Chapter 5

Tidal bores

A tidal bore (Figure 25) is perhaps the most spectacular tidal phenomenon that can be readily observed. It is truly a ‘tidal wave’ (a term often used incorrectly to describe tsunamis, which are not tidal phenomena). When a large tide enters a shallow, funnel-shaped estuary with a gently sloping bottom, its waveform is distorted and this can lead to an impressive rolling ‘wall of water’ travelling upriver. The word bore is thought to be derived from the Old Norse bára, meaning ‘wave’ or ‘billow’—apt, given their dynamics and appearance—and for tide enthusiasts (and many surfers) a well-developed tidal bore is the holy grail of natural occurrences.

25. A tidal bore (a) on the River Dee (UK) and secondary waves, or ‘whelps’ (b), behind the bore front.

The formation of a tidal bore

Tidal variations in water level at the mouth of an estuary create a wave that propagates upstream. This wave is gradually modified by changes in estuary width and depth, by friction with the bottom, and by the river flow seaward (Figure 26). Estuaries that narrow and shoal steadily with distance inland have a funnelling effect that amplifies the tidal wave, increasing its amplitude. In fact, the narrowing of the estuary is slightly more important to this amplifying effect than the shoaling.

26. Funnelling and progressive distortion of an incoming tidal wave in an estuary. At locations where both the tide and the estuary geometry are suitable, a tidal bore may form (denoted by an asterisk) and travel upriver.

The tidal wave slows as it moves into progressively shallower water. Since there is a fixed relationship between the speed of a wave, its wavelength, and its frequency (speed is wavelength multiplied by frequency) and the frequency is constant (being set by the regular, astronomically-generated tides), the slowing wave must also shorten. The overall result of this amplification (vertically) and compression (horizontally) is a wave that gets progressively steeper with distance travelled upstream.

One further consideration is the distortion of the wave by shallow-water effects (see Chapter 4). While the waveform is initially symmetrical at the estuary mouth (with the durations of both flood and ebb stages being equal), the deeper crest travels particularly fast and the wave becomes increasingly asymmetric as it progresses upstream, with a shorter, faster flood (i.e. a steep anterior slope to the tidal wave) and a longer, slower ebb (i.e. a more gradual posterior slope). Bottom friction and the adverse river outflow are also important factors in distorting the incoming tidal wave.

Where the tide and estuary geometry conspire to produce a strong flood-dominated asymmetry in the incoming tidal wave the stage is set for a tidal bore. For a gently sloping estuary bed, the steepened water surface of the incoming flood tide and its associated pressure gradient drive a fast and somewhat deeper flow (relative to the river level) upstream. At the transition between the two flows of different depths (one riverine and downstream, the other tidal and upstream) a sudden change in water level, or hydraulic jump, may form and travel upstream as a distinct waveform. This ‘hydraulic jump in translation’ (i.e. a travelling hydraulic jump), which marks the leading edge of the incoming tide, is the tidal bore. At a fixed location, the jump is observed and is immediately followed by a continuous (and usually rapid) rise in water level as the flood tide progresses.

Where and when to see a bore

Estuary shape is clearly important to the formation of a tidal bore, and a large tidal range is also crucial. The precise range required varies from place to place, but few bores are known to form where the tidal range is less than about 6 metres. For this reason, the geographical distribution of tidal bores closely matches that of large tides, particularly those belonging to a semi-diurnal tidal regime (diurnal tides are rarely steep enough to form bores—they have a longer wavelength, typically smaller amplitudes, and the initial rise in water level is slow enough that the water surface responds ‘normally’). The coasts of north-west Europe (particularly France and the United Kingdom), the Bay of Fundy in Canada, the north-east coast of South America, parts of the north coast of Australia, the Gulf of Alaska, and the East China Sea are tidal bore hotspots.

Around half of known tidal bores occur in rivers adjacent to basins that resonate with the tide. That isn’t to say such rivers host tidal bores with every tidal cycle. In many cases the very largest tides are needed for a bore to develop. Spring tides and particularly those occurring around the equinoxes are generally good times to observe tidal bores.

