The tide is the regular rising and falling of the ocean's surface caused by changes in gravitational forces external to the Earth. The main changing gravitational field is due to the Moon while a lesser field is caused by the Sun.
Since tides generate currents of conducting fluids within the Earth's magnetic field, they affect in return the magnetic field itself.
The loss of rotational energy of the earth, due to friction within the tides, and the gravitational effects caused by tidal deformations of the earth's body, are responsible for the slowdown of the earth's rotation and the increase of the distance to the moon, see Tidal force.
The maximum water level is called "high tide" or "high water" and the minimum level is "low tide" or "low water". High water occurs as two bulges in the height of the oceans; one bulge faces the moon and the other, on the opposite side of the earth, faces away from the moon. For an explanation see below under Tidal physics. There are two low waters positioned at about 90° of longitude from the high waters. At any given point on the ocean, there are normally two high tides and two low tides each day. The common names of the two high tides are the "high high" tide and the "low high" tide; the two low tides are called the "high low" tide and the "low low" tide. On average, high tides occur 12 hours 24 minutes apart. The 12 hours is due to the Earth's rotation, and the 24 minutes to the Moon's orbit. The 12 hours is half of a solar day and the 24 minutes is half of a lunar extension, which is 1/(29-day lunar cycle). The lunar cycle is what is tracked by tide clocks.
The time between high tide and low tide, when the water level is falling, is called the "ebb". The time between low tide and high tide, when the tide is rising, is called "flow" or "flood".
The height of the high and low tides (relative to mean sea level) also varies. Around new and full Moon when the Sun, Moon and Earth form a line, the tidal forces due to the Sun reinforce those of the Moon, due to the syzygy found at those times.
The tides' range is then at its maximum: this is called the "spring tide", or just "springs" and is derived not from the season of spring but rather from the German verb springen, meaning "to leap up". When the Moon is at first quarter or third quarter, the sun and moon are at 90° to each other and the forces due to the Sun partially cancel out those of the Moon. At these points in the Lunar cycle, the tide's range is at its minimum: this is called the "neap tide", or "neaps".
Spring tides result in high waters that are higher than average, low waters that are lower than average, slack water time that is shorter than average and stronger tidal currents than average. Neaps result in less extreme tidal conditions. Normally there is a seven day interval between springs and neaps.
The relative distance of the Moon from the Earth also affects tide heights: When the Moon is at perigee the range increases, and when it is at apogee the range is reduced. Every 7½ lunations, perigee and (alternately) either a new or full Moon coincide; at these times the range of tide heights is greatest of all, and if a storm happens to be moving onshore at this time, the consequences (in the form of property damage, etc.) can be especially severe (surfers are aware of this, and will often intentionally go out to sea during these times, as the waves are more spectacular than ever). The effect is enhanced even further if the line-up of the Sun, Earth and Moon is so exact that a solar or lunar eclipse occurs concomitant with perigee.
In most places there is a delay between the phases of the Moon and its effect on the tide. Springs and neaps in the North Sea, for example, are two days behind the new/full Moon and first/third quarter, respectively. The reason for this is that the tide originates in the southern oceans, the only place on the globe where a circumventing wave (as caused by the tidal force of the Moon) can travel unimpeded by land.
The resulting effect on the amplitude, or height, of the tide travels across the oceans. It is known that it travels as a single broad wave pulse northwards over the Atlantic. This causes relatively low tidal ranges in some locations (nodes) and high ones in other places. This is not to be confused with tidal ranges caused by local geography, as can be found in Nova Scotia, Bristol, the Channel Islands, and the English Channel. In these places tidal ranges can be over 10 metres.
The Atlantic tidal wave arrives after approximately a day in the English Channel area of the European coast and needs another day to go around the British Isles in order to have an effect in the North Sea. Peaks and lows of the Channel wave and North Sea wave meet in the Strait of Dover at about the same time but generally favour a current in the direction of the North Sea.
