both stratified and unstratified waters, but the average density on the stratified side of the front is less than that of the mixed water column on the other side.

Turbulent mixing of surface waters by winds will break down upper layers of the stratification and will reinforce mixing by tidal currents on the other side.

During winter in mid- and high latitudes, cooling and mixing by strong winds breaks down the stratification completely, causing the fronts to disappear.

Fronts are generally zones of convergence of surface water and are often visible as lines of froth and/or floating debris. They are also generally regions of elevated nutrient concentrations and hence of high biological production.

78

Figure 2.22 (a) Diagrammatic section (with greatly exaggerated vertical scale) through a tidal front between stratified and tidally mixed waters in a shallow sea (such as the North Sea).

Note that fronts are typically zones of transition rather than sharp boundaries.

(b) Satellite image of sea-surface temperature in the North Sea in June 1996, showing the Flamborough Head Front at about 54 ~ 30'N as a wavy boundary zone between well-mixed cooler water (<10 ~ to the south, and warmed stratified water (surface >11 ~ to the north.

(The colour scale has been chosen to show the position of the front as clearly as possible.) The front tends to disappear in winter, when winds are strong.

79 Tidal waves are progressive waves (Section 1.1.1), so we would expect tidal currents to be strongest at high and low tides, i.e. as the crest and trough of the tidal wave pass through. This is the case in the open ocean and along straight coastlines where cliffs enter relatively deep offshore waters (though there is some frictional retardation, leading to lateral current shear, and tidal currents close to shore are in general slower). Where coastlines are irregular, with bays and estuaries and/or there is a shelving sea-bed and relatively shallow offshore waters, tidal waves entering the bays and estuaries can be envisaged as being somewhat analogous to the long low swell waves that slide gently up beaches, often without breaking (cf. Figure 1.18(d)) - though of course on a time-scale of hours rather than seconds or minutes. In these circumstances, as anyone who has observed a tidal estuary can testify, tidal currents are minimal at both high and low water; i.e. there is slack water at those times (the 'turn of the tide'), and tidal currents tend to be strongest at around mid-tide during both ebb and flow phases.

Tidal currents in shallow seas are utilized by some bottom-dwelling (demersal) fish populations to save energy while migrating between their feeding and spawning grounds- a good example is afforded by plaice in the North Sea. When the tide is running in the required direction, the fishes swim with the current a few metres above the bottom. At slack water, they descend to the sea-bed and remain there during the other half of the tidal cycle (while the tidal currents flow in the opposite direction), ascending into the water column when the tide runs favourably once more. This selective tidal stream transport, as it is known, has been well documented for several decades, both by electronic tagging of fishes and by trawl catches at different tidal states.

In some larger embayments, reflection of the progressive tidal wave entering the basin will result in a standing wave being established if the basin is of appropriate length (Section 1.6.4). Under these circumstances, the tidal wave is reflected back to the entrance of the basin to coincide with the arrival of the next tidal wave. The result is to increase the amplitude of the tidal wave, and tidal ranges in such embayments can be very large. The length (270 km) and average depth (60 m) of the elongate Bay of Fundy, Nova Scotia, give it a natural resonant period almost exactly that of the semi-diurnal tide. As a result, there is a strong resonant oscillation, a tidal range of some 15 m at the head of the bay, and strong tidal currents, especially during mid-tide (cf. Figure 1.20(c) and (d)).

In the larger North Sea, the tidal oscillations are partly determined by the dimensions of the North Sea basin (which has a natural resonant period of about 40 hours, cf. Equation 1.18), and partly by the progressive semi- diurnal tides entering from the Atlantic (Figure 2.14). As a result, a standing wave with three nodes tends to develop in the North Sea. However, as the basin is large enough for the water to be deflected by the Coriolis force, the nodes of the three standing waves have become the amphidromic points of Figure 2.14. As a result, the progress of the tidal waves around the

amphidromic points in the North Sea resembles that in Figure 2.16(d).

80

Some British bays and estuaries have relatively large tidal ranges (see Figure 2.24 on p. 83), often because of resonance. In the Wash, for example, the range is nearly 7 m. In the Bristol Channel it is about 12 m, which is very large. Here, resonance is reinforced by the funnelling effect as the tidal wave travels up the narrowing Severn e s t u a r y - its crest length shortens and its height increases, cf. Equation 1.15, Section 1.5.1.

Resonance is also possible on continental shelves open to the ocean (i.e.

not enclosed, like the North Sea). The continental shelf bordering most continental regions is overlain by water rarely more than 200 m deep, and it extends to the shelf break, the edge of the shelf, which is effectively the top of the continental slope, where water depths increase relatively rapidly (see Chapter 3). Resonance is theoretically possible where the shelf width (the distance from the coast to the shelf break) is about one-quarter of the tidal wavelength (or simple multiples thereof, e.g. 3/4, 5/4). The relationship is identical to that shown in Figure 1.20(c), where 'basin length' = continental shelf width, and there is a node at the shelf break. In water depths of about 100 m, the tidal wavelength for M2 (the principal lunar semi-diurnal component, Table 2.1) is about 1400 km. A shelf width of some 350km is thus required for resonance to occur, and most continental shelves are narrower than this. Nonetheless, the wider the shelf, the more closely the conditions approach those required for resonance, and there is a rough correlation between shelf width and nearshore tidal range. Increased tidal range means increased tidal current speeds. For example, mean near-surface spring tidal current speeds around the British Isles exceed 1.5 m s -1 in places.

Strong tidal currents can be produced where the flow is constrained by the presence of islands, narrow straits or headlands. This is because of the requirement for continuity, i.e. volumes of water flowing into and out of a given space per unit time must be equal. If a current is forced to become narrower, it will speed up (a shoaling sea-floor can have a similar effect).

