Spatially, tidal range varies according to the hydrodynamic response of a particular ocean basin, shelf sea,
bay, or estuary to astronomical tidal forcing (Figure 1).
Tidal ranges are typically smallest in the open ocean,
along open ocean coastlines, and in almost fully enclosed
seas, such as the Mediterranean. Conversely, tidal ranges
are usually largest in semi-enclosed seas and funnelshaped entrances of bays and estuaries, such as the Bay
of Fundy in Canada or Bristol Channel in the UK, or
regions where a continental shelf has the right combination of depth and width for tidal resonance to occur, such
as on the northwest Australian shelf. Tides are often
crudely classified by their mean range into macrotidal
(>4 m), mesotidal (2–4 m), and microtidal (<2 m).
Bibliography
Davies, J. L., 1980. Geographical Variation in Coastal Development. New York: Longman.
Egbert, G. D., and Erofeeva, S., 2002. Efficient inverse modeling of
barotropic ocean tides. Journal of Atmospheric and Oceanic
Technology, 19(2), 183–204.
Haigh, I. D., Eliot, M., and Pattiaratchi, C., 2011. Modeling global
influences of the 18.6-year nodal cycle and quasi-4.4 year cycle
on high tidal levels. Journal of Geophysical Research-Oceans,
116, C06025, doi:10.1029/2010JC006645.
Stembridge, J. S., 1982. Tidal range and variation. In Schwartz,
M. L. (ed.), Encyclopedia of Beaches and Coastal Environments. Dordrecht: Springer.
Cross-references
Tidal Datum
Tides
TIDAL REFLECTION
Manuel Díez-Minguito, Asunción Baquerizo Azofra,
Miguel Ortega-Sánchez and Miguel A. Losada Rodríguez
Andalusian Institute for Earth System Research,
University of Granada, Granada, Spain
Synonyms
Tidal wave reflection
Definition
Tidal reflection is a transformation process experienced by
a tidal wave in which all or part of its energy bounces back
due to geometric variations in the boundaries.
Description
Reflection is a common phenomenon experienced by
waves, and water waves are not an exception. Tidal wave
reflection occurs in a wide range of spatial scales, ranging
from tens of meters to thousands of kilometers. Semienclosed bodies of water, such as estuaries, allow
(co-oscillating) tides to enter through their open boundaries. As the tidal wave propagates upstream, bathymetric
and topographic changes and the presence of obstacles
bounce back all or part of the incoming tidal energy. Prominent tidal reflections typically occur at abrupt channel
constrictions and at upstream dams and weirs (e.g., in
the Guadalquivir estuary in Spain and in the Ems in the
Netherlands). Tidal reflection changes the structure of
tidal currents and ranges, which in turn affects the dynamics of sediments and other solutes, and may also generate
residual movements with consequences in the long-term
morphology, water quality, and biota.
The prototypical case of tidal reflection is that of
a monochromatic tidal wave propagating into a straight,
frictionless channel of constant depth and width that is
closed at its head with an impermeable barrier. When the
traveling tidal wave encounters the head, all its energy is
reflected back as a sinusoidal wave of the same amplitude
and frequency that propagates in the opposite direction.
Physically, the oscillation resulting from their superposition is a standing wave with an antinode at the head, i.e.,
a position where the current vanishes and the amplitude
is twice the amplitude of the incoming wave. If the semienclosed body is long enough in comparison to tidal
wavelength, at even/odd multiples of a quarter of the
wavelength off the head, antinodes/nodes are observed.
A tidal node is a location where the free surface does not
vary (null tidal elevation), and maximum along-channel
current amplitude occurs. Because the wave length
depends on the tidal period, different constituents will
exhibit different nodal point locations. For standing
waves, the tidal elevation and the current velocity are
p/2 out of phase. In fact, the character of the tidal wave
is usually analyzed (although not uniquely characterized)
by comparing the phase lag between the high water and
the high water slack with the values that would be
obtained under ideal conditions for standing waves
(0) and progressive waves (T/4), where T is the tidal
period. Resonance phenomena are also possible and not
infrequent in estuaries. For a given constituent, resonance
may occur if the estuary length L is about a quarter wavelength of the forcing tide or odd multiples of thereof. This
means that the ratio of the maximum tide at the closed end
to the tide at the entrance becomes large. Perhaps the most
dramatic example of quarter-wave resonance is that
observed for the M2 semidiurnal tidal constituent in the
Bay of Fundy (Canada).
Friction dampens both the incident and reflected wave;
modifies their wave numbers, which depend on the alongchannel position; and also moves the position of nodes
and antinodes. If dissipation is significant and the estuary
is long enough, tidal energy may not reach the closed end
and no reflected wave is generated there. Even though the
incoming wave arrives with sufficient energy to the closed
end, the effective impact of tidal reflection may be limited
to a fraction of the estuary. The region of influence of tidal
reflection can be delimited by the position at which the
ratio between the amplitudes of the reflected and the incident waves is small. This practical approach requires separating the incident and the reflected wave by means of
704
TIDAL REFLECTION
bay, or estuary to astronomical tidal forcing (Figure 1).