The timing of a bore can be predicted with some certainty, and its anticipated time of arrival is usually given relative to the predicted time of high water at a nearby port. As we have seen, the high waters of spring tides always occur at around the same times of day for a given location, and so bores also occur at more or less fixed times for a given site. A word of warning is needed though: the speed of the bore (and its remarkability) can be affected by wind conditions, barometric pressure, and rainfall (which influences river flow/depth). The River Dee Bore in the United Kingdom, for example, frequently arrives at key observation points up to thirty minutes early or late. For the tidal bore observer or surfer, arriving earlier than the predicted time is best to avoid disappointment.

Types of tidal bore

Not all bores are equal. They come in a range of different strengths and sizes from place to place (from just a few centimetres to 6 metres in height). Even at the same site, they vary from one bore to the next. They also come in different forms, from smooth, non-breaking ‘undular’ waves (generally the most common and often experienced first as an apparent ‘buckling’ of the river surface), through a variety of breaking forms of increasing violence, and culminating in those with very odd behaviours (such as the generation of large jets of water extending ahead of the bore front).

The bore front represents a travelling discontinuity of water depth and flow velocity, which has historically elicited much interest among hydraulic engineers and applied mathematicians. The English engineer, hydrodynamicist, and naval architect William Froude (1810−79) is credited with a useful parameter for describing the likely character of a tidal bore. The tidal bore Froude number (Fr) is defined in a coordinate system that moves with the bore front (effectively bringing it ‘to rest’ for the sake of simplifying the mathematics) and is dimensionless (i.e. it has no physical units). It is the ratio of the bore speed (the bore’s observed upstream speed summed with the adverse downstream river speed) to the natural speed of a hypothetical ‘shallow-water’ gravity wave (see Glossary) travelling freely on the undisturbed river (i.e., a speed √(gd_a), where g is acceleration due to gravity and d_a is the water depth of the undisturbed river, ahead of the bore). For Fr < 1, the flow is said to be subcritical and no bore develops. For Fr > 1, the flow is supercritical, and various types of bore can form (see Table 3). As the ratio suggests, a tidal bore represents a hydrodynamic shock to the river system, with a wave being forced to travel faster than it would naturally in that environment. The Froude number can also be shown to depend on the ratio of the water depths behind and ahead of the bore (d_b/d_a; Figure 26): the greater this ratio, the greater the Froude number, and the stronger and more spectacular the bore.

Table 3. Types of tidal bore

The dependence of the Froude number on the ratio of depth behind to that ahead of the bore (d_b/d_a) tells us something about how the bore front might vary across the river. Near the banks, where the river is generally shallower, this ratio is greater, explaining why bores are frequently observed to be breaking near the banks but undular in the mid-channel (where the ratio is smaller). It also explains why bores may change their form as they travel upstream, for example from undular to breaking and back, responding to variations in river depth.

River beds with typical bank-to-bank cross-sections often cause bores to develop a curved shape, viewed from above. The near-bank parts of the bore propagate more slowly than the centre because they are in shallower water and the wave undergoes refraction (at both ends). At the outer edges of the river channel, the bore gains components of velocity directed towards the banks, approaching them obliquely with the potential for additional breaking to occur.

Whelps

Non-breaking, or undular, tidal bores often have a train of waves of decreasing amplitude following the lead wave (Figure 25(b)). In the UK, these secondary waves are referred to as whelps, whereas on the River Seine (France) they were known as éteules, or ‘stubble’ (possibly a reference to the appearance of a ploughed field after the harvest). Since they are of lesser height, these waves tend to move more slowly than the lead wave and are gradually left behind to eventually dissipate (physicists refer to such a wave packet as being weakly dispersive). Whelps can be seen for some time after the bore front’s passage, in some cases more than thirty minutes. They appear increasingly chaotic with time, partly because whelps are also refracted by the shoaling of the channel towards its banks and reflect off the banks to interact with each other behind the progressing bore.

The rumble

Large tidal bores produce noises that can be placed on a spectrum between ‘menacing rumble’ and ‘deafening roar’. In fact, the noise results from a cacophony of sounds produced by various physical processes: turbulence and entrained air bubbles in the bore front (where the bore breaks); the movement of sediments at the river bed; and interactions with obstacles to the flow and with the banks.

