A seiche (/sʃ/ SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbors, caves and seas. The key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave.

The term was promoted by the Swiss hydrologist François-Alphonse Forel in 1890, who was the first to make scientific observations of the effect in Lake Geneva.[1] The word had apparently long been used in the region to describe oscillations in alpine lakes. According to Wilson (1972),[2][3] this Swiss French dialect word comes from the Latin word siccus meaning "dry", i.e., as the water recedes, the beach dries. The French word sec or sèche (dry) descends from the Latin.

Seiches in harbours can be caused by long period or infragravity waves, which are due to subharmonic nonlinear wave interaction with the wind waves, having periods longer than the accompanying wind-generated waves.[4]

A standing wave (black) depicted as a sum of two propagating waves traveling in opposite directions (blue and red).

## Causes and nature

Seiches are often imperceptible to the naked eye, and observers in boats on the surface may not notice that a seiche is occurring due to the extremely long periods.

The effect is caused by resonances in a body of water that has been disturbed by one or more factors, most often meteorological effects (wind and atmospheric pressure variations), seismic activity, or tsunamis.[5] Gravity always seeks to restore the horizontal surface of a body of liquid water, as this represents the configuration in which the water is in hydrostatic equilibrium.

Vertical harmonic motion results, producing an impulse that travels the length of the basin at a velocity that depends on the depth of the water. The impulse is reflected back from the end of the basin, generating interference. Repeated reflections produce standing waves with one or more nodes, or points, that experience no vertical motion. The frequency of the oscillation is determined by the size of the basin, its depth and contours, and the water temperature.

The longest natural period of a seiche is the period associated with the fundamental resonance for the body of water—corresponding to the longest standing wave. For a surface seiche in an enclosed rectangular body of water this can be estimated using Merian's formula:[6][7]

${\displaystyle T={\frac {\ \ 2L\ \ }{\!\!\!{\sqrt {gh))))}$

where T is the longest natural period, L is the length, h the average depth of the body of water, and g the acceleration of gravity.[8]

Higher order harmonics are also observed. The period of the second harmonic will be half the natural period, the period of the third harmonic will be a third of the natural period, and so forth.

## Occurrence

Seiches have been observed on both lakes and seas. The key requirement is that the body of water be partially constrained to allow formation of standing waves. Regularity of geometry is not required; even harbours with exceedingly irregular shapes are routinely observed to oscillate with very stable frequencies.

### Lake seiches

Low rhythmic seiches are almost always present on larger lakes. They are usually unnoticeable among the common wave patterns, except during periods of unusual calm. Harbours, bays, and estuaries are often prone to small seiches with amplitudes of a few centimetres and periods of a few minutes.

The original studies in Lake Geneva by François-Alphonse Forel found the longitudinal period to have a 73-minute cycle, and the transversal seiche to have a period of around 10 minutes.[9] Another lake well known for its regular seiches is New Zealand's Lake Wakatipu, which varies its surface height at Queenstown by 20 centimetres in a 27-minute cycle. Seiches can also form in semi-enclosed seas; the North Sea often experiences a lengthwise seiche with a period of about 36 hours.

Differences in water level caused by a seiche on Lake Erie, recorded between Buffalo, New York (red) and Toledo, Ohio (blue) on November 14, 2003

The National Weather Service issues low water advisories for portions of the Great Lakes when seiches of 2 feet or greater are likely to occur.[10] Lake Erie is particularly prone to wind-caused seiches because of its shallowness and its elongation on a northeast-southwest axis, which frequently matches the direction of prevailing winds and therefore maximises the fetch of those winds. These can lead to extreme seiches of up to 5 metres (16 ft) between the ends of the lake.

The effect is similar to a storm surge like that caused by hurricanes along ocean coasts, but the seiche effect can cause oscillation back and forth across the lake for some time. In 1954, the remnants of Hurricane Hazel piled up water along the northwestern Lake Ontario shoreline near Toronto, causing extensive flooding, and established a seiche that subsequently caused flooding along the south shore.

