The Tidal Bore


A tidal bore may be created when a rising tide forces water up an estuary against the normal flow of a river. Its formation is aided by a narrowing, shallow estuary that increases the velocity of the tidal water while reducing the speed of gravity waves. The most important factor, however, is the tidal rise, so bores occur at spring tides near the equnoxes, when tides are the highest. The depth increases when a bore passes, and the current direction reverses. The bore may have various shapes, from a relatively smooth undulating front (as illustrated at the right) to a turbulent wall that emits a characteristic low roar. The tidal bore is not a solitary wave, or soliton, but a hydraulic jump, a superposition of finite-amplitude waves.

There are 60 or more examples of tidal bores around the world. The largert is at Qiantung in China, that can be 2.5 m high and runs for 14 miles. In North America, bores are uncommon except on the Bay of Fundy, which has the world's highest tides, notably on the Petitcodiac River. The bore on this river was nearly eliminated by the construction of a causeway in 1968 connecting Moncton and Riverview, but this was opened in April 2010 and the bore is back. There is a bore on Cook Inlet in Alaska. The Seine in France had a notable bore (called la barre, though mascaret is a more general name), but it has been greatly reduced by dredging and channel improvements. In South America, three rivers in Brazil have bores, including the large one on the Amazon. England is well-provided with bores, with at least 13, the most notable the Severn bore and the Trent eagre. The Severn bore is easy to see, and has become very popular with surfboarders. The picture above is of the Severn bore, moving toward you just south of Gloucester.

The nature of the bore depends on the Froude number of the flow, F = V/c where V is the flow velocity and c is the speed of gravity waves. When the water is shallow compared to the wavelength, c = √gh, where g = 9.8 m/s2 and h is the depth in m. In the case of the bore, V is the sum of the downstream flow velocity above the bore and the upstream velocity of the bore, that is, relative to the bore. When F < 1, the flow is said to be subcritical or smooth, while when F > 1, the flow is supercritical or rough. In the first case, the surface is smooth, while in the second case it is turbulent. When F < 1.7, the bore is undulatory and smooth. From 1.7 to 2.5, there are breaking rollers; from 2.5 to 4.5 a jump appears with oscillations. Above 4.5, the jump is stable and well-defined, a typical hydraulic jump.

When F > 1, waves cannot propagate in front of the bore, which is moving rapidly enough to overtake any that try. Waves can propagate in back of the bore, though the increased depth gives them a greater speed, assuming that the wavelength is greater than the depth. The ratio of the depth behind the bore, h" to the depth in front of the bore, h', is given by h"/h' = [√(1 + 8F2) - 1]/2, for F ≥ 1. When F = 1 (or smaller) there is only a smooth transition to the tidal water flowing upstream as the direction of flow reverses. F, and therefore the character of the bore, may vary across the width of the river because of differences of depth. When there is a lot of fresh water, increasin h', F is reduced and the bore may become undulatory or even disappear. By far, the most important parameter is F, which can be estimated from the appearance of the bore.

The Severn is the largest river in England, both in length (354 km from its source in mid-Wales to its mouth) and in flow (61.2 m3/s average). It is navigable in small boats to Stourport, and in ocean-going boats to Gloucester. It flows into the Bristol Channel, widening near Lydney and Sharpness into a broad, sandy estuary. The tidal range at Sharpness is 14.5 m, second only to the Bay of Fundy in the world. Southwesterly winds can increase the tide and affect the bore noticeably. There is a ship canal from Sharpness to Gloucester, on the eastern side, while the river moves beneath cliffs on the west. The river is still 200 ft. wide at Newnham, where there are good views from the churchyard high on the cliff. The A48 follows the western bank, by the popular viewing point at Church Lane, Minsterworth.

The Severn bore forms on the sandy flats south of Newnham, moving northwards at about 14 km/h past Minsterworth (where it is very conveniently observed at bank level) and passes west of Gloucester under Over bridge to Maisemore weir, which is its limit. There are about 25 large bores per year, in Feb-Apr and Aug-Oct when the tides at Sharpness are 9.5 m or more. In the predictions, bores are rated at 1 to 5 stars. For a depth of 2 m, the gravity wave velocity is 16 km/h, so with a bore velocity of 14 km/h, we are very close to a Froude number a bit greater than one. From the photographs, an undulatory bore seems relatively normal. I would think it would be better for surfboarding than the roaring wall of a strong bore.

The Trent eagre or aegir is not as strong as the Severn bore. It has been observed as far as Gainsborough. There are similar small bores on the other rivers entering the Humber estuary.

References

Read the Wikipedia articles "Tidal Bore", "Severn Bore" and "Hydraulic Jump" for a good introduction to the subject. A Google Search for "Severn Bore" gives many photos.

Severn Bore has full information on seeing the bore, including dates and maps.


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Composed by J. B. Calvert
Created 23 August 2010
Last revised