Amphidromic point
An amphidromic point, also called a tidal node, is a geographical location which has zero tidal
Amphidromic points occur because
In most locations the "principal lunar semi-diurnal", known as M2, 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
In real oceans, the tides cannot endlessly propagate as
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
Infinitely long channel
In an infinitely long channel, which can be viewed upon as a simplified approximation of the Atlantic Ocean and Pacific Ocean, the tide propagates as an incident and a reflective Kelvin wave. 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 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.[9] 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 1⁄4λ with reoccurring nodes at intervals of 1⁄2λ. In an idealized situation, amphidromic points can be found at the position of these nodes of the total tidal wave.[8] 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[8] However, tidal waves in the ocean are subject to friction from the seabed and from interaction with coastal boundaries. Moreover, variation in water depth influences the spacing between amphidromic points.[8][10]
Firstly, the distance between amphidromic points is dependent on the water depth:[8]
Where g is the
Locations with more shallow water depth have their amphidromic points closer to each other as the distance of the interval (1⁄2λ) of the nodes decreases. Secondly, energy losses due to friction in shallow seas and coastal boundaries result in additional adjustments of the tidal pattern.[15] Tidal waves are not perfectly reflected, resulting in energy loss which causes a smaller reflected wave compared to the incoming wave.[8] 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.[8]
The degree of displacement on the northern hemisphere for the first amphidrome is given by:[8]
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 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,[8] 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
It can occur that the amphidromic point moves inland of the coastal boundary.[15][16][17] 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, the oceans in the world are becoming subject to sea-level rise.[18][19] As the water depth increases, the wavelength of the tidal wave will increase. Consequently the position of the amphidromic points located at 1⁄4λ 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 1⁄2λ 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.[20] 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.[21] This causes the amphidromic points to move further away from the coastal boundaries and more towards the centre its channel/basin.
In the M2 tidal constituent
Based on Figure 1, there are the following clockwise and anticlockwise amphidromic points:
Clockwise amphidromic points
- north of the Seychelles
- near Enderby Land
- off Perth
- east of New Guinea
- south of Easter Island
- west of the Galapagos Islands
- north of Queen Maud Land
Counterclockwise amphidromic points
- near Sri Lanka
- north of New Guinea
- at Tahiti
- between Mexico and Hawaii
- near the Leeward Islands
- east of Newfoundland
- midway between Rio de Janeiro and Angola
- east of Iceland
- The islands of Madagascar and New Zealand 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
- Tides
- Theory of tides
References and notes
- JPL, Scientific Visualization Studio, and Television Production NASA-TV/GSFC
- doi:10.4138/729.
- ^ a b "Tides in two easy pieces - Earth 540: Essentials of Oceanography for Educators". Retrieved 21 July 2016.
- ISBN 978-0-521-79746-7.
- S2CID 38351145.
- ^ "Archived copy". Archived from the original on 2010-06-02. Retrieved 2010-08-23.
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: CS1 maint: archived copy as title (link) - ^ "Untitled Document". Retrieved 21 July 2016.
- ^ ISBN 978-1-139-23577-8.
- ^ ISBN 978-0-12-227090-1, retrieved 2021-05-15
- ^ ISSN 1042-8275.
- ISBN 978-1-118-47635-2, retrieved 2021-05-15
- ISSN 0036-8075.
- ISSN 8755-1209.
- )
- ^ ISSN 0956-540X.
- ISSN 0148-0227.
- S2CID 53365068.
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- PMID 28057920.