An amphidromic point, also called a tidal node, is a geographical location which has zero tidal
amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
for one
harmonic constituent of the
tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravity, gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another.
Tide t ...
. The
tidal range
Tidal range is the difference in height between high tide and low tide. Tides are the rise and fall of sea levels caused by gravitational forces exerted by the Moon and Sun and the rotation of Earth. Tidal range depends on time and location.
...
(the
peak-to-peak amplitude, or the height difference between high tide and low tide) for that harmonic constituent increases with distance from this point, though not uniformly. As such, the concept of amphidromic points is crucial to understanding tidal behaviour.
The term derives from the
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
words ''amphi'' ("around") and ''dromos'' ("running"), referring to the rotary tides which circulate around amphidromic points.
Amphidromic points occur because
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extr ...
within
oceanic basin
In hydrology, an oceanic basin (or ocean basin) is anywhere on Earth that is covered by seawater. Geologically, ocean basins are large geologic basins that are below sea level.
Most commonly the ocean is divided into basins fol ...
s,
sea
The sea, connected as the world ocean or simply the ocean, is the body of salty water that covers approximately 71% of the Earth's surface. The word sea is also used to denote second-order sections of the sea, such as the Mediterranean Sea, ...
s and bays, combined with the
Coriolis effect
In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
, creates a wave pattern — called an amphidromic system — which rotates around the amphidromic point.
At the amphidromic points of the dominant
tidal constituent
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another.
Tide tables c ...
, there is almost no vertical change in sea level from tidal action; that is, there is little or no difference between high tide and low tide at these locations. There can still be tidal currents since the water levels on either side of the amphidromic point are not the same. A separate amphidromic system is created by each periodic tidal component.
In most locations the
"principal lunar semi-diurnal", known as ''M''
2, is the largest tidal constituent. Cotidal lines connect points which reach high tide at the same time and low tide at the same time. In Figure 1, the low tide lags or leads by 1 hr 2 min from its neighboring lines. Where the lines meet are amphidromes, and the tide rotates around them; for example, along the Chilean coast, and from southern Mexico to Peru, the tide propagates southward, while from Baja California to Alaska the tide propagates northward.
Formation of amphidromic points
Tides are generated as a result of
gravitational attraction
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
by the
sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
and
moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
.
This gravitational attraction results in a
tidal force
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
that acts on the
ocean
The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wo ...
.
The ocean reacts to this external forcing by generating, in particular relevant for describing tidal behaviour,
Kelvin wave
A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the ...
s and
Poincaré waves (also known as
Sverdrup waves).
These tidal waves can be considered wide, relative to the
Rossby radius of deformation
In atmospheric dynamics and physical oceanography, the Rossby radius of deformation is the length scale at which rotational effects become as important as buoyancy or gravity wave effects in the evolution of the flow about some disturbance.
...
(~3000 km in the open ocean
), and shallow, as the water depth (''D'', on average ~4 kilometre deep
) in the ocean is much smaller (i.e. ''D''/''λ'' <1/20) than the
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
(''λ'') which is in the order of thousands of kilometres.
In real oceans, the tides cannot endlessly propagate as
progressive wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (r ...
s. The waves reflect due to changes in water depth (for example when entering
shelf seas) and at coastal boundaries.
The result is a
reflected wave that propagates in the opposite direction to the incident wave. The combination of the reflected wave and the incident wave is the total wave. Due to
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
between the reflected and the incident wave, the amplitude of the total wave can either be suppressed or amplified.
The points at which the two waves amplify each other are known as
antinodes and the points at which the two waves cancel each other out are known as
nodes
In general, a node is a localized swelling (a "knot") or a point of intersection (a Vertex (graph theory), vertex).
Node may refer to:
In mathematics
*Vertex (graph theory), a vertex in a mathematical graph
*Vertex (geometry), a point where two ...
. Figure 2 shows a λ resonator. The first node is located at λ of the total wave, followed by the next node reoccurring λ farther at λ.
A long, progressive wave travelling in a channel on a rotating earth behaves differently from a wave travelling along a non-rotating channel. Due to the
Coriolis force, the water in the ocean is deflected towards the right in the northern hemisphere and conversely in the southern hemisphere.
