Ocean Tides

Tides are the displacements of particles on Earth caused by the differential attraction of the moon and the sun. There are atmospheric tides, land or crustal tides, and ocean tides. Of these, ocean tides are the most apparent because the ocean, as a fluid, is more easily stretched out of shape by the gravitational pull of the moon.

Causes of Tides

Each particle in the ocean moves in response to the force of gravitational attraction exerted on it by both the sun and the moon. Although the sun is some 27 million times the size of the moon, the moon is the primary factor in the tidal movement of ocean waters. In fact, the moon’s power is more than double the periodic tidal-stretching force exerted by the sun because it is much closer to Earth. This is described by Newton’s universal law of gravity, which states that the gravitational force between two bodies is directly proportional to their masses, but inversely proportional to the square of the distance between their centers of mass. Thus, the proximity of the moon counts for more than the distant mass of the sun in solar and lunar relations with Earth.

In order to explain how tides are caused, tidal scientists use the concept of a theoretical “equilibrium tide.” This concept is based on an ideal in which the ocean waters are always in static equilibrium and in which no continents obstruct the flow of water on Earth’s surface. When the moon is directly above a particular location, its force of attraction causes the mass of water to bulge up directly under the moon and also on the opposite side of Earth. Meanwhile, in the opposite quadrants of the globe, two low-water troughs result from the movement of the water away from these areas. Thus, Earth rotates beneath tidal bulges and troughs, which results in high and low tides.

Tides generally follow the lunar day, which is twenty-four hours and fifty minutes, or the time it takes the moon to complete one full orbit of Earth. Some complex tidal cycles, however, result from the combined influences of the sun and moon. If there were no moon, the sun’s influence alone would cause tides to occur at the same time each day. However, because the plane of the moon’s orbit around Earth is in a different plane from that of Earth’s orbit around the sun, combinations of full diurnal and semidiurnal tides result. In most areas, semidiurnal tides are the rule, with high and low tides occurring twice each lunar day, averaging twelve hours and twenty-five minutes apart. Diurnal tides occur when only one high tide and one low tide take place in one lunar day. They are found in parts of the China Sea and the Gulf of Mexico. Mixed tides result from a combination of both diurnal and semidiurnal tidal oscillations. Such tides are found along the Pacific coast of North America and in parts of Australia.

Other Tide Variability Factors

Other factors that contribute to the variability of ocean tides are the phases of the moon, the position of the sun and moon relative to Earth, and the latitude and topography of the tide’s location on Earth. When the sun, moon, and Earth are aligned (in “conjunction” or “opposition”), then the combined gravitational effects of these bodies will exert additional gravitational pull on Earth, resulting in increased tidal amplitude. This phenomenon, when lunar and solar tides reinforce each other, is called the spring tide and occurs around the full and new moons. In between the spring tides, a neap tide takes place when the sun, moon, and Earth are positioned at the apexes of a triangle. At this time, during the first and third quarters of the moon’s phase, solar high tides are superimposed on lunar low tides, so resulting tides are the lowest in the month. In the open ocean, spring tides may be more than 1 meter high, while neap tides may be less than 1 meter. Tidal amplitude will also vary, depending on latitude and the declination of the moon.

Despite the complexity of the many variables that determine tidal behavior, tidal scientists can now predict the time and height of a tide anywhere, on any past or future date, given the one condition that they have sufficient information on how the local topography of the site modifies the tide. Local geographical conditions such as the width of a bay’s mouth, the uneven slope of the bottom, and the depth of the body of water are the types of features that determine the range, amplitude, and time of the local tide. It is observed that the island of Nantucket, off the coast of the U.S. state of Massachusetts, experiences a difference of no more than 0.3 meter between high and low water, while only a few hundred kilometers away, the Bay of Fundy, in the Canadian province of Nova Scotia, has the highest tides in the world, with a rise of 15 meters during spring tides. To account for such phenomena, scientists have developed a model of tidal oscillation, in which the ocean structure is divided up among a great many basins of water, each with its own depth, length, and resulting period of oscillation. The boundaries of each basin are determined by the surrounding land forms, both above and below the ocean, and the influences of gravitational attraction in each are always changing, as are the currents that flow in. Ordinarily, when water rocks up and down in a basin, the water at the rim is most active, while the least amount of motion occurs in the center of the basin around a tideless node. Thus the physical dimensions of these basins determine the period of oscillation of the waters throughout the basin.