Lake seiches can occur very quickly: on July 13, 1995, a large seiche on Lake Superior caused the water level to fall and then rise again by three feet (one metre) within fifteen minutes, leaving some boats hanging from the docks on their mooring lines when the water retreated.[11] The same storm system that caused the 1995 seiche on Lake Superior produced a similar effect in Lake Huron, in which the water level at Port Huron changed by 6 feet (1.8 m) over two hours.[12] On Lake Michigan, eight fishermen were swept away from piers at Montrose and North Avenue Beaches and drowned when a 10-foot (3.0 m) seiche hit the Chicago waterfront on June 26, 1954.[13]

Lakes in seismically active areas, such as Lake Tahoe in California/Nevada, are significantly at risk from seiches. Geological evidence indicates that the shores of Lake Tahoe may have been hit by seiches and tsunamis as much as 10 metres (33 ft) high in prehistoric times, and local researchers have called for the risk to be factored into emergency plans for the region.[14]

Earthquake-generated seiches can be observed thousands of miles away from the epicentre of a quake. Swimming pools are especially prone to seiches caused by earthquakes, as the ground tremors often match the resonant frequencies of small bodies of water. The 1994 Northridge earthquake in California caused swimming pools to overflow across southern California. The massive Good Friday earthquake that hit Alaska in 1964 caused seiches in swimming pools as far away as Puerto Rico.[15] The earthquake that hit Lisbon, Portugal, in 1755 caused seiches 2,000 miles (3,200 km) away in Loch Lomond, Loch Long, Loch Katrine and Loch Ness in Scotland[16] and in canals in Sweden. The 2004 Indian Ocean earthquake caused seiches in standing water bodies in many Indian states as well as in Bangladesh, Nepal, and northern Thailand.[17] Seiches were again observed in Uttar Pradesh, Tamil Nadu and West Bengal in India as well as in many locations in Bangladesh during the 2005 Kashmir earthquake.[18]

The 1950 Assam–Tibet earthquake is known to have generated seiches as far away as Norway and southern England. Other earthquakes in the Indian sub-continent known to have generated seiches include the 1803 Kumaon-Barahat, 1819 Allah Bund, 1842 Central Bengal, 1905 Kangra, 1930 Dhubri, 1934 Nepal-Bihar, 2001 Bhuj, 2005 Nias, 2005 Teresa Island earthquakes. The February 27, 2010 Chile earthquake produced a seiche on Lake Pontchartrain, Louisiana, with a height of around 0.5 feet. The 2010 Sierra El Mayor earthquake produced large seiches that quickly became an internet phenomenon.[19]

Seiches up to at least 1.8 m (6 feet) were observed in Sognefjorden, Norway, during the 2011 Tōhoku earthquake in Japan.[20][21]

### Sea and bay seiches

Seiches have been observed in seas such as the Adriatic Sea and the Baltic Sea. This results in the flooding of Venice and Saint Petersburg, respectively, as both cities are constructed on former marshland. In St. Petersburg, seiche-induced flooding is common along the Neva River in the autumn. The seiche is driven by a low pressure region in the North Atlantic moving onshore, giving rise to cyclonic lows on the Baltic Sea. The low pressure of the cyclone draws greater-than-normal quantities of water into the virtually land-locked Baltic. As the cyclone continues inland, long, low-frequency seiche waves with wavelengths up to several hundred kilometres are established in the Baltic. When the waves reach the narrow and shallow Neva Bay, they become much higher—ultimately flooding the Neva embankments.[22] Similar phenomena are observed at Venice, resulting in the MOSE Project, a system of 79 mobile barriers designed to protect the three entrances to the Venetian Lagoon.

In Japan, seiches have been observed in Nagasaki Bay, most often in the spring. During a seiche event on 31 March 1979, a water-level displacement of 2.78 metres (9.1 ft) was recorded at Nagasaki tide station; the maximum displacement in the whole bay is thought to have reached as much as 4.70 metres (15.4 ft). Seiches in Western Kyushu—including Nagasaki Bay—are often induced by a low in the atmospheric pressure passing South of Kyushu island.[23] Seiches in Nagasaki Bay have a period of about 30 to 40 minutes. Locally, seiches have caused floods, destroyed port facilities and damaged the fishery: hence the local word for seiche, あびき (abiki), from 網引き (amibiki), meaning 'the dragging-away of a fishing net'.

On occasion, tsunamis can produce seiches as a result of local geographic peculiarities. For instance, the tsunami that hit Hawaii in 1946 had a fifteen-minute interval between wave fronts. The natural resonant period of Hilo Bay is about thirty minutes. That meant that every second wave was in phase with the bay, creating a seiche. As a result, Hilo suffered worse damage than any other place in Hawaii, with the combined tsunami and seiche reaching a height of 26 feet (7.9 m) along the Bayfront, killing 96 people in the city alone. Seiche waves may continue for several days after a tsunami.

