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62-642: Mont-Saint-Michel Bay is about 500 km (190 sq mi) in size. The following towns and villages surround the bay, from north to south: Three small rivers end in the bay (and cross it at low tide): the Couesnon , now blocked to the west of Mont Saint-Michel by a causeway , the Sée and the Sélune . The very low slope of the bay and the very large tides formed a mascaret in those rivers that can travel upstream for many kilometers. Three larger rivers end in

124-445: A diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides vary on timescales ranging from hours to years due to a number of factors, which determine the lunitidal interval . To make accurate records, tide gauges at fixed stations measure water level over time. Gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to

186-677: A day were similar, but at springs the tides rose 7 feet (2.1 m) in the morning but 9 feet (2.7 m) in the evening. Pierre-Simon Laplace formulated a system of partial differential equations relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The Laplace tidal equations are still in use today. William Thomson, 1st Baron Kelvin , rewrote Laplace's equations in terms of vorticity which allowed for solutions describing tidally driven coastally trapped waves, known as Kelvin waves . Others including Kelvin and Henri Poincaré further developed Laplace's theory. Based on these developments and

248-523: A few days after (or before) new and full moon and are highest around the equinoxes, though Pliny noted many relationships now regarded as fanciful. In his Geography , Strabo described tides in the Persian Gulf having their greatest range when the moon was furthest from the plane of the Equator. All this despite the relatively small amplitude of Mediterranean basin tides. (The strong currents through

310-505: A given day are typically not the same height (the daily inequality); these are the higher high water and the lower high water in tide tables . Similarly, the two low waters each day are the higher low water and the lower low water . The daily inequality is not consistent and is generally small when the Moon is over the Equator . The following reference tide levels can be defined, from

372-451: A gravitational field that varies in time and space is present. For example, the shape of the solid part of the Earth is affected slightly by Earth tide , though this is not as easily seen as the water tidal movements. Four stages in the tidal cycle are named: Oscillating currents produced by tides are known as tidal streams or tidal currents . The moment that the tidal current ceases

434-464: A smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a prolate spheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's rotational effects on motion. Euler realized that the tidal force's horizontal component (more than the vertical) drives the tide. In 1744 Jean le Rond d'Alembert studied tidal equations for

496-526: A system of pulleys to add together six harmonic time functions. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s. The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary . Many large ports had automatic tide gauge stations by 1850. John Lubbock was one of

558-490: Is 97.8 km (60.8 mi) long, and its drainage basin is 1,124 km (434 sq mi). Its final stretch forms the border between the historical duchies of Normandy and Brittany . Its historically irregular course, alternating between two beds on the north and south of the Mont Saint-Michel but eventually definitely settling to the south bed, inspired the saying "The Couesnon in its madness placed

620-455: Is a useful concept. Tidal stage is also measured in degrees, with 360° per tidal cycle. Lines of constant tidal phase are called cotidal lines , which are analogous to contour lines of constant altitude on topographical maps , and when plotted form a cotidal map or cotidal chart . High water is reached simultaneously along the cotidal lines extending from the coast out into the ocean, and cotidal lines (and hence tidal phases) advance along

682-422: Is at once cotidal with high and low waters, which is satisfied by zero tidal motion. (The rare exception occurs when the tide encircles an island, as it does around New Zealand, Iceland and Madagascar .) Tidal motion generally lessens moving away from continental coasts, so that crossing the cotidal lines are contours of constant amplitude (half the distance between high and low water) which decrease to zero at

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744-418: Is called slack water or slack tide . The tide then reverses direction and is said to be turning. Slack water usually occurs near high water and low water, but there are locations where the moments of slack tide differ significantly from those of high and low water. Tides are commonly semi-diurnal (two high waters and two low waters each day), or diurnal (one tidal cycle per day). The two high waters on

806-457: Is called the spring tide . It is not named after the season , but, like that word, derives from the meaning "jump, burst forth, rise", as in a natural spring . Spring tides are sometimes referred to as syzygy tides . When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the Earth (in quadrature ), and the solar tidal force partially cancels