The first scientific field measurements of the rumble sound were carried out at the turn of the century in France by tidal bore expert Hubert Chanson. Chanson’s work identified three phases with distinct acoustic characteristics: first the approaching bore, with a sound intensity increasing with time; then the passing bore front, with a noise on average five times louder than the previous phase; and finally the upstream propagation of the bore, with the sounds of the flood tide behind it. Analysis showed most of the sound’s energy to be concentrated around the frequencies of 74 hertz and 131 hertz, perfectly audible to humans (the frequency range of the human ear is approximately 20 hertz to 20 kilohertz) but rather low in pitch. As Chanson points out, this is lower in pitch than the beating of a bass drum or the labouring of a locomotive train. The acoustic spectrum also showed a secondary peak at higher frequencies (8−10 kilohertz). Current thinking is that the low pitch rumbling is caused by air bubbles trapped in the turbulent bore front, while the weaker, higher pitch component may be produced by sediments being moved along the river bed (and in particular by particle collisions) beneath the bore.

The low pitch component of the tidal bore rumble is its defining characteristic. It is also the reason why so many bore anecdotes focus on how far away the bore could be heard, or how far in advance of the bore front’s arrival it could be anticipated. Low frequency sounds tend to travel further than higher frequency ones: less energy is ‘lost’ to the medium they travel through. Classic examples are the use of low frequency sound for fog horns and the low pitch thunder that may be heard emanating from distant lightning storms. All this adds up to stories of impressive distances covered by tidal bore rumbles.

Not all stories focus on distance, however: some concern direction. Waiting for one of the Bay of Fundy’s tidal bores in the fog for which the region is famous is reported to be an unnerving experience. Under these conditions, the rumble of the bore can be heard but, rather eerily, the direction of approach cannot easily be determined.

Death of a tidal bore

Like all good things, a tidal bore must end. As a bore propagates, its kinetic energy is lost owing to friction with the river bed, and to the viscosity of the water itself. The loss is augmented by any shore-break occurring as a result of refraction onto the river banks. Some energy is used in producing the rumble sound and some in moving sediments on the river bed. Where whelps are present, there may be some backward radiation of the bore’s energy (in the downstream direction relative to the progressing front). Generally, the energy passes to a cascade of turbulence on finer and finer scales, and ultimately the bore’s energy is dissipated as heat.

The energy loss is sensitive to the difference in water depth behind and in front of the bore. In fact, it increases in proportion to this difference cubed so that a large tidal bore tends to lose energy much faster than a smaller one. As a consequence of this energy loss, the bore slows down and at the point at which the bore speed equals the river’s flow speed it is halted. Any remaining waveform can even be carried back downstream by the river.

With access to a car and traffic-free roads, the death of a bore can be seen in action. We have ourselves witnessed impressive tidal bores in the UK at Saltney Ferry Bridge on the River Dee and at Minsterworth on the River Severn, only to be disappointed a short time later further inland near Chester Weir and Maisemore, respectively.

Hall of fame

In 1988, Susan Bartsch-Winkler and David Lynch from the United States Geological Survey (USGS) produced a catalogue of known tidal bores. It incorporated sixty-seven bores, in sixteen countries, spread across every continent except Antarctica. Many more are predicted to exist where conditions are suitable, but are either undiscovered or unreported. Humans worldwide have assigned fantastically evocative names to their local bores (Table 4) and they pervade cultural rituals and historical accounts. ‘Eagre’ (or ‘Aegir’) is a name used traditionally in the United Kingdom for bores on the rivers Trent, Ouse, and Severn. It has an uncertain etymology, but our favourite (and the most romantic) theory is that it is derived from the name of a jötunn in Norse mythology (i.e. the giant Ægir, king of the sea), given early Scandinavian influence on the British Isles. Bores even appear in classical literature (e.g. George Eliot’s The Mill on the Floss and Jules Verne’s Eight Hundred Leagues on the Amazon).