Tide-generated internal solitary waves (solitons) can excite coastal seiches at the following locations: Magueyes Island in Puerto Rico,[24][25][26] Puerto Princesa in Palawan Island,[27] Trincomalee Bay in Sri Lanka,[28][29] and in the Bay of Fundy in eastern Canada, where seiches cause some of the highest recorded tidal fluctuations in the world.[30] A dynamical mechanism exists for the generation of coastal seiches by deep-sea internal waves. These waves can generate a sufficient current at the shelf break to excite coastal seiches.[31]

Illustration of the initiation of surface and subsurface thermocline seiches.

### Underwater (internal) waves

Seiches are also observed beneath the surface of constrained bodies of water, acting along the thermocline.[32]

In analogy with the Merian formula, the expected period of the internal wave can be expressed as:[33]

${\displaystyle T={\frac {2L}{c))}$ with ${\displaystyle c^{2}=g{\frac {\rho _{2}-\rho _{1)){\rho _{2))}{\frac {h_{1}h_{2)){h_{1}+h_{2))))$

where T is the natural period, L is the length of the water body, ${\displaystyle h_{1},h_{2))$ the average thicknesses of the two layers separated by stratification (e.g. epilimnion and hypolimnion), ${\displaystyle \rho _{1},\rho _{2))$ the densities of these two same layers and g the acceleration of gravity.

As the thermocline moves up and down a sloping lake bed, it creates a 'swash zone', where temperatures can vary rapidly,[34] potentially affecting fish habitat. As the thermocline rises up a sloping lake bed, it can also cause benthic turbulence by convective overturning, whereas the falling thermocline experiences greater stratification and low turbulence at the lake bed.[35][36] Internal waves can also degenerate into non-linear internal waves on sloping lake-beds.[37] When such non-linear waves break on the lake bed, they can be an important source of turbulence and have the potential for sediment resuspension[38]

### Cave seiches

On September 19, 2022, a seiche reaching 4 feet (1.2 metres) occurred at Devils Hole at Death Valley National Park in the U.S. after a 7.6-magnitude earthquake hit western Mexico, about 1,500 miles (2,400 kilometres) away. Seiches were also observed in the cave after powerful earthquakes in 2012, 2018 and 2019.[39]

## Engineering for seiche protection

This section needs expansion. You can help by adding to it. (June 2008)

Engineers consider seiche phenomena in the design of flood protection works (e.g., Saint Petersburg Dam), reservoirs and dams (e.g., Grand Coulee Dam), potable water storage basins, harbours and even spent nuclear fuel storage basins.