868-446: Is never time for the fluid to "catch up" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonetheless causes rhythmic changes in sea surface height. When there are two high tides each day with different heights (and two low tides also of different heights), the pattern is called a mixed semi-diurnal tide . The changing distance separating the Moon and Earth also affects tide heights. When

930-408: Is not necessarily when the Moon is nearest to zenith or nadir , but the period of the forcing still determines the time between high tides. Because the gravitational field created by the Moon weakens with distance from the Moon, it exerts a slightly stronger than average force on the side of the Earth facing the Moon, and a slightly weaker force on the opposite side. The Moon thus tends to "stretch"

992-461: Is not the case due to the free fall of the whole Earth, not only the oceans, towards these bodies) a different pattern of tidal forces would be observed, e.g. with a much stronger influence from the Sun than from the Moon: The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the Sun is on average 389 times farther from the Earth, its field gradient

1054-402: Is shorter than average, and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven-day interval between springs and neaps. Tidal constituents are the net result of multiple influences impacting tidal changes over certain periods of time. Primary constituents include the Earth's rotation, the position of the Moon and Sun relative to the Earth,

1116-419: Is the time required for the Earth to rotate once relative to the Moon. Simple tide clocks track this constituent. The lunar day is longer than the Earth day because the Moon orbits in the same direction the Earth spins. This is analogous to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1: 05 + 1 ⁄ 2 (not at 1:00). The Moon orbits the Earth in the same direction as

1178-606: The Coriolis effect , is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere. The difference of cotidal phase from the phase of a reference tide is the epoch . The reference tide is the hypothetical constituent "equilibrium tide" on a landless Earth measured at 0° longitude, the Greenwich meridian. In the North Atlantic, because the cotidal lines circulate counterclockwise around

1240-722: The Euripus Strait and the Strait of Messina puzzled Aristotle .) Philostratus discussed tides in Book Five of The Life of Apollonius of Tyana . Philostratus mentions the moon, but attributes tides to "spirits". In Europe around 730 AD, the Venerable Bede described how the rising tide on one coast of the British Isles coincided with the fall on the other and described the time progression of high water along

1302-530: The North Sea . Much later, in the late 20th century, geologists noticed tidal rhythmites , which document the occurrence of ancient tides in the geological record, notably in the Carboniferous . The tidal force produced by a massive object (Moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector difference between the gravitational force exerted by

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1364-440: The lunar theory of E W Brown describing the motions of the Moon, Arthur Thomas Doodson developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies. Some of his methods remain in use. From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to

1426-478: The tide brings large quantities of sediment which cause large sandbars within the river. On the other, the three watercourses drive the sediment back out to sea. In the 20th century, the Couesnon was turned into a canal , to reduce the erosion of its banks. In 1969, a dam was built. These modifications, and the causeway linking Mont Saint-Michel to the mainland, have caused the buildup of mudflats. To prevent

1488-426: The Earth rotates on its axis, so it takes slightly more than a day—about 24 hours and 50 minutes—for the Moon to return to the same location in the sky. During this time, it has passed overhead ( culmination ) once and underfoot once (at an hour angle of 00:00 and 12:00 respectively), so in many places the period of strongest tidal forcing is the above-mentioned, about 12 hours and 25 minutes. The moment of highest tide

1550-419: The Earth slightly along the line connecting the two bodies. The solid Earth deforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularly horizontally (see equilibrium tide ). As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth's surface change constantly; although the ocean never reaches equilibrium—there

1612-586: The Earth's accumulated dynamic tidal response to the applied forces, which response is influenced by ocean depth, the Earth's rotation, and other factors. In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides. Daniel Bernoulli , Leonhard Euler , Colin Maclaurin and Antoine Cavalleri shared the prize. Maclaurin used Newton's theory to show that

1674-456: The Mont becoming too connected to the mainland, plans are in place to replace the causeway with a bridge, and to modify the dam so that the sediment can once again be driven out to sea. During spring tides , a tidal bore — a wave caused by the incoming tide — can be seen working its way up the river. The Couesnon flows through the following departments and towns: Summer flow is typically in

