DEFINITION OF TIDES

The periodic rise and fall of the ocean surface, and

alternate submersion and exposure of the intertidal zone

along coasts. Currents caused by the rise and fall of the sea

surface are the strongest currents in the ocean and were

attributed to the gravitational effects of the Sun and Moon

since at least the times of Pliny the Elder (23–79 C.E.).

The range in sea surface height between the high and

low is known as the tidal range, and this varies considerably

from barely detectable to more than 50 feet (15 m). Most

places have two high tides and two low tides each tidal day, a

period of about 24 hours and 50 minutes, corresponding to

the time between successive passes of the Moon over any

point. The tidal period is the time between successive high or

low tides. Places with two high and two low tides per day

have semidaily or semidiurnal tides. Fewer places have only

one high and one low tide per day, a cycle referred to as a

diurnal or daily tide. Semidiurnal tides are often not equal in

heights between the two highs and two lows.

Spring tides are those that occur near the full and new

Moons and have a tidal range larger than the mean tidal

range. In contrast, neap tides occur during the first and third

quarters of the Moon and are characterized by lower than

average tidal ranges.

Sir Isaac Newton was the first to clearly elucidate the

mechanics of tides, and how they are related to the gravita-

tional attraction of the Moon. In his equilibrium theory of

tides he assumed a nonrotating Earth, covered with water

and having no continents. In this simplified model aimed at

understanding the origin of tides, gravitational attraction

pulls the Earth and Moon toward each other, while centrifugal

forces act in the opposite direction and keep them apart.

Since the Moon is so much smaller than the Earth, the center

of mass and rotation of the Earth-Moon system is located

within the Earth 2,900 miles (4,670 km) from the Earth’s

center, on the side of the Earth closest to the Moon. This

causes unbalanced forces since a unit of water on the Earth’s

surface closest to the Moon is located 59 Earth radii from the

Moon’s surface, whereas a unit of water on the opposite side

of the Earth is located 61 Earth radii from the nearest point

on the Moon. Since the force of gravity is inversely proportional

to the distance squared between the two points, the

Moon’s gravitational pull is much greater for the unit of

water closer to the Moon. However, centrifugal forces that

act perpendicular to the axis of rotation of the Earth also

affect the tides and must be added with the gravitational

forces to yield a vector sum that is the tide producing force.

Together these forces result in the gravitational force of the

Moon exceeding the centrifugal force on the side of Earth

closest to the Moon, drawing water in a bulge toward the

Moon. On the opposite side of the Earth the centrifugal force

overbalances the gravitational attraction of the Moon so

there the water is essentially dragged away from the Earth.

The interaction of the gravitational forces and centrifugal

forces creates a more complex pattern of tides on Newton’s

model Earth. Directly beneath the Moon and on the

opposite side of the Earth, both the gravitational force and

the centrifugal force act perpendicular to the surface, but

elsewhere the vector sum of the two forces is not perpendicular

to the surface. The result of adding the centrifugal force

and gravity vectors is a two-sided egg-shaped bulge that

points toward and away from the Moon. Newton called

these bulges the equilibrium tide. The situation, however, is

even more complex, since the Sun also exerts a gravitational

attraction on the Earth and its water, forming an additional

egg-shaped bulge that is about 0.46 times as large as the

lunar tidal bulge.

If we consider the Earth to be rotating through the tidal

bulges on a water-covered planet, the simplest situation arises

with two high tides and two low tides each day, since the lunar

tides dominate over the effects of the solar tides. However, the

Earth has continents that hinder the equal flow of water, and

bays and estuaries that trap and amplify the tides in certain

places, plus frictional drag slows the passage of the tidal bulge

through shallow waters. In addition, the Coriolis Force must

be taken into account as tides involve considerable movement

of water from one place to another. These obstacles cause the

tides to be different at different places on the Earth, explaining

the large range in observed tidal ranges and periods.

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