This side-way component of the flow due to the Coriolis force causes a build-up of water that results in a
pressure gradient
In atmospheric science, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The p ...
.
The resulting slope develops until it is
equilibrium with the Coriolis force; resulting in
geostrophic balance
In atmospheric science, balanced flow is an idealisation of atmospheric motion. The idealisation consists in considering the behaviour of one isolated parcel of air having constant density, its motion on a horizontal plane subject to selected for ...
. As a result of this geostrophic balance, Kelvin waves (originally described by
Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, Mathematical physics, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy (Glasgow), Professor of Natural Philoso ...
) and Poincaré waves are generated. The amplitude of a Kelvin wave is highest near the coast and, when considering a wave on the northern hemisphere, decreases to further away from its right-hand coastal boundary.
The propagation of Kelvin waves is always alongshore and its amplification falls off according to the Rossby radius of deformation.
In contrast, Poincaré waves are able to propagate both alongshore as a free wave with a propagating wave pattern and cross-shore as a trapped wave with a
standing wave pattern.
Infinitely long channel
In an infinitely long channel, which can be viewed upon as a simplified approximation of the
Atlantic Ocean
The Atlantic Ocean is the second-largest of the world's five oceans, with an area of about . It covers approximately 20% of Earth's surface and about 29% of its water surface area. It is known to separate the " Old World" of Africa, Europe ...
and
Pacific Ocean
The Pacific Ocean is the largest and deepest of Earth's five oceanic divisions. It extends from the Arctic Ocean in the north to the Southern Ocean (or, depending on definition, to Antarctica) in the south, and is bounded by the continen ...
, the tide propagates as an incident and a reflective Kelvin wave as shown in Animation 1. The red coloured lines indicate high tide and the blue coloured lines indicate low tide. Furthermore, the
vectors field below the basin in Animation 1 show the direction and the strength of the tidal current. The amplitude of the waves decreases further away from the coast and at certain points in the middle of the basin, the amplitude of the total wave becomes zero. Moreover, the phase of the tide seems to rotate around these points of zero amplitude. These points are called amphidromic points. The sense of rotation of the wave around the amphidromic point is in the direction of the Coriolis force; anticlockwise in the
northern hemisphere
The Northern Hemisphere is the half of Earth that is north of the Equator. For other planets in the Solar System, north is defined as being in the same celestial hemisphere relative to the invariable plane of the solar system as Earth's Nort ...
and clockwise in the
southern hemisphere.
Semi-enclosed basin
In a semi-enclosed basin, such as the North Sea, Kelvin waves, though being the dominant tidal wave propagating in alongshore direction, are not able to propagate cross shore as they rely on the presence of lateral boundaries or the
equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...
.
As such, the tidal waves observed cross-shore are predominantly Poincaré waves. The tides observed in a semi-enclosed basin are therefore chiefly the summation of the incident Kelvin wave, reflected Kelvin wave and cross-shore standing Poincaré wave. An animation of the tidal amplitude, tidal currents and its amphidromic behaviour is shown in Animation 2.
Position of amphidromic points
Figure 2 shows that the first node of the total wave is located at λ with reoccurring nodes at intervals of λ. In an idealized situation, amphidromic points can be found at the position of these nodes of the total tidal wave.
When neglecting friction, the position of the amphidromic points would be in the middle of the basin, as the initial amplitude and the amplitude decay of the incident wave and the reflected wave are equal, this can be seen in Animations 1 and 2
However, tidal waves in the ocean are subject to friction from the
seabed
The seabed (also known as the seafloor, sea floor, ocean floor, and ocean bottom) is the bottom of the ocean. All floors of the ocean are known as 'seabeds'.
The structure of the seabed of the global ocean is governed by plate tectonics. Most of ...
and from interaction with coastal boundaries. Moreover, variation in water depth influences the spacing between amphidromic points.
Firstly, the distance between amphidromic points is dependent on the water depth:
Where ''g'' is the
gravitational acceleration
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies ...
, ''D'' is the water depth and ''T'' is the
period
Period may refer to:
Common uses
* Era, a length or span of time
* Full stop (or period), a punctuation mark
Arts, entertainment, and media
* Period (music), a concept in musical composition
* Periodic sentence (or rhetorical period), a concept ...
of the wave.
