Tides
Tides
Variables affecting tidal forces
Effect of the moon’s motion around Earth
Some side effects of the tides
Tides are deformations in the shape of a body caused by the gravitational force of one or more other bodies. All bodies in the universe exert tidal forces on each other, although the effects are generally too small to observe. As far as Earth is concerned, the most important tidal phenomena are the ocean and ground tides that occur as a result of the moon’s and the sun’s gravity.
History
one of the earliest careful observers of ocean tides was the Greek geographer Pytheas of Massalia. In about the third century BC, Pytheas traveled outside the Straits of Gibraltar and observed tidal action in the Atlantic Ocean. (Tides were essentially absent from the Mediterranean Sea, which was more familiar to the Greeks.) Pytheas proposed an explanation for tidal action: the pull of the moon on Earth’s oceans, he said, caused the tides. This explanation is now known to be basically correct, although it was not widely accepted by scientists until the eighteenth century. English physicist Sir Isaac Newton (1642–1727) first succeeded in mathematically describing the tides in what is known as the equilibrium tidal theory.
Theories of tidal action
The side of Earth that faces the moon experiences a larger gravitational pull, due to the moon’s closer proximity, than other parts of Earth. This force causes Earth itself to bulge slightly toward the moon. This bulge is termed an Earth tide. Since water is free to move horizontally, the oceans tend to flow over Earth’s surface and collect in a secondary bulge on top of the Earth tide; this water bulge is termed an ocean tide.
At the same time, an Earth tide and an ocean tide form on the opposite side of Earth, directly away from the moon. This second bulge forms as follows (focusing on the ocean tide alone, for clarity): the moon and Earth, like all pairs of bodies orbiting each other in space, actually orbit around their common center of mass (that is, the point where, if their individual centers were attached to opposite ends of a rigid stick, the stick could be suspended from a string and remain in balance).
In the case of the Earth-moon system, the common center of mass happens to be inside Earth, about 1,068 miles (663 km) beneath the surface along a line connecting the center of Earth to the center of the moon. As Earth and moon revolve around this point like dancers spinning with linked hands, all points on both bodies experience a centrifugal force. This centrifugal force has the same magnitude and direction at every point on and in Earth (i.e., away from the moon parallel to a line connecting the center of Earth to the center of the moon). Where Earth’s surface is at any angle other than 90° to the line connecting the center of Earth to the center of the moon, water experiences a horizontal component of this centrifugal force. On the half of Earth’s surface facing away from the moon, this horizontal force overcomes the pull of the moon’s gravity and causes water to flow over Earth’s surface to a point on the side of Earth directly opposite the moon-facing tidal bulge. A second tidal bulge thus forms on the side of Earth facing directly away from the moon. This bulge is slightly smaller than the moon-facing bulge because the imbalance between the moon’s gravitation and centrifugal force is smaller at this point. (The moon is closer to the moon-facing bulge, making its gravitation stronger there, whereas the centrifugal force considered here is the same everywhere on Earth.) The larger, moon-facing tide is termed the direct tide; the tide on the opposite side of Earth is termed the opposite tide.
These two tidal bulges—one moon-facing or direct, the other on the opposite side of Earth—are the high tides. Because Earth is spherical, these bulges are actually arcs, meeting at the poles to form a globe-girdling ring or belt of high tide aligned with the moon. (Centrifugal force and the moon’s gravity cancel exactly at the poles, so the high tide is, in this simplified model, highest at the equator and diminishes to zero toward the poles.) Movement of water to this high-tide belt causes a complementary belt of low water to form around Earth at 90° to the line connecting the centers of Earth and moon. This belt produces the phenomenon known as low tide.
The high-tide belt always lies along the line connecting the centers of Earth and moon; however, as Earth rotates daily on its axis, land areas approach this belt, pass through it, and leave it behind. Thus, from the point of view of an observer fixed to the surface of the rotating Earth, the ocean tides are continually sloshing up against some coastlines and draining away from others. As a result, most coastal areas experience two high tides and two low tides each day. One high tide corresponds to the high-tide arc facing the moon, and the other to the high-tide arc facing away from moon.
