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Oceanography: special waves

by Dr J Floor Anthoni 2000
www.seafriends.org.nz/oceano/waves.htm


When the continental crust under water moves suddenly, by an earth quake, it can cause a slow and very deep wave called a tsunami. If the slump is large enough, a mega tsunami may result.  The ocean knows several kinds of special waves like seiches, bores and internal waves. What kind of damage do these large waves cause under water to the rocky shore, and how do they work? This chapter helps you understand special waves.
tsunamis Tsunamis are caused by deep earthquakes which disturb the water above them, causing a wave front to radiate out at high speed. Tsunamis are unpredictable and can cause considerable damage. Mega tsunamis may occur when asteroids hit the ocean or when volcanoes erupt.
seiches and bores Seiches are standing waves in lakes, harbours and enclosed oceans. Bores are rapidly moving waves, caused by spring tides entering narrowing rivers.
internal waves Internal waves are an interesting phenomenon that cannot be observed from above. They propagate along layers caused by thermoclines, underlying fresh water and the like. They can cause sizeable undersea waves. 
wave damage Waves cause damage to the coast. Whereas healthy dunes and beaches are able to repair themselves, the rocky shore is not. This section looks at how waves cause damage to the rocky shore.
links
Useful links:
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Tsunamis in the Pacific OceanTsunamis
At intervals of from 5-15 years, and often without prior warning, the sea begins to heave and churn, sometimes receding to bare its floor, or suddenly rising far beyond the normal range of wave and tide. Flooding over breakwaters, tearing ships from their moorings, they leave wide spread destruction to shoreline habitations and facilities. From the map one can see that large tsunamis are rather rare. 13 of these were recorded over a time span of 110 years! (Japanese: tsu, "harbour," and nami, "wave"). The map shows the origin of major tsunamis in the Pacific Ocean from 1840 to 1960.

Tsunamis are caused by undersea earthquakes, seabed slides, or large volcanic eruptions (Krakatoa 1883), and are therefore equally impossible to predict. They are formed by a sudden uplift or subsidence of the sea bottom, as if a large plunger was suddenly moved up or down. The way they make themselves felt, varies considerably depending on the distance travelled, their magnitude and the form of the coast. Tsunamis are large waves travelling at high speed and limited by the narrow 4 km channel between the sea's surface and the deep ocean floor.
 

Many of a tsunami's properties can be understood with our knowledge of waves. In earlier subchapters on this page, reference has been made to tsunamis:
Tsunami waves The picture shows a recording of the Chilean tsunami wave of 22 May, 1960, as it was observed at Acapulco, Mexico, showing vertically the tide height in feet and horizontally time in hours. The first waves were less than half a metre high but three hours later many oscillations of about 1.5m occurred. With some 20 crests in 10 hours, the waves oscillated quite slowly but regularly. Perturbations of this nature cause large coastal and harbour currents. Compared with a typical tidal oscillation of 2m in 12.4 hours, the tsunami currents could have been 15 times stronger than normal tidal currents.

The source of this earthquake in 1960 extended over a distance of about 1,100 kilometres along the southern Chilean coast. Casualties included about 5,700 killed and 3,000 injured, and property damage amounted to many millions of dollars. Seismic sea waves excited by the earthquake caused death and destruction in Hawaii, Japan, and the Pacific coast of the United States.


 
Alaskan tsunamiDr William Van Dorn (1974) gave the following account of the great earthquake of 28 March 1964 on southeastern Alaska, and its tsunami: 

The volume of water displaced defies imagination. It involved a dislocation averaging 6 feet (1.8m) vertically over 100,000 square miles - thrice the size of Florida! About half this area was on land, and subsided; the other half, which included the entire 100-mile wide shelf bordering the Gulf of Alaska, was bulged upward - in some places as much as 50 feet (15m). The resulting mound of water poured off the shelf for two hours, and fanned out over the Pacific, creating widespread damage as far south as Crescent City, California, 1200 miles distant, where half of the business district was swept away.

Although this was by no means the most destructive tsunami in historical times, five of Alaska's seven largest communities were devastated by the combination of earthquake and wave damage. Its fishing industry and most seaport facilities were virtually destroyed, and only massive federal aid and years of effort have sufficed to restore its crippled economy.