Where the Cherbourg peninsula of north-west France reaches out towards the Channel Island of Alderney, spring tides can routinely generate currents of 10 knots (c. 5 m s -1) and interaction between tidal currents and other currents can result in confused seas - even white-capping - on an otherwise calm day.

The sea off the tip of Portland Bill, Dorset, can present similar problems.

Such areas are marked on navigational charts as 'overfalls', and are particularly to be avoided when waves are steepened by opposition to such tidal currents.

Currents associated with tidal flows include so-called 'hydraulic currents'.

Water tends to 'pile up' at the entrances to narrow straits, leading to a downward slope of the sea-surface in the direction of flow. This slope causes a horizontal pressure gradient along the strait, generating a 'hydraulic' component of the current. The tidal currents causing the legendary Lofoten Maelstrom off the northern coast of Norway, for example, are probably enhanced by hydraulic pressure gradients along channels between the Lofoten Islands. Renowned for centuries in Scandinavian folk lore, the Maelstrom gained world-wide notoriety for dangerous currents and whirlpools through the stories of Edgar Allan Poe (Descent into the Maelstrom, 1841) and Jules Verne (20 000 Leagues under the Sea, 1869). Sadly, as is often the case, reality does not quite live up to the legend. The tidal currents have been said to run at speeds of 5 or 6 m s -1. Although there are no current meter records against which to check these estimates, speeds nearer to 3 m s -1 are considered more likely by modem observers. Eddies and zones of lateral current shear appear on satellite images of the area, and the Maelstrom of legend could be a fictional amalgam of such eddies, especially as the tidal currents have long been known to rotate during the tidal cycle.

81 2.4.2 STORM SURGES

An additional complication in the prediction of tidal heights is that meteorological conditions can considerably change the height of a

particular tide, and the time at which it occurs. The wind can hold back the tide, or push it along, and changes in atmospheric pressure can also affect the water level.

Thus, not only wind changes but changes in atmospheric pressure can cause the actual water level to be very different from the predicted value, especially during storms. The combined effects of wind and low

atmospheric pressure can lead to exceptionally high tides, termed positive storm surges, which threaten low-lying coastal regions with the prospect of flooding. On the other hand, abnormally low tides, termed negative storm surges, may occur during periods of high atmospheric pressure, especially if there are strong offshore winds. Although less common, these surges can cause problems in shallow seas for large ships such as supertankers which have a relatively deep draught.

The most catastrophic positive surges are those caused by tropical cyclones (typhoons and hurricanes) or by severe depressions in temperate latitudes.

One of the worst in recent history struck the north coast of the Bay of Bengal in 1970, killing 250 000 people; a subsequent surge in 1985 caused the loss of 20 000 lives. The well-documented North Sea storm surge of

1953 led to sea-levels locally up to 3 m above normal and caused 1800 deaths in Holland and 300 in England. In this case (as with most positive surges), high spring tides, strong onshore winds and very low barometric pressure all combined to produce an abnormal rise in local sea-level. In

1986, more than 30 years after this disaster, a barrier 8 km long was built across the eastern Scheldt, completing the final stage of the Delta Project which is intended to protect the Netherlands from another such flood catastrophe. The Thames Barrage provides similar protection for the low- lying areas in and around London. Early warning of storm surges is now routine in many parts of the world (including eastern England and vulnerable parts of the Indian sub-continent), because accurate meteorological and tidal data have become more readily available, and forecasting is aided by satellite tracking of storms as well as by computer- modelling of past surges. Britain's storm-surge warning service is based at the Proudman Oceanographic Laboratory at Bidston on Merseyside, where the nation's tide-tables are also compiled.

Storm surges in the North Sea can, in theory, add as much as 4 m to the normal tidal height, but fortunately most storm surges (of which there are, on average, about five per year) increase high tide levels by only about 0.5 to 1 m. They are usually associated with eastward-moving depressions, and follow a three-phase pattern:

1 The first signs are evident as a relatively small positive storm surge in the North Atlantic, with water being displaced by south-westerly winds to the north-east Atlantic.

82

2 At the same time as the events in (1), a negative surge is experienced on the east coast of Britain as the south-westerly winds displace water to the north-east corner of the North Sea. This negative surge travels southwards down the east coast and swings eastward across the southern part of the North Sea, following the amphidromic system shown in Figure 2.14.

3 As the depression moves across Britain and out over the North Sea, the wind veers (i.e. swings in a clockwise direction) to blow from the north- west. The next high fide, by now travelling southwards down the North Sea, is thus reinforced not only by the wind but by the Atlantic surge referred to in (1) above, which by this time is displacing water into the northern part of the North Sea. This large positive surge travels down the east coast of Britain, and reaches a maximum in the south-western corner of the North Sea. The problem is compounded partly by the funnelling effect imposed by the basin shape (cf. Equation 1.15), and partly by the 'piling up' of water onshore because of the Coriolis force (Section 2.3): water being driven southwards by the strong winds is deflected to the fight, towards the east coast of England. In addition, the arrival of the surge may coincide with the arrival of the low pressure area in the centre of the depression, thus

increasing local sea-level still further.

Storms occur every winter and you might wonder why floods caused by storm surges are not more common. The answer is that severe flooding will only happen when low pressure and strong onshore winds coincide with a high spring t i d e - a storm surge at low tide can be considered a non-event.

Figure 2.23 A tidal curve for the Hudson River estuary near Albany, New York, showing a typical estuarine tide with peaks tending to catch up with the preceding trough. Numbers on the horizontal axis are time in hours.