The sun forms similar tidal bulges in Earth and its oceans, one set due to gravitation and the other to centrifugal force. However, sun’s tidal effect is slightly less than one half that of the moon. (It is both more massive than the moon and more distant; distance wins.) As the moon orbits Earth every 28 days, it twice comes into alignment with Earth and the sun—once when it is directly between Earth and the sun (i.e., when observers on Earth see the shadowed side of the moon) and once when Earth is directly between itself and the the sun (i.e., when observers on Earth see the illuminated or “full” side of the moon). When the moon and the sun are aligned, their tidal forces add up to produce a maximum tidal change. These maximal tides are termed spring tides because the waters of the ocean “spring up” higher (and sink lower) at these times. When the moon and the sun are at right angles to each other (i.e., when the moon is half-illuminated as seen from Earth), the solar and lunar tidal bulges do not add, and the least dramatic tides of the month are observed. These are termed neap tides.
Variables affecting tidal forces
Physicists have derived precise mathematical expressions to describe the gravitational effects of the moon and the sun on Earth. In theory, therefore, it should be possible to make precise predictions of the timing and sizes of all of ocean tides. In fact, absolutely precise predictions are not possible because a large number of factors contribute to the tides at a particular location. Primary among these is that the shape of ocean basins is so irregular that the water in them cannot behave in a simple way. Other variables also complicate the situation. These include variations in Earth’s axial rotation and variations in Earth-moon-sun positioning, including variations in orbital distance and inclination. Estimates of tidal behavior are therefore still based primarily on previous tidal observations, continuous monitoring of coastal water levels, and astronomical tables. (Comparison of predicted with measured tides along United States coasts can be checked at <http://tidesonline.nos.noaa.gov/>, a Website maintained by the U.S. government.)
Tide tables
Data about tidal patterns accumulated in various parts of the world are used to produce tide tables. Tide tables are constructed by examining records to find out, for any given location, the times at which high and low tides have occurred in the past and the levels that those tides have reached. These records are then used to predict the most likely times and levels expected for tides at various times in the future for the same locations. Because of differences in ocean bottoms, coastline shape, and other factors, unique tide tables must be constructed for each specific coastline in the world.
Semidiurnal and diurnal tides
In most places, tides are semidiurnal (twice-daily), meaning that there are two tidal cycles (with one high tide and one low apiece) each day. In other words, during a typical day the tides reach their highest point along the shore and their lowest point twice each day. The high-water level reached during one of the high tide stages is usually higher than the other high point, and the low water level reached during one of the low tide stages is usually lower than the other low tide point. This difference is called the diurnal inequality of the tides.
In a few locations, tides occur only once a day, with a single high tide and a single low tide. Such tidal cycles are known as diurnal (daily) tides. In both diurnal and semidiurnal settings, a rising tide is termed a flood tide and a falling tide is termed an ebb tide. The moment when the water reaches its highest point at high tide (or its lowest point at low tide) is called the slack tide, since the water level is then static, neither rising nor falling, at least for a short time.
Effect of the moon’s motion around Earth
As Earth spins on its axis, completing one turn every 24 hours, the moon orbits around Earth, completing one orbit every 28 days. Consequently, during the time Earth rotates once (24 hours), the moon has moved across about 1/28th of the sky. Earth, consequently, must rotate one day plus 1/28th of a day (about 50 minutes) to bring the moon into the same position overhead. This time period—24 hours, 50 minutes—is termed a lunar day. Since tides are caused by the moon, they recur on a lunar-daily schedule, rather than a 24-hour schedule, and consequently shift their times of occurrence with respect to the 24-hour clock. As a result, on a coast with diurnal tides, each day the high tide (or low tide) will occur 50 minutes later than the day before; on a semidiurnal coast, each high tide (or low tide) will occur 12 hours, 25 minutes later than the previous high tide.
Tidal currents
Any movement of ocean water caused by tidal action is known as a tidal current. In open water, tidal currents are relatively weak and tend to change direction slowly and regularly throughout the day. They form a kind of rotary pattern that sweeps around the ocean like the minute hand on a clock. Closer to land, however, tidal currents tend to change direction rather quickly, flowing toward land during high tide and away from land during low tide. In many cases, this onshore and offshore tidal current flows up the mouth of a river or some other narrow opening. The tidal current may then attain velocities as great as 9 mi (15 km) an hour with crests as high as 10 ft (3 m) or more.
All coastal locations (as well as very large lakes) experience some variation in tidal range during each lunar cycle, due to the affects of neap versus spring tides. Most tides attain less than 10 ft (3 m) in size; 3–10 ft (1–3 m) is common. In some places, however, the tides may be much greater. These locations are characterized by ocean bottoms that act as funnels through which ocean waters rush upward towards or downward away from the shore. In the Bay of Fundy, Canada for example, the tidal range may be as great as 46 ft (14 m). At the opposite extreme, the Mediterranean, Baltic, and Caribbean Seas have tides of less than a foot (0.3 m).