As a long-time student of tsunamis, I flew to Alaska within 24 hours of the quake, and made a ten-day aerial tour of the entire region affected, traveling by helicopter, navy aircraft and chartered bush plane. Among accounts of calamities too numerous to mention, is one of particular interest to mariners. Most of the Alaskan crab fleet was at anchor in Kodiak harbour when they received belated warning of "fifty-foot waves" passing Cape Chiniak, twenty miles to the south. Getting rapidly underway, they were well out into Chiniak Bay when they encountered the first incoming crest, estimated to be thirty feet (9m) high and breaking. The next instant they were making 16 knots (30 km/hr) sternway, and were carried over a mile back into the harbor, over a protective mole, and on up into the center of the waterfront business district. The crab boats, being rather stoutly constructed, were not appreciably damaged by this excursion into unfamiliar territory, but a number of buildings were knocked down by their gyrations. 

The lesson here is that the fleet was within the epicentral area of the earthquake, which was plainly felt by everyone. The first waves arrived some 45 minutes later. Had the fleet put to sea directly after the earthquake warning instead of waiting for further advisement, the catastrophe might have been avoided.
 

Alaska 1964
Some of the damage wrought by the 1964 Alaskan tsunami. Photo source US Geological Survey.
It is interesting but sad to note what happened to the old town of Valdez, which was built on unconsolidated and unstable deltaic sands and gravels. The shock waves from the 1964 earthquake, running ahead of the tsunami, caused the sediments under the waterfront area to spontaneously liquefy, causing a large section of the delta to slump into Port Valdez. Not only did this destroy the township, but it also displaced a large volume of water, generating a local tsunami. Since all of this occurred before the earthquake shaking ended, the town had no warning at all, and all people on the town docks at the time were killed by the tsunami. The combined effects of the earthquake, and the 9-12m local tsunami destroyed most of the waterfront and caused damage a considerable distance inland. To make things worse, the forces caused the tanks at the Union Oil Company to rupture, which started a fire that spread across the entire waterfront, finishing off the few structures still standing. 
Tsunamis 1990-1999Earthquakes and tsunamis could be monitored by sea-based monitoring stations. By placing these along seismically active zones, they could warn immediately after a potential earth quake occurred and when a tsunami wave passes by. By placing sensors on the bottom of the sea, large waves could be detected. Normal storm waves do not reach deep enough but a tsunami's long wave would, even though its amplitude might be very small. By means of satellite communication, the early warning signals could be transmitted to a tsunami co-ordination centre, with direct connections to coastal tsunami warning centres.

The map shows all major earthquakes of the 1990s as tabled below (Source: Scientific American, May 1999):
 

Date Place Max wave Fatalities
2 Sep 1992 Nicaragua 10m 170
12 Dec 1992 Flores Island 26m >1000
12 July 1993 Okushiri, Japan 31m 239
2 June 1994 East Java 14m 238
14 Nov 1994 Mindoro Island 7m 49
9 Oct 1995 Jalisco, Mexico 11m 1
1 Jan 1996 Sulawesi Island 3.4m 9
17 Feb 1996 Irian Jaya 7.7m 161
21 Feb 1996 North coast of Peru 5m 12
17 July 1998 Papua New Guinea 15m >2200

 
Why was the Sumatra tsunami so devastating?
The Sumatra-Andaman Islands Earthquake on December 26, 2004, happened in an area with high population densities along the coasts where it struck with maximal force (see red colours in the simulated image below). Yet some nations were more so affected than others. Why?
Calculated amplitude of the Sumatra tsunami
It has escaped scientists' attention that the worst affected areas had two things in common: they have neither experienced hurricanes nor tides. Thus people lived dangerously close to the water and often on ships that would not be seaworthy in areas where tropical cyclones are common. The following two maps illustrate the point:
tide amplitudes and phase worldwide
Hurricane paths and areas of the worldThe above map of the main tide component, the moon-tide, shows where the tide is zero or very small (dark blue areas). One can see that this is the case between Aceh (Sumatra) and Ceylon (Sri Lanka). In such areas the tide has never been able to shape the land as it does for instance where the tide is between 2-3m, as in the area north of Sumatra. The moon-tide is like a tsunami, happening twice daily. Combined with waves, and particularly those from storms, tides then erode the shoreline out, until a shore profile results that also resists tsunamis. On such coasts, a tsunami won't be able to run inland as far as it did in Aceh, resulting in less damage and fewer fatalities. 
Now notice that the same area is also located on or very close to the equator where hurricanes cannot happen because there is not enough coriolis force or spin to force winds into circular paths. Hurricanes do not happen either, north of their warm water zones.
Study both maps to find other tsunami-sensitive areas, such as north and west-Japan. The March 2011 tsunami indeed caused predictably much damage where the coast never experienced substantial tides nor storms.