The exact time and height of the tide at a particular coastal point is also greatly influenced by the local topography. There are some extreme cases: the Bay of Fundy, on the east coast of Canada, features the largest well-documented tidal ranges in the world, 16 metres (53 feet), because of the shape of the bay. Southampton in the United Kingdom has a double high tide caused by the flow of water around the Isle of Wight, and Weymouth, Dorset has a double low tide because of the Isle of Portland. Ungava Bay in Nunavut, north eastern Canada, is believed by some experts to have higher tidal ranges than the Bay of Fundy (about 17 metres or 56 feet), but it is free of pack ice for only about four months every year, whereas the Bay of Fundy rarely freezes even in the winter.
There are only very slight tides in the Mediterranean Sea and the Baltic Sea due to their narrow connections with the Atlantic Ocean. Extremely small tides also occur for the same reason in the Gulf of Mexico and Sea of Japan. On the southern coast of Australia, because the coast is extremely straight (partly due to the tiny quantities of runoff flowing from rivers), tidal ranges are equally small.
Ignoring external forces, the ocean's surface defines a geopotential surface or geoid, where the gravitational force is directly towards the centre of the Earth and there is no net lateral force and hence no flow of water.
Now consider the effect of added external, massive bodies such as the Moon and Sun. These massive bodies have strong gravitational fields that diminish with distance in space. It is the spatial differences in these fields that deform the geoid shape. This deformation has a fixed orientation relative to the influencing body and the rotation of the Earth relative to this shape drives the tides around. Gravitational forces follow the inverse-square law (force is inversely proportional to the square of the distance), but tidal forces are inversely proportional to the cube of the distance. The Sun's gravitational pull on Earth is 179 times bigger than the Moon's, but because of its much greater distance, the Sun's tidal effect is smaller than the Moon's (about 46% as strong). For simplicity, the next few sections use the word "Moon" where also "Sun" can be understood.
Since the Earth's crust is solid, it moves with everything inside as one whole, as defined by the average force on it. For a geoid shape this average force is equal to the force on its centre. The water at the surface is free to move following forces on its particles. It is the difference between the forces at the Earth's centre and surface which determine the effective tidal force.
At the point right "under" the Moon (the sub-lunar point), the water is closer than the solid Earth; so it is pulled more and rises. On the opposite side of the Earth, facing away from the Moon (the antipodal point), the water is farther than the solid earth, so it is pulled less and moves away from Earth, rising as well. On the lateral sides, the water is pulled in a slightly different direction than at the centre. The vectorial difference with the force at the centre points almost straight inwards to Earth. It can be shown that the forces at the sub-lunar and antipodal points are approximately equal and that the inward forces at the sides are about half that size. Somewhere in between there is a point where the tidal force is parallel to the Earth's surface. Those parallel components actually contribute most to the formation of tides, since the water particles are free to follow. The actual force on a particle is only about a ten millionth of the force caused by the Earth's gravity.
These minute forces all work together:
- pull up under and away from the Moon
- pull down at the sides
- pull towards the sub-lunar and antipodal points at intermediate points
So two bulges are formed pointing towards the Moon just under it and away from it on Earth's far side.
Tidal amplitude and cycle time
Since the Earth rotates relative to the Moon in one lunar day (24 hours, 48 minutes), each of the two bulges travels around at that speed, leading to one high tide every 12 hours and 24 minutes. The theoretical amplitude of oceanic tides due to the Moon is about 54 cm at the highest point. This is the amplitude that would be reached if the ocean were uniform with no landmasses and Earth not rotating.
The Sun similarly causes tides, of which the theoretical amplitude is about 25 cm (46 % of that of the Moon) and the cycle time is 12 hours.
At spring tide the two effects add to each other to a theoretical level of 79 cm, while at neap tide the theoretical level is reduced to 29 cm.