Locations with more shallow water depth have their amphidromic points closer to each other as the distance of the interval (λ) of the nodes decreases. Secondly, energy losses due to friction in shallow seas and coastal boundaries result in additional adjustments of the tidal pattern.
Tidal waves are not perfectly reflected, resulting in energy loss which causes a smaller reflected wave compared to the incoming wave.
Consequently, on the northern hemisphere, the amphidromic point will be displaced from the centre line of the channel towards the left of the direction of the incident wave.
The degree of displacement on the northern hemisphere for the first amphidrome is given by:
Where γ is the displacement of the amphidrome from the centre of the channel (''γ''=0), ''g'' is the gravitational acceleration, ''D'' is the water depth, ''f'' is the
Coriolis frequency
The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the latitude \varphi.
:f = 2 \Omega \sin \varphi.\,
The rotation rate o ...
and ''α'' is the ratio between amplitudes of the reflected wave and the incident wave. Because the reflected wave is smaller than the incident wave,
''α'' will be smaller than 1 and ''lnα'' will be negative. Hence the amphidromic displacement ''γ'' is to the left of the incident wave on the northern hemisphere.
Furthermore, a study has shown than there is a pattern of amphidrome movement related to
spring-neap cycles in the
Irish Sea
The Irish Sea or , gv, Y Keayn Yernagh, sco, Erse Sie, gd, Muir Èireann , Ulster-Scots: ''Airish Sea'', cy, Môr Iwerddon . is an extensive body of water that separates the islands of Ireland and Great Britain. It is linked to the Ce ...
.
The maximum displacement of the amphidrome from the centre coincides with
spring tides
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another.
Tide tables ca ...
, whereas the minimum occurs at
neaps. During spring tides, more energy is absorbed from the tidal wave compared to neap tides. As a result, the reflection coefficient ''α'' is smaller and the displacement of the amphidromic point from the centre is larger. Similar amphidromic movement is expected in other seas where
energy dissipation
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
due to friction is high.
It can occur that the amphidromic point moves inland of the coastal boundary.
In this case, the amplitude and the phase of the tidal wave will still rotate around an inland point, which is called a virtual or degenerate amphidrome.
Amphidromic points and sea level rise
The position of amphidromic points and their movement predominantly depends on the wavelength of the tidal wave and friction. As a result of enhanced
greenhouse gas emissions
Greenhouse gas emissions from human activities strengthen the greenhouse effect, contributing to climate change. Most is carbon dioxide from burning fossil fuels: coal, oil, and natural gas. The largest emitters include coal in China and ...
, the oceans in the world are becoming subject to
sea-level rise
Globally, sea levels are rising due to human-caused climate change. Between 1901 and 2018, the globally averaged sea level rose by , or 1–2 mm per year on average.IPCC, 2019Summary for Policymakers InIPCC Special Report on the Ocean and Cryo ...
. As the water depth increases, the wavelength of the tidal wave will increase. Consequently the position of the amphidromic points located at λ in semi-enclosed systems will move further away from the cross-shore coastal boundary. Furthermore, amphidromic points will move further away from each other as the interval of λ increases. This effect will be more pronounced in shallow seas and coastal regions, as the relative water depth increase due to sea-level rise will be larger, when compared to the open ocean. Moreover, the amount of sea-level rise differs per region. Some regions will be subject to a higher rate of sea-level rise than other regions and nearby amphidromic points will be more susceptible to change location. Lastly, sea-level rise results in less bottom friction and therefore less energy dissipation.
This causes the amphidromic points to move further away from the coastal boundaries and more towards the centre its channel/basin.
In the ''M''2 tidal constituent
Based on Figure 1, there are the following
clockwise
Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite ...
and anticlockwise amphidromic points:
Clockwise amphidromic points
* north of the
Seychelles
Seychelles (, ; ), officially the Republic of Seychelles (french: link=no, République des Seychelles; Creole: ''La Repiblik Sesel''), is an archipelagic state consisting of 115 islands in the Indian Ocean. Its capital and largest city, V ...
