# Tide

"Ebb tide" redirects here. For the song, see Ebb Tide.
 Image:Bay of Fundy High Tide.jpg The Bay of Fundy at high tide Image:Bay of Fundy Low Tide.jpg The same location at low tide

Tides are the cyclic rising and falling of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the Earth. Tides cause changes in the depth of the sea, and also produce oscillating currents known as tidal streams, making prediction of tides important for coastal navigation (see Tides and navigation, below). The strip of seashore that is submerged at high tide and exposed at low tide, the intertidal zone, is an important ecological product of ocean tides.

The changing tide produced at a given location on the Earth is the result of the changing positions of the Moon and Sun relative to the Earth coupled with the effects of the rotation of the Earth and the local bathymetry (the underwater equivalent to topography or terrain). Though the gravitational force exerted by the Sun on the Earth is almost 200 times stronger than that exerted by the Moon, the tidal force produced by the Moon is about twice as strong as that produced by the Sun. The reason for this is that the tidal force is related not to the strength of a gravitational field, but to its gradient. The field gradient decreases with distance from the source more rapidly than does the field strength; as the Sun is about 400 times further from the Earth than is the Moon, the gradient of the Sun's field, and thus the tidal force produced by the Sun, is weaker.

The first well-documented mathematical explanation of tidal forces was given in 1687 by Isaac Newton in the Philosophiae Naturalis Principia Mathematica.

## Tidal terminology

The maximum water level is called "high tide" or "high water" and the minimum level is "low tide" or "low water." If the ocean were a constant depth, and there were no land, high water would occur as two bulges in the height of the oceans--one bulge facing the Moon and the other on the opposite side of the earth, facing away from the Moon. There would also be smaller, superimposed bulges on the sides facing toward and away from the Sun. For an explanation see below under Tidal physics. At any given point in the ocean, there are normally two high tides and two low tides each day just as there would be for an earth with no land; however, rather than two large bulges propagating around the earth, with land masses in the way the result is many smaller bulges propagating around amphidromic points, so there is no simple, general rule for predicting the time of high tide from the position of the Moon in the sky. The common names of the two high tides are the "high high" tide and the "low high" tide; the difference in height between the two is known as the "daily inequality." The daily inequality is generally small when the Moon is over the equator. 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. This is the "principal lunar semi-diurnal" period, abbreviated as the M2 tidal component, and it is, on average, half the time separating one lunar zenith from the next. The M2 component is usually the biggest one, but there are many others as well due to such complications as the tilt of the Earth's rotation axis and the inclination of the lunar orbit. 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." At the times of high tide and low tide, the tide is said to be "turning," also slack tide.

Image:Lunar-Phase-Diagram.png
The Earth and Moon, looking at the North Pole

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 (a condition known as syzygy), the tidal forces due to the Sun reinforce those of the Moon. 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 verb "to jump" or "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 larger at these times.) 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.

## Tidal physics

Ignoring complications arising from ocean currents, the ocean's surface is closely approximated by an equipotential surface, which is commonly referred to as the geoid. Since the gravitational force is equal to the gradient of the potential, there are no tangential forces on such a surface, and the ocean surface is thus in gravitational equilibrium.

Now consider the effect of external, massive bodies such as the Moon and Sun. These bodies have strong gravitational fields that diminish with distance in space and which act to alter the shape of an equipotential surface on the Earth. This deformation of the geoid has a fixed orientation in space relative to the influencing body, and it is the rotation of the Earth relative to this shape that causes the daily tidal cycle. Gravitational forces follow an 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. While the Sun's gravitational pull on Earth is on average 179 times greater than the Moon's, since its distance is much larger, the Sun's tidal effect is about 46% smaller.

Image:Tide moon gravity differential.png
The Moon exerts its gravitational pull differently on different parts of the earth. The farther the Moon, the weaker its pull. Imagine a shell of the outer Earth, this diagram shows the Moon's gravity differential over the thickness of the shell.
Image:Field tidal.png
The Moon's gravity differential field at the surface of the earth is known as the Tide Generating Force. This is the primary mechanism that drives tidal action and explains two bulges, accounting for two high tides per day. Other forces, such as the Sun's gravity, also add to tidal action.

