Tide

It has been suggested that Earth tide be merged into this article or section. (Discuss)

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 oceans. Tides cause changes in the depth of the marine and estuarine water bodies and produce oscillating currents known as tidal streams, making prediction of tides important for coastal navigation (see Tides and navigation). The changing tide produced at a given location is the result of the changing positions of the Moon and Sun relative to the Earth coupled with the effects of Earth rotation and the local oceanographic conditions such as bathymetry. ^[1] Sea level measured by coastal tide gauges may also be strongly affected by weather influences such as wind.

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.

Tidal terminology

"High tide" or "high water" is reached when the water level stops rising; the water level then falls until it reaches "low tide" or "low water". At any given point in the ocean, there are normally two high tides and two low tides each day because of the gravitational pull of the Moon. However, land masses and changing water depth cause high and low tides to propagate 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. It takes 12 hours for the Earth to complete half a rotation, and 24 additional minutes of rotation to catch up with the Moon, which has moved along its orbit in the meantime. This time interval is the "principal lunar semi-diurnal" period, known as the M₂ tidal constituent, and it is, on average, half the time separating one lunar zenith from the next. The M₂ constituent is usually the biggest one (and therefore the one tracked by simple tide clocks), 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.

When the water level is falling it is called the ebb tide, and when it is rising it is called the flood tide. At times of high tide and low tide, the tide is said to be turning. This period is also known as slack tide.

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 tide's range is then maximum: this is called the "spring tide," or just "springs" and is derived not from the season of spring but rather from the verb meaning "to jump" or "to leap up". When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the earth, and the forces due to the Sun partially cancel those of the Moon. At these points in the lunar cycle, the tide's range is 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 is increased 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.

Timing

In most places there is a delay between the phases of the Moon and the 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. This is because 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 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 others. This is not to be confused with tidal ranges caused by local geography, as can be found in Nova Scotia, the Bristol Channel, 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. Highs 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 bathymetry. 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 ft), because of the shape of the bay. Southampton in the United Kingdom has a double high tide caused by the interaction between the different tidal harmonics within the region. This is contary to the popular belief that the flow of water around the Isle of Wight creates two high waters. The Isle of Wight is important, however, as it is responsible for the 'Young Flood Stand', which describes the pause of the incoming tide about three hours after low water. Ungava Bay in Northern Quebec, north eastern Canada, is believed by some experts to have higher tidal ranges than the Bay of Fundy (about 17 metres or 56 ft), but it is free of pack ice for only about four months every year, whereas the Bay of Fundy rarely freezes.

There are only very slight tides in the Mediterranean Sea and the Baltic Sea owing 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.

Tidal physics

See also: Tidal force

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

Though the gravitational force exerted on the Earth by the Sun is almost 200 times stronger than that exerted on the Earth by the Moon, the tidal force produced by the Moon is about twice as strong as that produced by the Sun. This is because the tidal force is related not to the strength of a gravitational field but to its gradient. 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 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. 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.

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 as great as the Moon's, the Sun is on average 389 times as far away as the Moon, making the Sun's tidal effect only 46% as large as the Moon's.

For simplicity, consider the tidal influence caused by the Moon: it should be understood that the same description 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

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 were 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 propagation 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 along the equator halfway around the Earth (by comparison, the natural period of the Earth's lithosphere is about 57 minutes).

Tidal lag

See also: Tidal acceleration

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, gives 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 analysis

Careful Fourier and data analysis over a 19 year period ( the National Tidal Datum Epoch in the US) uses carefully selected frequencies called the tidal harmonic constituents. This analysis can be done using only the knowledge of the period of forcing, but without detailed understanding of the physical mathematics, which means that useful tidal tables have been constructed for well over a century. ^[2] The resulting amplitudes and phases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours (the semidiurnal constituents), but there are major constituents near 24 hours (diurnal) as well. Longer term constituents are 14 day or fortnightly, monthly, and semiannual. Most coastline is dominated by semidiurnal tides, but some areas such as the [[South China Sea] and the Gulf of Mexico are primarily diurnal. In the semidiurnal areas, the primary constituents M₂(lunar) and S₂(solar) periods differ slightly so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period). ^[3]

M₂ is the largest semidiurnal tidal constituent. The amplitude is half of the full tidal range. Points are cotidal points if they reach high tide at the same time and low tide at the same time. The tide at each cotidal line differs by 1 hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich. Where the lines meet are amphidromic points and the tide rotates around them. For example, from Baja California to Alaska and from France to Ireland the M₂ tide propagates northward. The M₂ tide propagates counterclockwise around New Zealand. Cotidal lines 180° around the amphidromes are in opposite phase: high tide across from low tide. Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so the M₂ patterns cannot be used for other tides.

Tides and navigation

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 draft 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 with "soundings" and the use of bathymetric contour lines to depict the shape of the submerged surface. These depths are relative to a "chart datum", which is typically 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. All of these are continuum mechanical phenomena, the first two being fluids and the third solid (with various modifications).

Atmospheric tides are negligible from ground level and aviation altitudes, drowned by the much more important effects of weather. Atmospheric tides are both gravitational and thermal in origin, and are the dominant dynamics from about 80 km to 120 km where the molecular density becomes too small to be considered fluid.

Terrestrial tides or Earth tides that affect the entire mass of the Earth. The Earth's crust shifts (up/down, east/west, north/south) in response to the Moon's and Sun's gravitation, ocean tides, and atmospheric loading. While negligible for most human activities, the semidiurnal amplitude of terrestrial tides can reach about 55 cm at the equator (15 cm is due to the Sun) which is important in GPS calibration and VLBI measurements. Also to make precise astronomical angular measurements requires knowledge of the earth's rate of rotation and nutation, both of which are influenced by earth tides. The semi-diurnal M₂ Earth tides are nearly in phase with the Moon with tidal lag of about two hours. Terrestrial tides also need to be taken in account in the case of some particle physics experiments (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.

The galactic tide is the tidal force exerted by galaxies on stars within them and satellite galaxies orbiting them. The effects of the galactic tide on the Solar System's Oort cloud are believed to be the cause of 90 percent of all observed long-period comets. ^[5]

Misapplications

Tsunamis, the large waves that occur after earthquakes, are sometimes called tidal waves, but this name is due to their resemblence to the tide, rather than any actual link to the tide itself. 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.

See also

Wikipedia information about Tide This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Tide". It may not have been reviewed by professional editors (see full disclaimer). Help contribute to Americola and edit this article.