amphidromic systems are typically Kelvin waves, namely,
gravity waves influenced by earth rotation. They propagate along the coast, leaving it to the right (left) in the
northern (southern) hemisphere when facing in the direction of wave propagation. Their tidal ranges decrease
exponentially with increasing distance to the coast, and
currents are in geostrophic balance in the direction perpendicular to the propagation. With a few exceptions, the tidal
waves of amphidromic systems tend to rotate anticlockwise in the northern hemisphere and clockwise in the
southern hemisphere. Again, local resonance is possible
if the dimensions of the basin match the tidal wavelength.
For instance, the North Sea provides a good example of
a resonant amphidromic system.
Summary
Tidal wave reflection is a quite common transformation
process experienced by a tidal wave and occurs simultaneously in a wide range of spatial scales. Sometimes
the reflection is prominent (in terms of fraction of
reflected energy), as for instance at a head weir, but sometimes is subtle, as occurs when tides propagate into
a long, weakly convergent estuary. This phenomenon
can even change the wave nature. Tidal reflection may
generate residual movements which in turn influence to
a greater extent long-term estuarine morphology and
water quality.
Bibliography
Officer, C. B., 1976. Physical Oceanography of Estuaries (and
Associated Coastal Waters). New York: Wiley.
Ray, R., 2007. NASA-GSFC, NASA-JPL, Scientific Visualization
Studio, and Television Production NASA-TV/GSFC. TOPEX/
Poseidon: Revealing Hidden Tidal Energy.
Valle-Levinson, A. (ed.), 2010. Contemporary Issues in Estuarine
Physics. Cambridge: Cambridge University Press.
TIDES
Ivan D. Haigh
Ocean and Earth Science, National Oceanography Centre,
University of Southampton, European Way,
Southampton, UK
Definition
Tides are the regular and predictable rise and fall of the sea
caused by the gravitational attraction and rotation of the
earth, moon, and sun system.
Introduction
Tides are the regular and predictable rise and fall of the sea
caused by astronomical forcing. The study of tides has
a long history and is perhaps the oldest branch of physical
oceanography (Cartwright, 1999). One of the fascinations
of tides is the number and diversity of the practical and
scientific applications (Pugh, 1987). These include concern with problems of navigation, coastal flooding and
erosion, transport of pollutants, and the extraction of tidal
power. Tides also have a controlling influence on geological, sediment transport, water quality, and marine biological processes.
Tides are normally used to refer to the vertical change
in sea level, whereas the term tidal currents is used for
the horizontal movement of water (Parker, 2005). Sea
level relates to the vertical change in the height of the
sea surface which occurs over all time and space scales
from many different mechanisms (including waves,
seiches, storm surges, tsunamis), with tides being the
most predictable and the dominant component of
sea-level variability in many parts of the world’s oceans
and coasts. Water level is the height of the sea surface
above some reference level or benchmark, often called
a tidal datum. Mean sea level is the average height of
the sea over longer periods of time (usually a month or
year), and hence the shorter-term variations of the tide
are filtered out.
Tide-generating force
Newton’s laws of gravitation attraction and motion form
the basis for physical understanding of how tides are generated. The universal law of gravitational attraction states
that the force (F) of attraction of two particles of masses
M 1 and M 2 separated by distance R is
F ¼ G
M 1 M 2
R
2
ð1Þ
where G is the universal gravitational constant. Newton’s
laws of motion assert that a body (e.g., an element of seawater) remains at rest or constant velocity, unless acted
upon by a force, and that force is the product of a body’s
mass and acceleration.
To begin, consideration is given to the moon’s role in
generating tides. The earth and moon form a single system, mutually revolving around a common center of mass
(known as the barycenter), with a period of 27.32 days.
The earth is 81 times larger than the moon, and as
a result the location of the barycenter lies within the earth.
The earth and moon circle about the barycenter, without
any rotation in absolute space. Therefore, each point on
the earth travels in circles which have the same radius.