Opposing Tidal Bulges

When the pull of the moon creates a high tide on the side of Earth closest to it, a high tide occurs simultaneously on the opposite side of the planet. Logically, one would not expect this to be the case. To understand this, it is necessary to know that the moon and Earth revolve not only around each other but also around a common center of gravity located 1,600 kilometers below the surface of Earth. As the Earth and moon revolve, the centrifugal force stretches the oceans outward against Earth’s gravity. At its center, Earth is not still but is moving in a circle that is a small fraction of the size of the moon’s orbit. This invisible revolution of Earth around the moon produces a centrifugal force throughout Earth, which varies as the moon revolves and pulls Earth’s surface out of shape. It is the resulting “prolate,” or lemon-shaped, elongations of Earth that are observed as the tides. The tides nearest the moon are caused by gravitational attraction. On the side of Earth farthest from the moon, however, the centrifugal force is greater than the pull of the moon. To compound the complexity of the situation, the moon’s gravitational force is also pulling the ocean floor of that area away from the waters there. Thus high tides are produced on both sides of Earth in line with the moon.

Because tides are actually long waves, an observer on the moon might expect to see the two tidal bulges move around Earth at a speed consistent with the pace of the moon. Instead, tidal waves move out of step with the moon. Keeping pace with the moon would be possible under two conditions: if the oceans of the world were 22 kilometers deep (they average a bit more than 3 kilometers deep) and if there were no continents obstructing the movement of tidal waves. Thus, the speed of the movement of the tides is only 1,100 to 1,300 kilometers per hour, and the tides do not keep up with the moon as it travels westward around the terrestrial globe.

Earth’s Angular Momentum

The angular momentum of Earth is slowed by ocean tides. Because the momentum of the Earth-moon system is conserved, the slowing of Earth results in a speeding up of the moon’s rotation around Earth. For unknown geophysical reasons, several abrupt increases in the length of Earth’s day, some approaching 1 millisecond, have been observed over the past several decades. Ocean tides are not responsible for these abrupt changes but rather for small, steady increases over millennia. However, the U.S. National Bureau of Standards must sometimes add a “leap second” to the Earth year to take into account the observed slowing of Earth. Assuming that the position of Earth’s orbital distance with respect to the sun has not changed, the number of days in a year has changed from about 400 during the Devonian period to about 365 at the current time. Thus, the current length of a day is now quite a bit longer than it was during the Devonian, about 400 million years ago. Over this same time period, the moon’s angular momentum is estimated to have increased by about 1.6 percent. As Earth’s rotation slows and the moon revolves around Earth more quickly, the moon moves farther away from Earth. Accordingly, the moon has moved about 1.6 kilometers away from Earth in the last 100,000 years.

Study of Ocean Tides

Tides are not simple to predict. Qualitative prediction of the tides has been going on in harbors around the world for centuries, but quantitative prediction began in the nineteenth century, when people first designed tide-predicting machines to help forecast the tides. The first such machine was invented in 1872 by Lord Kelvin, who is often referred to as the first electrical engineer. Kelvin’s machine was capable of drawing a line picture of the curve of the tide, and for this achievement he was knighted. Soon after this breakthrough, an employee of the United States Coast and Geodetic Survey invented a tide-predicting machine that showed the times and heights of the tides. The survey later designed a simpler machine that combines the capabilities of both previous inventions: It gives the curve of the tides as well as the times and the heights of the tides. Unfortunately, these machines are not completely reliable because other factors, such as heavy storms, winds, or accumulation of sand as a result of wave action, can have dramatic impact on the water levels. Tide tables can only give the approximate high and low tides.

Today, tide-predicting machines have been replaced by faster digital computers. Tidal analysis still involves many complex computations, and predictions can be made only for places where a long series of observations are available. For each given spot on Earth, and for given time intervals, observations must be made that provide the value of the gravitational acceleration, the deflection of the vertical, and the measurements for the elevation of the water level. With this set of numbers in hand, the matter of prediction becomes one of extrapolating from the past into the future. Thus, around the coasts of the world, in inlets, in tidal rivers, and on islands, the water levels caused by tidal forces are carefully recorded. These measurements are analyzed locally. Once these measurements of the water level at a given place are taken within specified time intervals, the phases and amplitudes of the tide can be determined by a number of mathematical methods. Then, knowing the phases and amplitudes, scientists can reproduce the measurements according to a harmonic series. This harmonic method is a fairly reliable means of tidal prediction for deep-water ports, but in shallow-water areas, nonharmonic methods may need to be used. Finally, a determination of harmonic constants is made by national authorities, and the resulting data are sent to the International Hydrographic Bureau in Monaco. As a result, hydrographic offices in countries around the globe publish tide tables forecasting the high- and low-water times and water heights for the world’s ports.