1736-536: The Mont in Normandy" (" le Couesnon en sa folie mit le Mont en Normandie "), as the Mont is just to the Norman side of the river's current mouth. However, the administrative boundary separating the two regions does not depend on the course of the river, and is about six kilometers west of the Mont. The Couesnon, the Sée and the Sélune form part of the complex water system of the bay of Mont Saint-Michel. On one side,

1798-427: The Moon and its phases. Bede starts by noting that the tides rise and fall 4/5 of an hour later each day, just as the Moon rises and sets 4/5 of an hour later. He goes on to emphasise that in two lunar months (59 days) the Moon circles the Earth 57 times and there are 114 tides. Bede then observes that the height of tides varies over the month. Increasing tides are called malinae and decreasing tides ledones and that

1860-459: The Moon is closest, at perigee , the range increases, and when it is at apogee , the range shrinks. Six or eight times a year perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range . The difference between the height of a tide at perigean spring tide and the spring tide when the moon is at apogee depends on location but can be large as a foot higher. These include solar gravitational effects,

1922-462: The Moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Whereas the gravitational force subjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance. If the tidal force caused by each body were instead equal to its full gravitational force (which

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1984-457: The Moon's altitude (elevation) above the Earth's Equator, and bathymetry . Variations with periods of less than half a day are called harmonic constituents . Conversely, cycles of days, months, or years are referred to as long period constituents. Tidal forces affect the entire earth , but the movement of solid Earth occurs by mere centimeters. In contrast, the atmosphere is much more fluid and compressible so its surface moves by kilometers, in

2046-449: The Moon's tidal force. At these points in the lunar cycle, the tide's range is at its minimum; this is called the neap tide , or neaps . "Neap" is an Anglo-Saxon word meaning "without the power", as in forðganges nip (forth-going without-the-power). Neap tides are sometimes referred to as quadrature tides . Spring tides result in high waters that are higher than average, low waters that are lower than average, " slack water " time that

2108-449: The Moon. Abu Ma'shar discussed the effects of wind and Moon's phases relative to the Sun on the tides. In the 12th century, al-Bitruji (d. circa 1204) contributed the notion that the tides were caused by the general circulation of the heavens. Simon Stevin , in his 1608 De spiegheling der Ebbenvloet ( The theory of ebb and flood ), dismissed a large number of misconceptions that still existed about ebb and flood. Stevin pleaded for

2170-684: The Northumbrian coast. The first tide table in China was recorded in 1056 AD primarily for visitors wishing to see the famous tidal bore in the Qiantang River . The first known British tide table is thought to be that of John Wallingford, who died Abbot of St. Albans in 1213, based on high water occurring 48 minutes later each day, and three hours earlier at the Thames mouth than upriver at London . In 1614 Claude d'Abbeville published

2232-531: The Sun and moon. Pytheas travelled to the British Isles about 325 BC and seems to be the first to have related spring tides to the phase of the moon. In the 2nd century BC, the Hellenistic astronomer Seleucus of Seleucia correctly described the phenomenon of tides in order to support his heliocentric theory. He correctly theorized that tides were caused by the moon , although he believed that

2294-531: The Two Chief World Systems , whose working title was Dialogue on the Tides , gave an explanation of the tides. The resulting theory, however, was incorrect as he attributed the tides to the sloshing of water caused by the Earth's movement around the Sun. He hoped to provide mechanical proof of the Earth's movement. The value of his tidal theory is disputed. Galileo rejected Kepler's explanation of

2356-423: The amphidromic point, the high tide passes New York Harbor approximately an hour ahead of Norfolk Harbor. South of Cape Hatteras the tidal forces are more complex, and cannot be predicted reliably based on the North Atlantic cotidal lines. Investigation into tidal physics was important in the early development of celestial mechanics , with the existence of two daily tides being explained by the Moon's gravity. Later

2418-429: The amphidromic point. For a semi-diurnal tide the amphidromic point can be thought of roughly like the center of a clock face, with the hour hand pointing in the direction of the high water cotidal line, which is directly opposite the low water cotidal line. High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. This rotation, caused by