Table 4. Some well-known tidal bores

One of the most impressive tidal bores occurs on the Qiantang River in China. Named the ‘Silver Dragon’, the Qiantang Bore can attain a height of 4 metres and speeds of up to 12 metres per second. The bore travels around 100 kilometres upriver from the funnel-shaped estuary in which it forms. Captain William Usborne Moore, a British Admiralty hydrographer whose efforts to survey the area in the late 1800s were severely hampered by the bore, noted that its rumble could be heard an hour ahead of its arrival.

The Qiantang bore is famously associated with a myth that it was unleashed as a punishment upon a 5th-century bc emperor who had ordered the suicide of a popular general, Wu Tzu-Hsü, and had his body thrown into the river. However, by the 1st century ad Chinese scholars had already noted the correlation between the bore’s behaviour and the phases of the Moon. By 1056 ad, a table predicting the occurrence of the bore had been constructed, making it arguably the first ever tide table. The Silver Dragon is something of a spectacle, which today attracts tens of thousands of visitors a year. There is even an annual Qiantang Tidal Bore Watching Festival, which takes place around the autumnal equinox. The bore still manages to surprise, however: it regularly overtops levees, sweeping away onlookers and causing fatalities.

In Brazil, the Amazon River and its tributaries host tidal bores known as Pororoca. The name is thought to be derived from a word meaning ‘great roar’ in the language of the indigenous Tupi people. Albert Defant, a physical oceanographer, claimed the sound of the main Amazon bore could be heard at a distance of 22 kilometres. During its passage it renders the river impassable, but it is the sheer scale of the bore that makes it particularly noteworthy. The bore front is, at points, kilometres wide and owing to the Amazon’s gently sloping bed it penetrates further inland than any other bore, up to 800 kilometres. An impressive train of whelps follows the lead wave, with several observers reporting many tens of large whelps disappearing over a distant horizon.

Some bores on the Amazon’s tributaries are unusual in that they effectively form more than 100 kilometres inland. By contrast, Brazil’s Araguari River to the north hosts a bore that forms up to 10 kilometres offshore, aided by the shoaling of the incoming tide over extensive delta deposits.

The River Severn in the United Kingdom has a tidal bore that has become a famous surfing attraction. At the landward end of the Bristol Channel (which has one of the largest tidal ranges in the world), the Severn Bore was first surfed in 1955 by Lieutenant-Colonel ‘Mad Jack’ Churchill (whose nickname was earned rather more for his military exploits than for his daredevil surfing). It has been surfed ever since and has often been the bore ridden in Guinness World Record attempts for ‘longest surfing ride on a river bore’ (distances surfed standing up on the bore have been over 12 kilometres, taking well over an hour). The bore occurs on about 130 days per year (usually twice per day—morning and night), occasionally achieving heights greater than 2 metres and speeds of around 6 metres/second. Severn Bore predictions are assigned star-ratings, with ‘5*’ representing an exceptional bore and attracting large crowds. It’s good to know it is not just oceanographers that get a little over-enthusiastic about tidal bores.

Tidal bores and people

Tidal bores can be useful. Their strong flood currents represent the fastest way to pass upriver. They are surfed for leisure, and are woven into the fabric of diverse cultures worldwide. On the other hand, they can be a nuisance to shipping and at worst just plain dangerous. The River Seine (France) formerly hosted a substantial bore (Figure 27), or mascaret in French, known as La Barre or Le Mascaret, which had a sinister reputation for wrecking ships and causing human fatalities. Alexander the Great, 4th-century bc leader of the Greek kingdom of Macedon, is thought to have fallen foul of a tidal bore on the Indus River in modern-day Pakistan. Alexander’s fleet was stranded by a violent wave surging upriver, only to be re-floated about twelve hours later by a similar but smaller incoming tide.

27. Bore on the River Seine before its near elimination in the 1960s.

Human influence on tidal bores to date has been largely destructive. The Seine Bore has been almost eliminated by waterway engineering and dredging that has altered the river mouth. A once powerful bore on the Colorado River in Mexico (known as El Burro, or ‘the donkey’) is now much reduced by patterns of dredging and silting at the mouth. The bore on the Petitcodiac River (Bay of Fundy, Canada) all but disappeared after the construction of a causeway. The River Severn Bore will likely be subject to the same fate if certain proposed schemes to harness tidal energy were to go ahead.

