Tide
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The tide is the regular rising and falling of the ocean's surface caused by changes in gravitational forces external to the Earth. The primary changing gravitational field is due to the Moon while the secondary field is caused by the Sun.
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Types of Tides
Bay_of_Fundy_High_Tide.jpg
Bay_of_Fundy_Low_Tide.jpg
The maximum water level is called high tide; the minimum level is low tide. The time between high tide and low tide is called ebb or falling tide, the time between low tide and high tide is called flow, flood, or rising tide. At any given point on the ocean, there are normally two high tides and two low tides each day. 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 tides' range is then at its maximum: this is called the spring tide, or just springs (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 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.
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 greatened 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, northeastern 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 is only a slight tide in the Mediterranean due to the narrow connection with the 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.
Tidal Physics
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 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 sublunar 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 sublunar 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 one 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- and contralunar 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 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 rather large: 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 until the stored energy dissipated completely (this 30 h 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.
Tidal Lag
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.
Alternative Explanation
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. 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 and Navigation
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 for the area of interest. Tidal charts come in sets, each one 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).
All nautical charts have depth markings on them which give "chart datum" - the depth of water at that point during the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons). Heights and times of low and high tide on each day are available in "tide tables". The actual depth of water at the given points at these times can then be calculated by adding the figures given to the depth given on the chart. Depths for intervening times can be calculated from tidal curves (each port has its own). If an accurate curve is not available, the rule of twelths 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 Twelths" in particular should be used with caution)
Other Tides
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 (http://news-service.stanford.edu/news/2000/march29/linac-329.html)). 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 kilometer-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 (http://accelconf.web.cern.ch/accelconf/e00/PAPERS/MOP5A04.pdf) for circular accelerators, particle beam energy (http://accelconf.web.cern.ch/accelconf/p93/PDF/PAC1993_0044.PDF).
The first mathematical explanation of tidal forces was given in 1687 by Isaac Newton in the Philosophiae Naturalis Principia Mathematica.
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.
See also
- coastal erosion
- Hough function
- primitive equations
- storm tide
- tidal bore
- tidal island
- tidal resonance
- rip tide
- tide pool
- slack water
- tidal power
External links
- "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. (http://www.jal.cc.il.us/~mikolajsawicki/Tides_new2.pdf)
- Direct and opposite tides, from the Center for Operational Oceanographic Products and Services (http://www.co-ops.nos.noaa.gov/restles3.html) (This site uses the concept of centrifugal force.)
- Earth tides calculator (http://aiuas3.unibe.ch/dpgm/zm_graph_tide.html)ca:Marea
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