Tidal ranges are typically smallest in the open ocean,
along open ocean coastlines, and in almost fully enclosed
seas, such as the Mediterranean. Conversely, tidal ranges
are usually largest in semi-enclosed seas and funnelshaped entrances of bays and estuaries, such as the Bay
of Fundy in Canada or Bristol Channel in the UK, or
regions where a continental shelf has the right combination of depth and width for tidal resonance to occur, such
as on the northwest Australian shelf. Tides are often
crudely classified by their mean range into macrotidal
(>4 m), mesotidal (2–4 m), and microtidal (<2 m).
Bibliography
Davies, J. L., 1980. Geographical Variation in Coastal Development. New York: Longman.
Egbert, G. D., and Erofeeva, S., 2002. Efficient inverse modeling of
barotropic ocean tides. Journal of Atmospheric and Oceanic
Technology, 19(2), 183–204.
Haigh, I. D., Eliot, M., and Pattiaratchi, C., 2011. Modeling global
influences of the 18.6-year nodal cycle and quasi-4.4 year cycle
on high tidal levels. Journal of Geophysical Research-Oceans,
116, C06025, doi:10.1029/2010JC006645.
Stembridge, J. S., 1982. Tidal range and variation. In Schwartz,
M. L. (ed.), Encyclopedia of Beaches and Coastal Environments. Dordrecht: Springer.
Cross-references
Tidal Datum
Tides
TIDAL REFLECTION
Manuel Díez-Minguito, Asunción Baquerizo Azofra,
Miguel Ortega-Sánchez and Miguel A. Losada Rodríguez
Andalusian Institute for Earth System Research,
University of Granada, Granada, Spain
Synonyms
Tidal wave reflection
Definition
Tidal reflection is a transformation process experienced by
a tidal wave in which all or part of its energy bounces back
due to geometric variations in the boundaries.
Description
Reflection is a common phenomenon experienced by
waves, and water waves are not an exception. Tidal wave
reflection occurs in a wide range of spatial scales, ranging
from tens of meters to thousands of kilometers. Semienclosed bodies of water, such as estuaries, allow
(co-oscillating) tides to enter through their open boundaries. As the tidal wave propagates upstream, bathymetric
and topographic changes and the presence of obstacles
bounce back all or part of the incoming tidal energy. Prominent tidal reflections typically occur at abrupt channel
constrictions and at upstream dams and weirs (e.g., in
the Guadalquivir estuary in Spain and in the Ems in the
Netherlands). Tidal reflection changes the structure of
tidal currents and ranges, which in turn affects the dynamics of sediments and other solutes, and may also generate
residual movements with consequences in the long-term
morphology, water quality, and biota.
The prototypical case of tidal reflection is that of
a monochromatic tidal wave propagating into a straight,
frictionless channel of constant depth and width that is
closed at its head with an impermeable barrier. When the
traveling tidal wave encounters the head, all its energy is
reflected back as a sinusoidal wave of the same amplitude
and frequency that propagates in the opposite direction.
Physically, the oscillation resulting from their superposition is a standing wave with an antinode at the head, i.e.,
a position where the current vanishes and the amplitude
is twice the amplitude of the incoming wave. If the semienclosed body is long enough in comparison to tidal
wavelength, at even/odd multiples of a quarter of the
wavelength off the head, antinodes/nodes are observed.
A tidal node is a location where the free surface does not
vary (null tidal elevation), and maximum along-channel
current amplitude occurs. Because the wave length
depends on the tidal period, different constituents will
exhibit different nodal point locations. For standing
waves, the tidal elevation and the current velocity are
p/2 out of phase. In fact, the character of the tidal wave
is usually analyzed (although not uniquely characterized)
by comparing the phase lag between the high water and
the high water slack with the values that would be
obtained under ideal conditions for standing waves
(0) and progressive waves (T/4), where T is the tidal
period. Resonance phenomena are also possible and not
infrequent in estuaries. For a given constituent, resonance
may occur if the estuary length L is about a quarter wavelength of the forcing tide or odd multiples of thereof. This
means that the ratio of the maximum tide at the closed end
to the tide at the entrance becomes large. Perhaps the most
dramatic example of quarter-wave resonance is that
observed for the M2 semidiurnal tidal constituent in the
Bay of Fundy (Canada).
Friction dampens both the incident and reflected wave;
modifies their wave numbers, which depend on the alongchannel position; and also moves the position of nodes
and antinodes. If dissipation is significant and the estuary
is long enough, tidal energy may not reach the closed end
and no reflected wave is generated there. Even though the
incoming wave arrives with sufficient energy to the closed
end, the effective impact of tidal reflection may be limited
to a fraction of the estuary. The region of influence of tidal
reflection can be delimited by the position at which the
ratio between the amplitudes of the reflected and the incident waves is small. This practical approach requires separating the incident and the reflected wave by means of
704
TIDAL REFLECTION