2480-547: The atmosphere which did not include rotation. In 1770 James Cook 's barque HMS Endeavour grounded on the Great Barrier Reef . Attempts were made to refloat her on the following tide which failed, but the tide after that lifted her clear with ease. Whilst she was being repaired in the mouth of the Endeavour River Cook observed the tides over a period of seven weeks. At neap tides both tides in

2542-568: The bay has been under restoration work. Polders have been developed in Mont-Saint-Michel Bay from the 8th century or earlier than that. Between "Pointe de Château-Richeux" and Mont Saint-Broladre seashell deposits have been used to create levees around Dol marsh. To the East of Sainte-Anne chapel is the "Duchesse-Anne" levee. It is 20 kilometres (12 mi) long. It was built during the 11th century using granite rocks. It marks

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2604-756: The bay: the Sélune , the Sée and mainly the Couesnon that, accordingly to some local folk stories, was originally the boundary between Normandy and Brittany but then moved to the West of the Mont placing it in Normandy. In reality the boundary is not at the river location but 4 kilometres (2.5 mi) further to the west, at the foot of Mont Saint-Broladre . Some of the biggest tides in Europe occur in Mont-Saint-Michel Bay: with an average 10 metres (33 ft) amplitude, they reach 12 metres (39 ft) in average and up to 16 metres (52 ft) during

2666-410: The coast. Semi-diurnal and long phase constituents are measured from high water, diurnal from maximum flood tide. This and the discussion that follows is precisely true only for a single tidal constituent. For an ocean in the shape of a circular basin enclosed by a coastline, the cotidal lines point radially inward and must eventually meet at a common point, the amphidromic point . The amphidromic point

2728-566: The combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun ) and are also caused by the Earth and Moon orbiting one another. Tide tables can be used for any given locale to find the predicted times and amplitude (or " tidal range "). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of

2790-480: The daily tides were explained more precisely by the interaction of the Moon's and the Sun's gravity. Seleucus of Seleucia theorized around 150 BC that tides were caused by the Moon. The influence of the Moon on bodies of water was also mentioned in Ptolemy 's Tetrabiblos . In De temporum ratione ( The Reckoning of Time ) of 725 Bede linked semidurnal tides and the phenomenon of varying tidal heights to

2852-420: The entry of the bay (the sea level around the mont Saint-Michel is above the low tide level) and its actual speed is closer to a walking human, the fastest observed being around 6.1 km/h. The tides mix the water, creating a rich local ecosystem . The intertidal zone , the coastal area affected by the tides is about 200 km2 wide. During the highest tide, a tidal bore can be observed—less so since

2914-538: The first to map co-tidal lines, for Great Britain, Ireland and adjacent coasts, in 1840. William Whewell expanded this work ending with a nearly global chart in 1836. In order to make these maps consistent, he hypothesized the existence of a region with no tidal rise or fall where co-tidal lines meet in the mid-ocean. The existence of such an amphidromic point , as they are now known, was confirmed in 1840 by Captain William Hewett, RN , from careful soundings in

2976-477: The highest tides . This is due in part to the low depth of the bay and the barrier effect from the Cotentin Peninsula . The ocean moves very fast, both at low and at high tide , up to 10 kilometres (6.2 mi) away. The tides have been described by Victor Hugo as " à la vitesse d'un cheval au galop (as swiftly as a galloping horse)". In reality the full extent of the tides is only visible at

3038-420: The highest level to the lowest: The semi-diurnal range (the difference in height between high and low waters over about half a day) varies in a two-week cycle. Approximately twice a month, around new moon and full moon when the Sun, Moon, and Earth form a line (a configuration known as a syzygy ), the tidal force due to the Sun reinforces that due to the Moon. The tide's range is then at its maximum; this

3100-415: The idea that the attraction of the Moon was responsible for the tides and spoke in clear terms about ebb, flood, spring tide and neap tide , stressing that further research needed to be made. In 1609 Johannes Kepler also correctly suggested that the gravitation of the Moon caused the tides, which he based upon ancient observations and correlations. Galileo Galilei in his 1632 Dialogue Concerning