http://library.buffalo.edu/asl/guides/indian-ocean-disaster.html - valuable links re Sumatra tsunami.

Also read Tsunami by Frank I Gonzalez. Scientific American, May 1999. (Available from the Seafriends library)
Visit a page on tsunamis and good advice for survival.
 

Mega-tsunamis
Based on findings and projections of British geologist Simon Day, the BBC television programme, in October 2000, screened a disturbing documentary about the possibility of a mega tsunami arising from a collapse of the Cumbre Vieja volcano on the island of La Palma in the Canarias archipelago. The resulting shock wave could send a massive wave all across the Atlantic Ocean, to swamp large areas of America's east coast. Headlines in newspapers ran like this:
It was a scene straight from a disaster movie but a disaster on such an epic scale that even the most flamboyant Hollywood director would hesitate to suggest it might ever happen. Imagine being transported in your tiny fishing boat on the crest of a wave 1,600ft high - three times the height of Blackpool Tower- over forests and glaciers and living to tell the tale. That is what happened to fishermen Howard Ulrich and his son Sonny on a July evening in 1958 in Lituya Bay, Alaska.
On 8 July 1958 a 7.5 magnitude (others say 8.3) earthquake occurred along the Fairweather Fault, running along a trench near Lituya Bay. As a result, a massive land slide originating from 1000m altitude, while possibly shifting 30 million m3 of earth, plunged into the bay. The wave it caused, denuded the sides of the bay up to 516m high near the slide, and the rest of the shoreline between 200 and 30m high as it moved away towards the entrance. Simon Day extrapolated that if the entire west flank of the Cumbre Vieja mountain did the same, but with 1000 times more earth, it would send 650m shockwaves across the ocean, that would still be 40-50m high when reaching the USA, 6500 km away. 
But computer models do not agree, and tsunami expert Charles Mader advised that the wave would have a short wave length (less than 10 minutes), rapidly decaying to a deep water wave before it reached the US.

The La Palma story helps us to brush up our knowledge of the physics of waves (see above). Whether originating from an underwater land slide, the explosion of a volcano or the impact of an asteroid, waves still obey the same physical laws.

Impulse and energy: There are two aspects of a disturbance that we need to distinguish: suddenness (velocity, v) and volume (mass, m). The two combined create impulse or impact (v x m), and kinetic energy (0.5 x v x v x m). Impulse determines how much matter will be moved by the disturbance (water and earth and buildings), which is often more destructive than the energy content of the disturbance. Think for instance of the huge energy contained in normal moon tides, which causes no harm because tides move slowly.

Physical limitations: The critical element is how a wave (a surface wave) moves through a narrow channel of 6000 km long but only 4km deep, the Atlantic Ocean. And there's an obstacle in the middle as well, the Mid-atlantic Ridge. Such waves are physically limited to travel no faster than 700-800 km/h, giving them a wave period of around 2 minutes (120 sec) and a wave length of 26 km (see equations above). This narrow channel soon dampens the quicker components of a disturbance. Think for instance of a sudden movement, like throwing a pebble into a pool. As the pebble displaces water outward, it also produces a wave moving inward and upward, which dissipates most of the energy and impact. So, as far as underwater tsunamis are concerned, the long-distance component is proportional only to the amount of earth shifted (in 2 minutes). An underwater slip or slump consists of a volume of mud sliding down hill. Since the velocity of such incidents is roughly the same, their impact depends on mass only.
Impacts from outside, however, can produce larger waves. Asteroids are a point in case. They travel at speeds between 10-70 km/s (usually around 20 km/s=70,000 km/h), such that a 1km3 asteroid can produce a 70-90m deep water wave 100 km away from impact, but such impacts occur about once in 100,000 years. (Please note that not all scientists agree on these figures)