Deep-ocean tidal currents also occur. In fact, it has recently been discovered that about half of the energy input by Earth-moon-sun system as it drags tides around Earth is dissipated in deep-ocean currents, and the rest in shallow-ocean currents. Some 3×1012 watts of energy are dissipated through friction in deep-ocean circulation alone, with profound long-term effects on Earth’s climate.
Some side effects of the tides
(1) Because Earth’s comparatively rapid rotation is continually dragging the tidal bulges away from their ideal locations, the moon-facing bulge is always slightly ahead of the moon in the direction of its orbit. (The moon orbits in the same sense as Earth spins.) The gravitational pull of the bulge thus tends to accelerate the moon slightly, which causes it to orbit slightly higher above Earth. The moon thus moves about 1.2 inches (3 cm) farther from Earth every year. As it moves away, the magnitude of the tides slowly decreases. (2) Tidal friction is slowing Earth’s axial spin. During the Jurassic period, for example, approximately 180 million years ago, the day was less than 23 hours long; when life first appeared on Earth, it was only about 20 hours long. Tidal friction long ago caused the moon to slow its own axial spin to the point where it now always keeps the same side facing Earth. This is a common effect in bodies orbiting more massive ones, as for example the inner moons of Saturn and Jupiter. (3) Stresses in Earth’s crust caused by the tides tend to trigger earthquakes. Frequency analysis of all recorded earthquakes shows that they have a strong tendency to occur on a semidiurnal basis, in accord with tidal stress.
Tidal power plants
Engineers have long recognized that the movement of tidal currents might be an inexpensive, efficient, and environmentally safe source of power for human use. In general, the plan would be to construct a dam across the entrance of an estuary through which tidal currents flow with significant speed. Then, as tidal currents flow into and out of the estuary twice each day, they could be used to drive turbines which, in turn, could be used to operate electrical generators.
One of the few commercial tidal power stations in operation is located at the mouth of the La Rance River in France. Tides at this location reach a maximum of 44 ft (13.5 m). Each time the tide comes in, a dam at the La Rance station holds water back until it reaches its maximum depth. At that point, gates in the dam are opened and water is forced to flow into the La Rance River, driving a turbine and generator in the process. Gates in the dam are then closed, trapping the water inside the dam. At low tide, the gates open once again, allowing water to flow out of the river, back into the ocean. Again the power of moving water is used to drive a turbine and generator.
The plant is able to produce electricity only four times each day, during each of two high tides and each of two low tides. It generates a modest 250 megawatts in this way with an efficiency about equal to that of a fossil-fuel plant, 25%. With present technology, few other sites exist where tidal power generation is currently considered economically feasible.
See also Alternative energy sources; Gravity and gravitation.
Resources
BOOKS
Pugh, David. Changing Sea Levels: Effects of Tides, Weather and Climate. Cambridge, UK: Cambridge University Press, 2004.
PERIODICALS
Kasahara, Junzo. “Tides, Earthquakes, and Volcanoes.” Science Vol. 297 (July 19, 2002): 348-349.
KEY TERMS
Diurnal —Occurring once per day.
Ebb tide —The period when the water level is falling; the period after high tide and before low tide.
Flood tide —The period when the water level is rising; the period after low tide and before high tide.
High tide —The event corresponding to the largest increase in water level in an area that is induced by tidal forces.
Low tide —The event corresponding to the largest decrease in water level in an area that is induced by tidal forces.
Neap tides —Period of minimum tidal range that occurs about every two weeks when moon and sun are at 90° to each other, that is, at the first and third quarter moons.
Period —The interval of time between two recurring events, such as the high tides in an area.
Semidiurnal —Occuring twice per day.
Slack tide —Period during which the water level is neither rising nor falling.
Spring tides —Period of maximum tidal range; occurs about every two weeks, when Moon and sun are in line with each other, i.e., at the new and full moons.
Tidal current —Horizontal movement of water due to tidal forces.
Tidal range —Vertical distance between high tide and low tide during a single tidal cycle.
Wunsch, Carl. “Moon, Tides and Climate.” Nature 405 (June 15, 2000): 743-744.
OTHER
National Oceanic and Atmospheric Administration, U.S. Department of Commerce. “Our Restless Tides: A Brief Explanation of the Basic Astronomical Factors which Produce Tides and Tidal Currents.” February, 1998. <http://www.co-ops.nos.noaa.gov/restles1.html> (accessed November 27, 2006).
K. Lee Lerner
Larry Gilman
David E. Newton