For simplicity, consider the tidal influence cause by the Moon: it should be understood that the same desciption applies to the Sun as well. 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 from the moon than the solid earth, so it is pulled less and effectively moves away from Earth (i.e. the Earth moves more toward the Moon than the water does), 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 (at 55° from the orbital plane) 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.

### 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 tidal bulges travels around at that speed relative to an observer on Earth, 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, which corresponds to the amplitude that would be reached if the ocean possessed a uniform depth, there were no landmasses, and the Earth was not rotating. The Sun similarly causes tides, of which the theoretical amplitude is about 25 cm (46% of that of the Moon) with a cycle time of 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. Since the orbit of the Earth about the Sun, and the Moon about the Earth, are elliptical, the amplitudes of the tides change somewhat as a result of the varying Earth-Sun and Earth-Moon distances. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach 93 cm.

Real amplitudes differ considerably, not only because of variations in ocean depth, and the obstacles to flow caused by the continents, but also because the natural period of wave propogation is of the same order of magnitude as the rotation period: about 30 hours. If there were no land masses, it would take about 30 hours for a long wavelength ocean surface wave to propagate halfway around the Earth (by comparison, the natural period of the Earth's lithosphere is about 57 minutes). If the Moon suddenly vanished, and there were no land, the level of the oceans would oscillate with a period of 30 hours and with an amplitude that would slowly decrease as energy was dissipated. This 30 hour value is a simple function of terrestrial gravity, the average depth of the oceans, and the circumference of the Earth.

### Tidal lag

Because the Moon's tidal forces drive the oceans with a period of about 12.42 hours, which is considerably less than the natural period of the oceans, complex resonance phenomena take place. This, as well as the effects of friction, give rise to an average lag time of 12 minutes between the occurrence of high tide and lunar zenith. This tidal lag time corresponds to an angle of about 3 degrees between the position of the Moon, the center of the Earth, and the location of the global average high tide. This tidal lag gives rise to a gravitational torque on the Moon that results in the gradual transfer of angular momentum to its orbit, and a gradual increase in the Earth-Moon separation. As a result of the principle of conservation of angular momentum, the rotational velocity of the Earth is correspondingly slowed. Thus, over geologic time, the Moon recedes from the Earth and the length of the terrestrial day increases. See tidal acceleration for further details.

Tidal flows are of profound importance in navigation and very significant errors in position will occur if they 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.

The timings and velocities of 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, with 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 the direction and the average flow speed (usually in knots) for spring and neap tides. 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 to counteract the effects of tides on navigation is to (1) calculate a "dead reckoning" position (or DR) from distance and direction of travel, (2) mark this on the chart (with a vertical cross like a plus sign) and (3) draw a line from the DR in the direction of the tide. The distance the tide will have moved the boat along this line is computed by the tidal speed, and this 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 by the use of contour plots. These depths are relative to a "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 minimum water depth possible during the tidal cycle. "Drying heights" may also be shown on the chart, which 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.

## Other tides

In addition to oceanic tides, there are atmospheric tides as well as terrestrial tides (solid earth tides) that affect the rocky mass of the Earth. Atmospheric tides may be negligible for everyday phenomena, drowned by the much more important effects of weather and solar thermal tides. However, there is no strict upper limit to the Earth's atmosphere, and the tidal pull increases with the distance from the Earth's centre.

The Earth's crust, on the other hand, rises and falls imperceptibly in response to the Moon's gravitational attraction. 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).

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 were designed while taking terrestrial tides into account for proper operation. Among the effects that need to be taken into account are circumference deformation for circular accelerators and particle beam energy.

Since tidal forces generate currents of conducting fluids within the interior of the Earth, they affect in turn the Earth's magnetic field itself.

Tsunamis, 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, hurricane tide, and red tide. The term tidal wave appears to be disappearing from popular usage.

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