The problem of the measurement of tidal displacements in the open ocean has yet to be solved. This situation results from the fact that tidal sea-level records pertain primarily to coastal locations, and there are few or no measurements from the open ocean.

Significance

Knowledge of ocean tides serves crucial purposes in the fields of navigation, coastal engineering, and tidal power generation. In addition, it holds a key position in relation to geophysics, marine geodesy, and astronomy.

Tides are of vital importance in navigation. Although the tides have become more predictable, and hence tamer, they still both help and hinder all mariners. The Coast Pilots and Sailing Directions for different parts of the world reveals the menacing possibilities which tides in various places are known to cause. Tidal currents often move violently when opposed by winds or confined in narrow channels. People have been swept off boats by an onslaught of giant waves when sailing in a flood tide through narrow straits. At certain stages of the tide, the waters can have dangerous eddies, whirlpools, or bores. A bore is created when a large portion of the flood tide enters a channel at once as one wave. Wherever they occur, they control the schedule of all shipping, as well as the rhythm of harbor life in the area. Even where there are no bores, the largest oceangoing liner must wait for slack water before entering a harbor where rushing tidal currents can fling it against piers. Since it is to the ship’s advantage to sail in the direction of the tidal current flow, knowledge of tides is invaluable. All navigators approaching a coast rely on tide tables to supplement the information on depths in their nautical charts.

Coastal-engineering work is dependent on knowledge of the tides for such undertakings as the management of tidal estuaries, construction of harbors, and damming of tidal rivers. Another practical aspect of tide information concerns the handling of problems that arise from the pollution of coastal waters and the ocean.

Tidal power generation is a new field that has gained increasing attention because of the shortage of available energy sources. Humans have long dreamed of harnessing the tidal forces for their energy needs. In 1966, the first tidal power station ever built was completed in the La Rance estuary in France. Construction of the project took place just after the Suez crisis, when France felt uncertain about the future of its oil supply. The half-mile Rance Dam was built to harness energy from the very large tides of the area—with a mean range of nearly 8.5 meters and rising to more than 13 meters at equinoctial spring tides. This power installation transmits electricity to Paris and the surrounding area, producing more than 580 billion watt-hours of energy a year but costing slightly more than the cost of operation of hydroelectric plants. In 1968, the Soviet Union finished construction on a 400-kilowatt tidal plant north of Murmansk, at a site where the maximum tide is less than 4 meters in height. In 2004, China announced plans for a tidal plant that would be the world’s largest, sited where a famous bore occurs on the mouth of the Yalu River. In the United States, at Passamaquoddy Bay in Maine, a major tidal power plant project was abandoned because of the expense of maintaining the pipes and machinery in saltwater, and of transmitting the electricity generated to the nearest big users.

Additional areas of practical concern involving tides include the correlation of tides with earthquakes, volcanic eruptions, and geyser activity. Some scientists believe that the pressures exerted by water moving with the tides can trigger earthquakes.

Principal Terms

basins: container-like places on the ocean floor, usually elliptical, circular, or oval in shape, varying in depth and size

bore: a sudden rise in water level in a river channel manifested as an incoming wave of tidal waters

diurnal tide: having only one high tide and one low tide each lunar day; tides on some parts of the Gulf of Mexico are diurnal

mixed tide: having the characteristics of diurnal and semidiurnal tidal oscillations; these tides are found on the Pacific coast of the United States

neap tide: a tide with the minimum range, or when the level of the high tide is at its lowest

range: the difference between the high-tide water level and the low-tide water level

semidiurnal: having two high tides and two low tides each lunar day

spring tide: a tide with the maximum range, occurring when lunar and solar tides reinforce each other a few days after the full and new moons

Bibliography

Boyle, Godfrey, ed. Renewable Energy. 2d ed. New York: Oxford University Press, 2004. Provides a complete overview of renewable energy resources. Discusses solar energy, bioenergy, geothermal energy, hydroelectric energy, tidal power, wind energy, and wave energy, as well as the basic physics principles, technology, and environmental impact. Contains references and a further reading list. An excellent starting point, although the advanced technical details of these power supplies are limited.

Christopherson, Robert W., and Mary-Louise Byrne. Geosystems: An Introduction to Physical Geography. Toronto: Pearson Prentice Hall, 2006. Begins with the basic principles of Earth-sun interactions to deliver an in-depth overview of Earth as a whole made up of individual systems, of which the oceans and their behavior is a major part.