Real amplitudes differ considerably, not only because of global topography as explained above, but also because the natural period of the oceans is in the same order of magnitude as the rotation period: about 30 hours (by comparison, the natural period of the Earth's crust is about 57 minutes). This means that, if the Moon suddenly vanished, the level of the oceans would oscillate with a period of 30 hours with a slowly decreasing amplitude while dissipating the stored energy. This 30 hour value is a simple function of terrestrial gravity and the average depth of the oceans.
The distances of Earth from the Moon or the Sun vary, because the orbits are not circular, but elliptical. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. So if both are in closest position and aligned, the theoretical amplitude would reach 93 cm.
Because the Moon's tidal forces drive the oceans with a period of about 12.42 hours (half of the Earth's synodic period of rotation), which is considerably less than the natural period of the oceans, complex resonance phenomena take place. The lag between the Moon's passage and the tidal response varies between 2 hours in the southern oceans, to two days in the North Sea. The global average tidal lag is six hours (which means low tide occurs when the Moon is at its zenith or its nadir, a result that goes against common intuition). Tidal lag and the transfer of momentum between sea and land causes the Earth's rotation to slow down and the Moon to be moved further away in a process known as tidal acceleration.
Some other explanations in articles on the physics of tides include the (apparent) centrifugal force on the Earth in its orbit around the common centre of mass (the barycentre) with the Moon. The barycentre is located at about ¾ of the radius from the Earth's centre. It is important to note that the Earth has no "rotation" around this point. It just "displaces" around this point in a circular way (see figure). Every point on Earth has the same angular velocity and the same radius of orbit, but with a displaced centre. So the centrifugal force is uniform and does not contribute to the tides. However, this uniform centrifugal force is just equal (but with opposite sign) to the gravitational force acting on the centre of mass of Earth. So subtracting the gravitational force at the centre of Earth from the local gravitational forces at the surface, has the same effect as adding the (uniform) centrifugal forces. Although these two explanations seem very different, they yield the same results.
Tides & fluids
Tides and tidal effects happen in general whenever a mass with some volume moves in a gravitational field that is not uniform. This is, they always happen. For example, in one way or the other, all objects moving in space will see some form of tidal forces. By acting on an ideal rigid body, by definition tides will not deform the body. Many bodies which are moving within the solar system, for example, are not rigid but merely balls of gas or fluids, hovering in empty space (Sometimes they have a very thin solid crust). Tidal forces generate pressure differences between different volumes within such objects, and thus generate material currents on or within such bodies. The following argument applies in general to all such bodies, but the discussion here is restricted to a simplified Earth - Moon system (the sun also generates tides in real life, which are about half as strong as the moon's tides).
The moon's tidal effects generate an acceleration field at the surface regions of the earth which point in its direction or the opposite direction. This field is equivalent in strength to the weight of one tenth of a microgram per kilogram material. In other words, each kilogram of material at the surface of the earth experiences an "upward" force that is equivalent to the weight of one tenth of a microgram.
It is perfectly clear that nothing starts to move upward because of this. What happens instead, especially within fluids, is a change in the statical pressure within the fluid, because the masses on top lose a little bit of weight. There will be a pressure difference to neighbouring regions, and a material current will start to flow into this regions, until the pressure difference due to tide is balanced by a higher level of the fluids surface.
In the earth's oceans, the secondary effects of the material currents amplify the tidal effects by as much as a factor of 20. An equipotential surface of the ocean in a tide region would be 2 ft (60 cm) above normal level, but some coastlines experience tides of 40 ft (12 m) or more.
It is important to notice that pressure differences and thus material currents are not only generated in the earth's oceans, but in the interior of the earth as well.
The tides continously excite (seismic) waves within the earth which can be measured by seismology.
Tidal flows are of profound importance in navigation and very significant errors in position will occur if tides are not taken into account. Tidal heights are also very important; for example many rivers and harbours have a shallow "bar" at the entrance which will prevent boats with significant draught from entering at certain states of the tide.