Projected sea-level rise is likely to alter the picture somewhat with respect to the distribution of tidal bores. It is difficult to say how exactly, but coastal tidal regimes and estuarine morphologies will change with sea-level rise and some known bores may disappear while new bores may emerge elsewhere.

Impact on estuarine processes and ecosystems

Tidal bores influence physical processes in their host estuaries, and in turn affect the ecosystems they support. They present unique flow conditions and are associated with turbulent mixing and the transport of suspended material upstream, both as larger objects (e.g. logs, stunned fish) and as clouds of turbid, sediment-laden water. They scour the river bed, periodically redistributing sediments, and sharp jumps can also be seen in water temperature and salinity following the passage of a bore.

The ecological importance of tidal bores can be seen in the behaviours they elicit in coastal and marine animals. Diverse organisms have been reported (scientifically and/or anecdotally) to feed immediately behind a tidal bore: piranhas (Amazon River, Brazil), bald eagles and beluga whales (Turnagain Arm, Alaska), sharks (Broad Sound, Australia), and crocodiles (Daly River, Australia) are all believed to use tidal bores to their advantage. Hubert Chanson reports that swans regularly ride upstream on the bores of the Garonne and Dordogne Rivers (France), though whether this is out of pleasure or convenience it is difficult to say.

Bores in other settings

Bores can form under circumstances different to those described above. A bore may form in a river that does not typically host one if it is affected by a tsunami or extreme weather event. A bore-like wave can even form on broad sand flats where there is a very large tidal range. The Baie du Mont St Michel (France) hosts such a feature, which is famed for travelling faster than a horse can gallop. ‘Internal bores’ are known to form when internal tides (i.e. tidal perturbations of the interface between layers of different density in the ocean—see Chapter 6) break on the outer margins of continental shelves.

Bore-like features have also been reported for various layers in the atmosphere. For example, undular bores in the troposphere are believed to be responsible for the ‘morning glory’ clouds seen over northern Australia’s Gulf of Carpentaria, and atmospheric bores have been measured near thunderstorms on the central plains of the USA. Such atmospheric undular bores may even be occurring on Mars, and have been proposed as an explanation for long, linear clouds sometimes seen along the flanks of the Tharsis volcanoes.

Waves generated by the rush of water from a burst dam (‘dam-break waves’) also take the form of bores. In fact, such a wave has a key role in D. H. Lawrence’s short novel The Gypsy and the Virgin. In Christopher Miles’s film adaptation of the story the wave is actually ‘played’ by the Severn Tidal Bore, which makes a cameo appearance presumably because it was less expensive and more predictable than the bursting of a dam.

Tidal races

An impressive hydraulic phenomenon, known as a tidal race, is an area of rough water created by fast tidal streams flowing over a shallow, uneven seabed. Significant races are marked on charts as navigational hazards. Some of the more accessible ones attract kayakers who enjoy the steep, fixed water surface with currents flowing up the face of the wave.

When a flow passes over an underwater precipice it is reasonable to suppose that the flow will slow down in the deeper water beyond the precipice (Figure 28).

28. Formation of a tidal race.

In order to decelerate the water, there must be a force acting to slow it down. As is usual with tidal currents, this force is provided by a sloping water surface which creates a pressure gradient force. The water surface rises to create the slope as the water flows over the precipice, making a wave that is fixed in position.

At the jump, the water is flowing ‘uphill’. The attraction for a kayaker is that they can hold themselves on the face of the wave with their weight balanced by the drag of the water carrying them upwards. The stationary wave, once formed, can last for an hour or more. Famous examples occur at The Bitches in west Wales (UK) and Race Rocks in British Columbia (Canada). When the tide turns so that the water is flowing up the underwater precipice, the surface steps down into the shallower water (so the surface keeps the same shape as in the illustration). Now, however, the flow is going ‘downhill’ (i.e. down the surface slope) and so is no good for holding a kayak in position.