## Notes

1. ^ Darwin, G. H. (1898). The Tides and Kindred Phenomena in the Solar System. London: John Murray. pp. 21–31.
2. ^ Rabinovich, Alexander B. (2018). "Seiches and Harbor Oscillations". Handbook of Coastal and Ocean Engineering. World Scientific. pp. 243–286. doi:10.1142/9789813204027_0011. ISBN 978-981-320-401-0.
3. ^ Wilson, Basil W. (1972). Seiches. Advances in Hydroscience. Vol. 8. Elsevier. pp. 1–94. doi:10.1016/b978-0-12-021808-0.50006-1. ISBN 978-0-12-021808-0.
4. ^ Munk, Walter H. (1950). Origin and generation of waves. 1st International Conference on Coastal Engineering, Long Beach, California. Council on Wave Research, American Society of Civil Engineers. doi:10.9753/icce.v1.1. ISSN 2156-1028. Archived from the original on 2017-01-11. Retrieved 2017-04-19.
5. ^ Tsunamis are normally associated with earthquakes, but landslides, volcanic eruptions and meteorite impacts all have the potential to generate a tsunami.
6. ^ Proudman, J. (1953). Dynamical oceanography. London: Methuen. §117 (p. 225). OCLC 223124129.
7. ^ Merian, J. R. (1828). Ueber die Bewegung tropfbarer Flüssigkeiten in Gefässen [On the motion of drippable liquids in containers] (thesis) (in German). Basel: Schweighauser. OCLC 46229431.
8. ^ As an example, the period for a seiche wave in a body of water 10 meters deep and 5 kilometers long would be 1000 seconds or about 17 minutes, while a body about 300 km long (such as the Gulf of Finland) and somewhat deeper has a period closer to 12 hours.
9. ^ Lemmin, Ulrich (2012), "Surface Seiches", in Bengtsson, Lars; Herschy, Reginald W.; Fairbridge, Rhodes W. (eds.), Encyclopedia of Lakes and Reservoirs, Encyclopedia of Earth Sciences Series, Springer Netherlands, pp. 751–753, doi:10.1007/978-1-4020-4410-6_226, ISBN 978-1-4020-4410-6
10. ^ Pierce, T. (July 5, 2006). "MARINE AND COASTAL SERVICES ABBREVIATIONS AND DEFINITIONS" (PDF). National Weather Service, Office of Climate, Water, and Weather Services. Archived from the original (PDF) on May 17, 2008. Retrieved April 19, 2017.
11. ^ Korgen, Ben (February 2000). "Bonanza for Lake Superior: Seiches Do More Than Move Water". seagrant.umn.edu. University of Minnesota Duluth. Archived from the original on 2007-12-27.
12. ^ "Lake Huron Storm Surge July 13, 1995". NOAA. Archived from the original on 2008-09-16. Retrieved 2009-03-13.
13. ^ "Huge Lake Wave Hits Chicago; Four Drowned, Ten Are Missing". The New York Times. Vol. 103, no. 35218. 27 June 1954. Archived from the original on 2 October 2021. Retrieved 2 October 2021.
14. ^ Brown, Kathryn (10 June 2000). "Tsunami! At Lake Tahoe?". Science News. 157 (24): 378–380. doi:10.2307/4012358. JSTOR 4012358.
15. ^ "Seiche". www.soest.hawaii.edu. Archived from the original on 2019-01-26. Retrieved 2019-03-12.
16. ^ "Seismic Seiches". USGS Earthquake Hazards Program. Abridged from Earthquake Information Bulletin, January–February 1976, Volume 8, Number 1. Archived from the original on 20 April 2017. Retrieved 19 April 2017.
17. ^ In fact, "one person drowned in a pond as a result of a seiche in Nadia, West Bengal". "26 December 2004, M9.1 "Boxing Day" Earthquake & Tsunami/Sumatra-Andaman Earthquake/Indian Ocean Tsunami". Amateur Seismic Centre. Pune. 22 Feb 2008. Archived from the original on 21 January 2007. Retrieved 19 April 2017.
18. ^ "M7.6 Kashmir-Kohistan Earthquake, 2005". Amateur Seismic Centre. Pune. 31 Oct 2008. Archived from the original on 6 June 2017. Retrieved 19 April 2017.
19. ^ "Arizona Geology: Video of seiche in Devils Hole pupfish pond. (Posted: April 27, 2010)". 2010-04-27. Archived from the original on 2014-12-19. Retrieved 17 October 2014.
20. ^ Fjorden svinga av skjelvet Archived 2011-03-18 at the Wayback Machine Retrieved on 2011-03-17.
21. ^ Johnson, Scott K. (30 June 2013). "Japanese earthquake literally made waves in Norway". Ars Technica. Archived from the original on 30 July 2022. Retrieved 18 April 2019.
22. ^ This behaves in a fashion similar to a tidal bore where incoming tides are funneled into a shallow, narrowing river via a broad bay. The funnel-like shape increases the height of the tide above normal, and the flood appears as a relatively rapid increase in the water level.