Freuchen, Peter. Peter Freuchen’s Book of the Seven Seas. Guilford, Conn.: The Lyons Press, 2003. A well-written general-interest book that gives a very clear explanation of the tides. Includes scientific explanations for laypersons of all ages, as well as folklore and history as the author imagined it. An entertaining book full of photographs.

Garrison, Tom S. Essentials of Oceanography. 6th ed. Belmont, Calif.: Brooks/Cole Cengage Learning, 2012. An undergraduate textbook designed for nonscience students in an introductory oceanography course that presents an entertaining overview of the ocean environment.

‗‗‗‗‗‗‗. Oceanography: An Invitation to Marine Science. Belmont, Calif.: Brooks/Cole, Cengage Learning, 2010. Discusses the circulation of the oceans, including deep water and surface currents. Also discusses various aspects of waves and the physics of tides. Abundant diagrams aid readers from the layperson to advanced undergraduates.

Gregory, R. L., ed. Tidal Power and Estuary Management. Dorchester, England: Henry Ling, 1978. A collection of papers presented at the Symposium on Tidal Energy and Estuary Management, held under the auspices of the Colston Research Society at the University of Bristol in 1978. Written by eminent authorities in the field of estuary management, many of them associated with tidal power production. Presents a holistic picture of the research and thinking in two of the fields most intensively concerned with the tides. Includes the viewpoints of engineers, botanists, zoologists, mathematicians, and economists to make interesting reading.

Hamblin, Kenneth W., and Eric H. Christiansen. Earth’s Dynamic Systems. 10th ed. Upper Saddle River, N.J.: Prentice Hall, 2003. A geology textbook that offers an integrated view of Earth’s interior not common in books of this type. Includes excellent illustrations, diagrams, and charts, as well as a glossary and laboratory guide. Suitable for high school readers.

Komar, Paul D. Beach Process and Sedimentation. Upper Saddle River, N.J.: Prentice Hall, 1998. Provides extensive treatment of waves, longshore currents, and sand transport on beaches. Presents and elaborates upon equations and mathematical relationships. College-level material. Intended for those interested in the specifics of coastal processes.

Koppel, Tom. Ebb and Flow: Tides and Life on Our Once and Future Planet. Ontario: Dundern Press, 2007. Presents a discussion of how tides influence the interaction between the ocean and humans. Blends detailed descriptions of the development of tidal theory, tidal influence of coastline characteristics, and current knowledge of tides into a single theme. Easily accessible to the general public and of interest to any ocean-lover.

McCully, James Greig. Beyond the Moon: A Conversational, Common Sense Guide to Understanding the Tides. Hackensack, N.J.: World Scientific Publishing, 2006. Written in a manner that can easily be understood by the layperson. Covers the physics concepts behind tidal motions. Gradually guides the reader through the topics to reach a strong understanding by the end.

Melchoir, Paul. The Tides of the Planet Earth. Elmsford, N.Y.: Pergamon Press, 1978. Written by one of the foremost authorities on tides. Suited for college-level readers who are not intimidated by technical language and who understand some mathematics or are willing to skip through it. Extensive bibliography covers all papers to 1978 published on the subject of tides and related topics. The introduction gives a brief summary of the relation of tidal research to the fields of astronomy, geodesy, geophysics, oceanography, hydrology, and tectonics, as well as a brief history of discoveries made about tides.

Schwartz, M. Encyclopedia of Coastal Science. Dordrecht: Springer, 2005. Contains many articles specific to ocean and beach dynamics. Also discusses coastal habitat management topics, hydrology, geology, and topography. Articles may run multiple pages and have diagrams. Each article has bibliographical information and cross referencing.

Talley, Lynne D., George L. Pickard, William J. Emery, and James H. Swift. Descriptive Physical Oceanography: An Introduction. 6th ed. London: Elsevier, 2011. An introductory college-level textbook for students who will specialize in the field of oceanography.

Wilhelm, Helmut, Walter Zuern, Hans-Georg Wenzel, et al., eds. Tidal Phenomena. Berlin: Springer, 1997. A collection of lectures from leaders in the fields of earth sciences and oceanography. Examines Earth’s tides and atmospheric circulation. Complete with illustrations and bibliographical references. Can be understood by someone without a strong knowledge of the earth sciences.

Wylie, Francis E. Tides and the Pull of the Moon. Brattleboro, Vt.: Stephen Greene Press, 1979. Presents a lucid account of lunar and tidal phenomena and their influences on daily life. Includes information from science, history, and marine lore. Contains extensive bibliographical notes at the end of each chapter to guide readers to excellent sources on each topic covered. A complete introduction for anyone interested in the subject.