* near
Enderby Land
Enderby Land is a projecting landmass of Antarctica. Its shore extends from Shinnan Glacier at about to William Scoresby Bay at , approximately of the earth's longitude. It was first documented in western and eastern literature in February 18 ...
* off
Perth
Perth is the capital and largest city of the Australian state of Western Australia. It is the fourth most populous city in Australia and Oceania, with a population of 2.1 million (80% of the state) living in Greater Perth in 2020. Perth is ...
* east of
New Guinea
New Guinea (; Hiri Motu
Hiri Motu, also known as Police Motu, Pidgin Motu, or just Hiri, is a language of Papua New Guinea, which is spoken in surrounding areas of Port Moresby (Capital of Papua New Guinea).
It is a simplified version of ...
* south of
Easter Island
Easter Island ( rap, Rapa Nui; es, Isla de Pascua) is an island and special territory of Chile in the southeastern Pacific Ocean, at the southeasternmost point of the Polynesian Triangle in Oceania. The island is most famous for its nearl ...
* west of the
Galapagos Islands
* north of
Queen Maud Land
Queen Maud Land ( no, Dronning Maud Land) is a roughly region of Antarctica claimed by Norway as a dependent territory. It borders the claimed British Antarctic Territory 20° west and the Australian Antarctic Territory 45° east. In addit ...
Counterclockwise amphidromic points
* near
Sri Lanka
Sri Lanka (, ; si, ශ්රී ලංකා, Śrī Laṅkā, translit-std=ISO (); ta, இலங்கை, Ilaṅkai, translit-std=ISO ()), formerly known as Ceylon and officially the Democratic Socialist Republic of Sri Lanka, is an ...
* north of
New Guinea
New Guinea (; Hiri Motu
Hiri Motu, also known as Police Motu, Pidgin Motu, or just Hiri, is a language of Papua New Guinea, which is spoken in surrounding areas of Port Moresby (Capital of Papua New Guinea).
It is a simplified version of ...
* at
Tahiti
Tahiti (; Tahitian ; ; previously also known as Otaheite) is the largest island of the Windward group of the Society Islands in French Polynesia. It is located in the central part of the Pacific Ocean and the nearest major landmass is Austr ...
* between
Mexico
Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...
and
Hawaii
Hawaii ( ; haw, Hawaii or ) is a state in the Western United States, located in the Pacific Ocean about from the U.S. mainland. It is the only U.S. state outside North America, the only state that is an archipelago, and the only stat ...
* near the
Leeward Islands
* east of
Newfoundland
* midway between
Rio de Janeiro
Rio de Janeiro ( , , ; literally 'River of January'), or simply Rio, is the capital of the state of the same name, Brazil's third-most populous state, and the second-most populous city in Brazil, after São Paulo. Listed by the GaWC as a b ...
and
Angola
, national_anthem = " Angola Avante"()
, image_map =
, map_caption =
, capital = Luanda
, religion =
, religion_year = 2020
, religion_ref =
, coordina ...
* east of
Iceland
Iceland ( is, Ísland; ) is a Nordic island country in the North Atlantic Ocean and in the Arctic Ocean. Iceland is the most sparsely populated country in Europe. Iceland's capital and largest city is Reykjavík, which (along with its s ...
* The islands of
Madagascar
Madagascar (; mg, Madagasikara, ), officially the Republic of Madagascar ( mg, Repoblikan'i Madagasikara, links=no, ; french: République de Madagascar), is an island country in the Indian Ocean, approximately off the coast of East Africa ...
and
New Zealand
New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island count ...
are amphidromic points in the sense that the tide goes around them in about 12 and a half hours, but the amplitude of the tides on their coasts is in some places large.
See also
*
Kelvin wave
A Kelvin wave is a wave in the ocean or atmosphere that balances the Earth's Coriolis force against a topographic boundary such as a coastline, or a waveguide such as the equator. A feature of a Kelvin wave is that it is non-dispersive, i.e., the ...
*
Tides
*
Theory of tides
The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans (especially Earth's oceans) under the gravitational loading of anot ...
References and notes
{{DEFAULTSORT:Amphidromic Point
Wave mechanics
Tides