3162-468: The interaction was mediated by the pneuma . He noted that tides varied in time and strength in different parts of the world. According to Strabo (1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the moon's position relative to the Sun. The Naturalis Historia of Pliny the Elder collates many tidal observations, e.g., the spring tides are

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3224-412: The month is divided into four parts of seven or eight days with alternating malinae and ledones . In the same passage he also notes the effect of winds to hold back tides. Bede also records that the time of tides varies from place to place. To the north of Bede's location ( Monkwearmouth ) the tides are earlier, to the south later. He explains that the tide "deserts these shores in order to be able all

3286-514: The more to be able to flood other [shores] when it arrives there" noting that "the Moon which signals the rise of tide here, signals its retreat in other regions far from this quarter of the heavens". Later medieval understanding of the tides was primarily based on works of Muslim astronomers , which became available through Latin translation starting from the 12th century. Abu Ma'shar al-Balkhi (d. circa 886), in his Introductorium in astronomiam , taught that ebb and flood tides were caused by

3348-420: The obliquity (tilt) of the Earth's Equator and rotational axis, the inclination of the plane of the lunar orbit and the elliptical shape of the Earth's orbit of the Sun. A compound tide (or overtide) results from the shallow-water interaction of its two parent waves. Because the M 2 tidal constituent dominates in most locations, the stage or phase of a tide, denoted by the time in hours after high water,

3410-408: The problem from the perspective of a static system (equilibrium theory), that provided an approximation that described the tides that would occur in a non-inertial ocean evenly covering the whole Earth. The tide-generating force (or its corresponding potential ) is still relevant to tidal theory, but as an intermediate quantity (forcing function) rather than as a final result; theory must also consider

3472-431: The range of 4.2 cubic metres per second (150 cu ft/s). the pH has been measured at 8.26 (Hogan, 2006) and summer water temperature as 19 degrees Celsius in the area of the mouth. Water turbidity is moderate with a Secchi disc reading of 14 centimetres. Electrical conductivity at the mouth is high even at the verge of the tidal influence. Tide Tides are the rise and fall of sea levels caused by

3534-412: The reference (or datum) level usually called mean sea level . While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to change from thermal expansion , wind, and barometric pressure changes, resulting in storm surges , especially in shallow seas and near coasts. Tidal phenomena are not limited to the oceans, but can occur in other systems whenever

3596-448: The sense of the contour level of a particular low pressure in the outer atmosphere. In most locations, the largest constituent is the principal lunar semi-diurnal , also known as the M2 tidal constituent or M 2 tidal constituent . Its period is about 12 hours and 25.2 minutes, exactly half a tidal lunar day , which is the average time separating one lunar zenith from the next, and thus

3658-561: The southern border of the polders. In 1856, M. Mosselman, founder of the "Cie des Polders de l'Ouest", was given a concession to cultivate 3,800 hectares of shoreline between Sainte-Anne chapel , Moidrey bay , Roche-Torin and the Mont Saint Michel . Couesnon The Couesnon ( French pronunciation: [kwenɔ̃] ; Breton : Kouenon ) is a river running from the département of Mayenne in north-western France, forming an estuary at Mont Saint-Michel . It

3720-404: The tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see Timing ). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure . Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have

3782-494: The tides. Isaac Newton (1642–1727) was the first person to explain tides as the product of the gravitational attraction of astronomical masses. His explanation of the tides (and many other phenomena) was published in the Principia (1687) and used his theory of universal gravitation to explain the lunar and solar attractions as the origin of the tide-generating forces. Newton and others before Pierre-Simon Laplace worked

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3844-480: The work " Histoire de la mission de pères capucins en l'Isle de Maragnan et terres circonvoisines ", where he exposed that the Tupinambá people already had an understanding of the relation between the Moon and the tides before Europe. William Thomson (Lord Kelvin) led the first systematic harmonic analysis of tidal records starting in 1867. The main result was the building of a tide-predicting machine using

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