Diminishing with distance travelled: Once the wave is on its way, it fans out over 180 degrees, becoming weaker as it 'dilutes' over a larger area, while encountering resistance as well. The wave weakens roughly inversely to distance travelled, thus at 1000km distance, the wave is 100 times (computers say 200 times) smaller (its energy 10,000 times less) than it was at 10km distance. The 1964 tsunami in Alaska shifted some 500 km3 of earth, starting a deep water wave of 30m, which diminished to 0.3m at 1500 km distance, then increased to 3-6m as it ran up the shallows. This wave caused substantial damage to boats, piers and the business district in Crescent City, California. The 1960 Chilean earthquake may have shifted over 1500 km3 (my estimate), causing extensive coastal damage locally and as far away as Hawaii (15 hours) and Japan (22 hours), but was hardly noticeable in New Zealand (18 hours later).

Mountain slide: According to Simon Day, in the case of the Cumbre Vieja, as much as 500 billion tonnes (200 km3) of earth could suddenly slide into the ocean, creating 650m waves locally. In his model he used a solid wedge, which slid rapidly, but natural slumps break up and slide more gradually. Since earth is between 2 and 3 times 'heavier' above water, land slides can acquire 2-3 times more momentum from their mass, and another similar amount from their higher speed, totalling perhaps 10 times. This would suggest that the La Palma island mega tsunami would equate to an under water slump of no more than 2000 km3.

Meteorites: Meteorite impact studies suggest that such an impact (equal to 10,000 Mt TNT) equates to that of a 500m diameter asteroid (0.037 km3). Such waves would diminish to less than one metre at 6000 km, but would still be capable of causing much damage through their variable 'run-up' effect.

Run-up: Tsunamis cause more or less damage depending on how they run up the coast. As they enter shallow water, the waves rise and slow down. Depending on the shape of the sea bottom and that of bays, their size increases between two (normal) and forty times (very abnormal). A 1m wave could thus rise to 2m (normal rise, within normal tidal range) or 40m, causing extreme damage very locally.

Conclusion: although scientific knowledge and computer models are not able to disprove Simon Days' findings, common sense evaluation of the situation makes 40-50m tall waves swamping America and Britain, highly unlikely.
 


Seiches and bores
Oscillations of lake water levels were first studied in Lake Geneva in Switzerland, where they are called seiches. Seiches are standing waves that slosh to and fro in deep lakes, from one end to another. Changes in barometric pressure or other disturbances may start such standing waves. The speed and length of standing waves is given by the basin's depth and the distance between shores. In this manner each enclosed body of water has its own standing wave characteristics.

At the entrances to semi-enclosed harbours, waves or an incoming tide may start oscillations that bounce to and fro between the shores of the harbour. Such oscillations can be started by large wave trains, gusty winds and may damage moored boats.

When a spring tide comes in on a gently sloping shore which narrows into a river entrance, the tide currents can become strong enough to displace outflowing water and to rise up, forming a fast moving vertical wall of water. Such a wave, characterised by a surge of water moving swiftly upstream, headed by a wave or series of waves, is called a bore (Old-Nordic bara=wave. A bore is also called an eagre).
A famous bore, known as the Mascaret on the French river Seine, forms on spring tides and reaches some 50km inland. The bore can reportedly outrun a horse (about 35km/hr). Other famous bores are found in the Fu-chun River in china, the Amazon River in Brasil, the Severn in England and the Petitcodiac River in New Brunswick, Canada.



 
Internal waves
Internal waves are a class of gravity waves to be found almost entirely under the surface. They propagate along the boundaries of layers of water with differing densities:
  • A thermocline forms when the sea heats up. Warm water being lighter than cold water, remains on top. A temperature gradient develops into a sharp thermocline. The water on top may be 4 degrees warmer and 0.2% less dense.
  • Fresh water flowing from large rivers, is lighter than salt water and stays on top of it for many kilometres and several metres depth. In fiords, the fresh water may form a 5m deep layer. The fresh water is about 3.5% less dense.