23. ^ Hibiya, Toshiyuki; Kinjiro Kajiura (1982). "Origin of the Abiki Phenomenon (a kind of Seiche) in Nagasaki Bay" (PDF). Journal of Oceanographical Society of Japan. 38 (3): 172–182. doi:10.1007/BF02110288. S2CID 198197231. Archived from the original (PDF) on 2011-05-27. Retrieved 2009-02-26.
24. ^ Giese, Graham S.; R. B. Hollander; J. E. Fancher; B. S. Giese (1982). "Evidence of coastal Seiche excitation by tide-generated internal solitary waves". Geophysical Research Letters. 9 (12): 1305–1308. Bibcode:1982GeoRL...9.1305G. doi:10.1029/GL009i012p01305.
25. ^ Giese, Graham S.; David C. Chapman; Peter G. Black; John A. Fornshell (1990). "Causation of Large-Amplitude Coastal Seiches on the Caribbean Coast of Puerto Rico". J. Phys. Oceanogr. 20 (9): 1449–1458. Bibcode:1990JPO....20.1449G. doi:10.1175/1520-0485(1990)020<1449:COLACS>2.0.CO;2.
26. ^ Alfonso-Sosa, Edwin (September 2012). "Estimated Speed of Aves Ridge Solitons Packets by Analysis of Sequential Images from the Moderate Resolution Imaging Spectroradiometer(MODIS)" (PDF): 1–11. doi:10.13140/RG.2.2.14561.45929. Archived from the original on 2022-07-30. Retrieved 2022-07-30. ((cite journal)): Cite journal requires |journal= (help)
27. ^ Giese, Graham S.; David C. Chapman; Margaret Goud Collins; Rolu Encarnacion; Gil Jacinto (1998). "The Coupling between Harbor Seiches at Palawan Island and Sulu Sea Internal Solitons". J. Phys. Oceanogr. 28 (12): 2418–2426. Bibcode:1998JPO....28.2418G. doi:10.1175/1520-0485(1998)028<2418:TCBHSA>2.0.CO;2. S2CID 55974279.
28. ^ Wijeratne, E. M. S.; P. L. Woodworth; D. T. Pugh (2010). "Meteorological and internal wave forcing of seiches along the Sri Lanka coast". Journal of Geophysical Research: Oceans. 115 (C3): C03014. Bibcode:2010JGRC..115.3014W. doi:10.1029/2009JC005673.
29. ^ Alfonso-Sosa, Edwin (April 2014). "Tide-Generated Internal Solitons in Bay of Bengal Excite Coastal Seiches in Trincomalee Bay" (PDF): 1–16. doi:10.13140/RG.2.2.32105.70242. Archived from the original on 2022-07-30. Retrieved 2022-07-30. ((cite journal)): Cite journal requires |journal= (help)
30. ^ Canada, Parks Canada Agency, Government of (2017-03-28). "index". www.pc.gc.ca. Archived from the original on 2016-03-04. Retrieved 9 April 2018.
31. ^ Chapman, David C.; Graham S. Giese (1990). "A Model for the Generation of Coastal Seiches by Deep-Sea Internal Waves". J. Phys. Oceanogr. 20 (9): 1459–1467. Bibcode:1990JPO....20.1459C. doi:10.1175/1520-0485(1990)020<1459:AMFTGO>2.0.CO;2.
32. ^ The thermocline is the boundary between colder lower layer (hypolimnion) and warmer upper layer (epilimnion).
33. ^ Mortimer, C. H. (1974). Lake hydrodynamics. Mitt. Internat. Verein. Limnol. 20, 124–197.
34. ^ Cossu, R.; Ridgway, M.S.; Li, J.Z.; Chowdhury, M.R.; Wells, M.G. (2017). "Wash-zone dynamics of the thermocline in Lake Simcoe, Ontario". Journal of Great Lakes Research. 43 (4): 689–699. doi:10.1016/j.jglr.2017.05.002. ISSN 0380-1330.
35. ^ Cossu, Remo; Wells, Mathew G. (2013-03-05). "The Interaction of Large Amplitude Internal Seiches with a Shallow Sloping Lakebed: Observations of Benthic Turbulence in Lake Simcoe, Ontario, Canada". PLOS ONE. 8 (3): e57444. Bibcode:2013PLoSO...857444C. doi:10.1371/journal.pone.0057444. ISSN 1932-6203. PMC 3589419. PMID 23472085.
36. ^ Bouffard, Damien; Wüest, Alfred (2019-01-05). "Convection in Lakes" (PDF). Annual Review of Fluid Mechanics. 51 (1): 189–215. Bibcode:2019AnRFM..51..189B. doi:10.1146/annurev-fluid-010518-040506. ISSN 0066-4189. S2CID 125132769.
37. ^ Boegman, L.; Ivey, G. N.; Imberger, J. (September 2005). "The degeneration of internal waves in lakes with sloping topography" (PDF). Limnology and Oceanography. 50 (5): 1620–1637. Bibcode:2005LimOc..50.1620B. doi:10.4319/lo.2005.50.5.1620. ISSN 0024-3590. S2CID 55292327. Archived (PDF) from the original on 2019-04-29. Retrieved 2020-09-06.
38. ^ Boegman, Leon; Stastna, Marek (2019-01-05). "Sediment Resuspension and Transport by Internal Solitary Waves". Annual Review of Fluid Mechanics. 51 (1): 129–154. Bibcode:2019AnRFM..51..129B. doi:10.1146/annurev-fluid-122316-045049. ISSN 0066-4189. S2CID 126363796.
39. ^ "Mexico earthquake caused waves at California's Death Valley". BNO News. September 21, 2022. Retrieved September 22, 2022.