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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.
The maximum water level is called high tide; the minimum level is low 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 height of the high and low tides (relative to mean sea level) also varies. Around new and full Moon, the tidal forces due to the Sun reinforce those of the Moon. The tide's range is at its maximum: this is called the spring tide, or just springs. 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.
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 standing wave northwards over the Atlantic. This causes relatively low tidal differences in some locations (knots) and high ones in other places. This is not to be confused with tidal differences caused by local geography, as can be found in Nova Scotia, Bristol, the Channel Islands, and the English Channel. In these places tidal differences 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 islands in order to be effective in the North Sea. Peaks and lows of the Channel wave and North Sea wave meet in Dover Strait / Pas de Calais 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 tidal range 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 becuase of the Isle of Portland. Also there is only a slight tide in the Mediterranean due to the narrow connection with the ocean.
If we ignore external forces, the ocean's surface defines a geopotential surface or geoid, where the gravitational force is directly downward and there is no net lateral force and hence no flow of water.
Now add external, massive objects such as the moon and sun, which move relative to the earth. These massive objects have strong gravitational fields and the relative movement results in strong changing gravitational fields. It is these changing fields that drive the tides. Gravitational forces follow the inverse-square law (force is proportional to the square of the distance), but tidal forces are proportional to the cube of the distance. The much greater distance of the Sun makes its tidal forces on the Earth much smaller than the Moon's (about 40% as strong).
It is easy to understand one high tide per lunar day (24 hours, 48 minutes). This is the time it takes the earth to rotate on its axis and return to its original orientation to the moon. The moon's gravitational force pulls on the earth creating a high tide on the moon side of the earth, which travels around the earth in one lunar day.
However, there are two high tides in a lunar day. The second is quite easy to understand once one realizes that the earth is not fixed in space but is in fact revolving around the moon. Imagine a solid bar connecting the earth to the moon. This earth-moon system rotates about an axis that is somewhere between the gravitational centers of the earth and moon. Because the earth is rotating about this earth-moon axis, there is a centrifugal force outwards on the earth exactly opposite of the moon. This is the second high tide. It turns out that the forces creating both high tides are exactly equal.
The theoretical amplitude of oceanic tides is about 1 metre at the equator, but the real value differs 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). 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), complex resonance phenomena take place; the main outcome of which being that the 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).
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 sollicitation. The amplitude of terrestrial tides is about 1.5 metres at the equator, 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.
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 often called tidal waves, but have nothing to do with the tides.
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