Because of the small difference in density between such layers, the corresponding restoring force for gravity waves is much less than that for surface waves (which is the weight difference between water and air). From the speed equation for gravity waves, it follows that internal waves move much more slowly but at a fixed rate, which also depends on the depth of the boundary layer. For instance, for a thermocline at 10m with a difference of 0.15% density, the wave velocity would be 0.4m/s (1.4 km/hr). For a fresh water layer of 5m depth, the wave velocity would be 1.3 m/s (6.1 km/hr).

Internal waves require very little energy to be set in motion. The tidal current flowing over a sea bottom discontinuity could create packets of internal waves. Internal wave amplitudes of tens of metres and periods of up to 12 hours have been measured in the open ocean. Internal waves can also produce standing waves (like seiches) in enclosed bays. Because these waves are difficult to observe, very little is known about them.
 

The wave phase velocity of gravity waves in a two layer ocean is given by:
c x c = g x d x (p2 - p1) / p2
where c = phase velocity (m/s), g = acceleration of gravity (9.8 m/s/s), d = thickness of the upper layer (m)
p1 = density of top layer (g/cm/cm), p2 = density of deep layer (g/cm/cm).
From this formula it follows that the wave velocity of internal waves depends both on the thickness of the layer and the relative difference in density between the two layers.
It is interesting to note that the water particles above the layer move clockwise whereas those below move counter clockwise.
deadwaterAlthough they did not know what caused it, seamen were familiar with a strange phenomenon, called deadwater. When travelling into a fiord, or near an ice shelf, their slow ships seemed to come to a halt, and even at full power they would only make very slow headway. Later, scientists discovered its cause, an internal wave created by the ship's movement. It appears as if the ship is travelling uphill against the heavier salt water crest. A 1000 tonne ship could experience it as a 20 tonne drag, because salt water of 3.5% is about 2% denser than fresh water. 
Internal waves arising from temperature or saline differences, can reach magnitudes of 40m, bringing deep nutrient-rich water right into the shallow light zone where it causes sudden and dense plankton blooms. 
The polar explorer Fridtjof Nansen, leader of the Norwegian North Polar expedition to the Arctic in 1893-1896 reported the following experience aboard the small research vessel Fram, as he was tracking the ice dirft across the Arctic:
On tuesday, August 29th, 1893, the Fram got into open water in the sound between the Isle of Taimur and the Almvist Islands and steamed in calm water through the sound to the north-east. . . . We approached the ice to make fast to it, but the Fram had got into dead-water, and made hardly any way, in spite of the engine going at full pressure. It was such slow work that I thought I would row ahead to shoot seal. . . . the speed must have reduced to 1 - 1.5 knot in the dead-water. . . The water at the surface was almost fresh, whereas through the bottom-cock of the engine room we got perfectly salt water.
In 1963, the nuclear submarine USS Thresher was lost with all hands on board. Prior to the sinking there had been no indication of equipment malfunction or unusual storm weather. While submerged, submarines attain neutral buoyancy by flooding or jettisoning seawater from a series of ballast tanks. An effective way for a submarine to avoid detection by suface vessels is to dive and cruise silently along density discontinuities (pycnoclines), which tend to reflect the engine noise downward and sonar pulses from above upward. Navy scientists speculate that the USS Thresher was probably cruising along a pycnocline when it encountered a large internal wave. Because of its neutral buoyancy, it is thought that the submarine suddenly slid down the wave's back side, down to greater depths. Unable to compensate for this sudden fall, the submarine exceeded its design depth and imploded with loss of all life.
Source: Paul R Pinet: Oceanography.1992.