Hence, they experience an equal centrifugal force (F c ),
directed parallel to a line joining the centers of the earth
and moon. While the centrifugal force is the same everywhere on the earth, the gravitational force varies with location and is directed toward the center of the moon. The
local gravitation force (F g ) is given by
F g ¼ G
M e M m
R À r
ð
Þ
2
ð2Þ
where M e and M m are the mass of the earth and moon,
respectively, and r is the distance between the earth’s
706
TIDES
gravity waves influenced by earth rotation. They propagate along the coast, leaving it to the right (left) in the
northern (southern) hemisphere when facing in the direction of wave propagation. Their tidal ranges decrease
exponentially with increasing distance to the coast, and
currents are in geostrophic balance in the direction perpendicular to the propagation. With a few exceptions, the tidal
waves of amphidromic systems tend to rotate anticlockwise in the northern hemisphere and clockwise in the
southern hemisphere. Again, local resonance is possible
if the dimensions of the basin match the tidal wavelength.
For instance, the North Sea provides a good example of
a resonant amphidromic system.
Summary
Tidal wave reflection is a quite common transformation
process experienced by a tidal wave and occurs simultaneously in a wide range of spatial scales. Sometimes
the reflection is prominent (in terms of fraction of
reflected energy), as for instance at a head weir, but sometimes is subtle, as occurs when tides propagate into
a long, weakly convergent estuary. This phenomenon
can even change the wave nature. Tidal reflection may
generate residual movements which in turn influence to
a greater extent long-term estuarine morphology and
water quality.
Bibliography
Officer, C. B., 1976. Physical Oceanography of Estuaries (and
Associated Coastal Waters). New York: Wiley.
Ray, R., 2007. NASA-GSFC, NASA-JPL, Scientific Visualization
Studio, and Television Production NASA-TV/GSFC. TOPEX/
Poseidon: Revealing Hidden Tidal Energy.
Valle-Levinson, A. (ed.), 2010. Contemporary Issues in Estuarine
Physics. Cambridge: Cambridge University Press.
TIDES
Ivan D. Haigh
Ocean and Earth Science, National Oceanography Centre,
University of Southampton, European Way,
Southampton, UK
Definition
Tides are the regular and predictable rise and fall of the sea
caused by the gravitational attraction and rotation of the
earth, moon, and sun system.
Introduction
Tides are the regular and predictable rise and fall of the sea
caused by astronomical forcing. The study of tides has
a long history and is perhaps the oldest branch of physical
oceanography (Cartwright, 1999). One of the fascinations
of tides is the number and diversity of the practical and
scientific applications (Pugh, 1987). These include concern with problems of navigation, coastal flooding and
erosion, transport of pollutants, and the extraction of tidal
power. Tides also have a controlling influence on geological, sediment transport, water quality, and marine biological processes.
Tides are normally used to refer to the vertical change
in sea level, whereas the term tidal currents is used for
the horizontal movement of water (Parker, 2005). Sea
level relates to the vertical change in the height of the
sea surface which occurs over all time and space scales
from many different mechanisms (including waves,
seiches, storm surges, tsunamis), with tides being the
most predictable and the dominant component of
sea-level variability in many parts of the world’s oceans
and coasts. Water level is the height of the sea surface
above some reference level or benchmark, often called
a tidal datum. Mean sea level is the average height of
the sea over longer periods of time (usually a month or
year), and hence the shorter-term variations of the tide
are filtered out.
Tide-generating force
Newton’s laws of gravitation attraction and motion form
the basis for physical understanding of how tides are generated. The universal law of gravitational attraction states
that the force (F) of attraction of two particles of masses
M 1 and M 2 separated by distance R is
F ¼ G
M 1 M 2
R
2
ð1Þ
where G is the universal gravitational constant. Newton’s
laws of motion assert that a body (e.g., an element of seawater) remains at rest or constant velocity, unless acted
upon by a force, and that force is the product of a body’s
mass and acceleration.
To begin, consideration is given to the moon’s role in
generating tides. The earth and moon form a single system, mutually revolving around a common center of mass
(known as the barycenter), with a period of 27.32 days.
The earth is 81 times larger than the moon, and as
a result the location of the barycenter lies within the earth.
The earth and moon circle about the barycenter, without
any rotation in absolute space. Therefore, each point on
the earth travels in circles which have the same radius.
Hence, they experience an equal centrifugal force (F c ),
directed parallel to a line joining the centers of the earth
and moon. While the centrifugal force is the same everywhere on the earth, the gravitational force varies with location and is directed toward the center of the moon. The
local gravitation force (F g ) is given by
F g ¼ G
M e M m
R À r
ð
Þ
2
ð2Þ
where M e and M m are the mass of the earth and moon,
respectively, and r is the distance between the earth’s
706
TIDES