Tidal flow can be found by looking at a tidal chart or tidal stream atlas for the area of interest. Tidal charts come in sets, each diagram of the set covering a single hour between one high tide and another (they ignore the extra 24 minutes) and give the average tidal flow for that one hour. An arrow on the tidal chart indicates direction and two numbers are given: average flow (usually in knots) for spring tides and neap tides respectively. If a tidal chart is not available, most nautical charts have "tidal diamonds" which relate specific points on the chart to a table of data giving direction and speed of tidal flow.
Standard procedure is to calculate a "dead reckoning" position (or DR) from distance and direction of travel and mark this on the chart (with a vertical cross like a plus sign) and then draw in a line from the DR in the direction of the tide. Measuring the distance the tide will have moved the boat along this line then gives an "estimated position" or EP (traditionally marked with a dot in a triangle).
Nautical charts display the "charted depth" of the water at specific locations and on contours. These depths are relative to "chart datum", which is the level of water at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minumum water depth possible during the tidal cycle. "Drying heights" may also be shown on the chart. These are the heights of the exposed seabed at the lowest astronomical tide.
Heights and times of low and high tide on each day are published in "tide tables". The actual depth of water at the given points at high or low water can easily be calculated by adding the charted depth to the published height of the tide. The water depth for times other than high or low water can be derived from tidal curves published for major ports. If an accurate curve is not available, the rule of twelfths can be used. This approximation works on the basis that the increase in depth in the six hours between low and high tide will follow this simple rule: first hour - 1/12, second - 2/12, third - 3/12, fourth - 3/12, fifth - 2/12, sixth - 1/12.
(N.B. It would be foolish to attempt navigation without some training and the "Rule of Twelfths " in particular should be used with caution)
In addition to oceanic tides, there are atmospheric tides as well as terrestrial tides (land tides), affecting the rocky mass of the Earth. Atmospheric tides are negligible, drowned by the much more important effects of weather and the solar thermal tides. The Earth's crust, on the other hand, rises and falls imperceptibly in response to the Moon's solicitation. The amplitude of terrestrial tides can reach about 55 cm at the equator (15 cm of which are due to the Sun), and they are nearly in phase with the Moon (the tidal lag is about two hours only) - which means that they reinforce the apparent oceanic tides.
While negligible for most human activities, terrestrial tides need to be taken in account in the case of some particle physics experimental equipments (Stanford online). For instance, at the CERN or SLAC, the very large particle accelerators are designed while taking terrestrial tides into account for proper operation. Indeed, despite their kilometre-range dimension, centimetric deformations might lead to their malfunctioning as a physics experimental apparatus. Among the effects that need to be taken into account are : circumference deformation for circular accelerators, particle beam energy.
The first mathematical explanation of tidal forces was given in 1687 by Isaac Newton in the Philosophiae Naturalis Principia Mathematica. Yet Lucio Russo, an Italian scholar, in his book Flussi e Riflussi (yet to be published in English) demonstrates that hellenistic Greeks already had understood tides in terms of the gravitational pull of the Moon and the Sun. In particular it emerges that Seleuc of Babylon (2 B.C.) used his gravitational explanation to prove that it was the Earth to revolve around the Sun, not the opposite.
Tsunami, the large waves that occur after earthquakes, are sometimes called tidal waves, but have nothing to do with the tides. Other phenomena unrelated to tides but using the word tide are rip tide, storm tide, and hurricane tide. The term tidal wave appears to be disappearing from popular usage.
- Coastal erosion
- Hough function
- Primitive equations
- Storm tide
- Tidal bore
- Tidal island
- Tidal resonance
- Rip tide
- Tide pool
- Slack water
- Tidal power
- "Myths about Gravity and Tides" - an extended and revised version of the paper originally published in “The Physics Teacher” 37, October 1999, pp. 438 - 441.
- Misconceptions about tides
- Direct and opposite tides, from the Center for Operational Oceanographic Products and Services (This site uses the concept of centrifugal force.)
- Earth tides calculatorca:Marea
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