How waves damage the rocky shore
Actual shore profilesWhen waves roll along in deep water, the water particles hardly move at all, relative to each other. But once a wave enters shallow water, the situation changes. At its foot, the wave meets a boundary that won't move and as a consequence, the water particles move relative to that boundary. At its top, the wave breaks, sending rushes of water forward. At these two points, the bottom and the top, the coast appears under severest attack of the waves. Depending on the amount of exposure and depth, the rock face is ground to a shape of minimal erosion, such that any point deviating from this shape, would erode faster than its surroundings. Although affected by the vagaries of rock hardness and homogenity, a typical coastal profile emerges. 
In deep water, the profile plunges down vertically to over 20m depth. These steep rock walls bounce waves back into sea, without absorbing much of their energy at all. So erosion rates near the surface are low. In moderately deep water, a drop-off may exist but the slope becomes more gradual. Platforms are a consistent feature of the shore. In the diagram with actual north-facing shore profiles, one can see a platform developing in the sea urchin habitat, and perhaps also one lower down. Because the urchins graze their patch thoroughly, the stoneleaf algae (Lithothamnion sp) thrive, protecting the rock. What are the forces of the waves that carve these shapes?

How waves damage the rocky shoreWhen a mass of water is on the move, it is much harder to stop than air. Water is about 800 times heavier than air. So it can turn and lift boulders. Enormous pressure waves can develop when water is squeezed into a crack or cave. But most damage is caused by the friction of water, as it races along a rock face (shearing). Creatures attached to the rock may be ripped and their bodies washed up on a beach. At the bottom, where the sand or pebbles can move freely, rocks and organisms become sand-blasted and erosion here is high during large storms. The freely moving sand may be deposited on deep rock flats, smothering the attached organisms.

Ironically, scientists discovered that the hardness of the rock has little bearing on its rate of wear [Taylor, 2000]. Such findings go against all logic, but nature can be perplexing. What is often overlooked, is the protection afforded by organisms living on the rock. Even a thin scum of algae prevents water and sand from touching its surface, and although the living skin may suffer damage, it is capable of repairing itself. The 'living skin' idea could explain why soft rock is protected relatively better (because it is easier to attach to), than hard rock such as granite (is too smooth for attachment). It could explain the existence of platforms (because these are the best form for sun-loving plants) and why the shoreline erodes so slowly despite the enormous forces occurring in the wave zone. It could also explain why shaded coasts wear faster (because the protective film grows slower), and why coastal erosion is increasing everywhere in the world (because protective organisms are disappearing due to pollution and mud).

Among the rock-protecting creatures one can find both animals (that don't need sunlight) and plants (that do need sunlight). Animals: barnacles, mussels. Plants: various matting algae, pink paint (Lithothamnion sp), large algae.

Amongst the living skin, also creatures can be found that are capable of drilling into soft rock. They do so by means of scraping, assisted by excreting acids. Particularly limestone-rich rocks can be attacked in this way.

Reader please note that the above are my own observations that have not been confirmed by scientific method. Floor Anthoni
Taylor, Anna. Geography Dept, Univ Canterbury: Erosion of shore platforms, East Coast, South Island, New Zealand. International Coastal Symposium 2000, Rotorua, New Zealand.
 

f014616: Live paua abraded by pebbles
These live paua shells (abalone Haliotis iris), living close to the bottom of a shallow cave in northern New Zealand, have been abraded by shingle, showing their finely polished nacre. It was like happening upon Aladdin's cave of treasures. The rocks were finely polished too.
By night, pauas leave their sleeping places to browse the rocks that are exposed to sunlight by day.
f014619: Haliotis iris polished by shingle
Close-up of a polished paua shell. Notice that the rock is covered by a rock-hard pink alga, affectionately called 'pink paint' (Lithothamnion sp.). It is apparently hardy and resilient enough to repair damage from both the grazing of paua and abrasion from shingle. This most amazing rock lining lives from shallow rock pools, down to 50m depth. Here it thrives in the darkness of this cave.
f025404: Pink paint, Lithothamnia
Close-up of pink paint (Lithothamnion sp) on the side of a rock at 20m depth. The edges of each plant (leaf) can clearly be distinguished. Top left, part of a kelp's holdfast (Ecklonia radiata) is seen. A number of top shells can be distinguished, grazing the pink paint.
f012120: Young kelp plants stripped by waves
These young kelp plants had settled in shallow water (6m), the domain of the sea urchins. During a storm (cyclone Fergus), their canopies were stripped off, causing almost full mortality. It is amazing to see how sharp the boundaries of storm damage are. Only one metre deeper, none of the kelp plants was affected.


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