Oceanography: waves

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For the creatures in the sea, ocean currents allow their larvae to be dispersed and to be carried great distances. Many creatures spawn only during storms when large waves can mix their gametes effectively.

Coastal creatures living in shallow water experience the brunt of the waves directly. In order to survive there, they need to be robust and adaptable. Thus waves maintain a gradient of bio-diversity all the way from the surface, down to depths of 30m or more. Without waves, there would not be as many species living in the sea.

Waves pound rocks and make them erode faster, but sea organisms covering these rocks, delay this process. Waves make beaches by transporting sand from deeper down towards the shore and by washing the sand and removing fine particles. Waves stir and suspend the sand so that currents or gravity can transport it.
 

Waves are oscillations in the water's surface. For oscillations to exist and to propagate, like the vibrating of a guitar string or the standing waves in a flute, there must be a returning force that brings equilibrium. The tension in a string and the pressure of the air are such forces. Without these, neither the string nor the flute could produce tones. The standing waves in musical instruments bounce their energy back and forth inside the string or the flute's cavity. The oscillations that are passed to the air are different in that they travel in widening spheres outward. These travelling waves have a direction and speed in addition to their tone or timbre. In air their returning force is the compression of the air molecules. In surface waves, the returning force is gravity, the pull of the Earth. Hence the name 'gravity waves' for water waves.

In solids, the molecules are tightly connected together, which prevents them from moving freely, but they can vibrate. Water is a liquid and its molecules are allowed to move freely although they are placed closely together. In gases, the molecules are surrounded by vast expanses of vacuum space, which allows them to move freely and at high speed. In all these media, waves are propagated by compression of the medium. However, the surface waves between two media (water and air), behave very different and solely under the influence of gravity, which is much weaker than that of elastic compression, the method by which sound propagates.
 

If each water particle makes small oscillations around its spot, relative to its neighbours, waves can form if all water particles move at the same time and in directions that add up to the wave's shape and direction. Because water has a vast number of molecules, the height of waves is theoretically unlimited. In practice, surface waves can be sustained as high as 70% of the water's depth or some 3000m in a 4000m deep sea (Van Dorn, 1974).
Note that the water particles do not travel but only their collective energy does! Waves that travel far and fast, undulate slowly, requiring the water particles to make slow oscillations, which reduces friction and loss of energy.

In the diagram some familiar terms are shown. A floating object is observed to move in perfect circles when waves oscillate harmoniously sinus-like. If that object hovered in the water, like a water particle, it would be moving along diminishing circles, when placed deeper in the water. At a certain depth, the object would stand still. This is the wave's base, precisely half the wave's length. Thus long waves (ocean swell) extend much deeper down than short waves (chop). Waves with 100 metres between crests are common and could stir the bottom down to a depth of 50m. Note that the depth of a wave has little to do with its height! But a wave's height contains the wave's energy, which is unrelated to the wave's length. Long surface waves travel faster and further than short ones.

Water waves can store or dissipate much energy. Like other waves (alternating electric currents, e.g.), a wave's energy is proportional to the square of its height (potential). Thus a 3m high wave has 3x3=9 times more energy than a 1m high wave. When fine-weather waves of about 1m height pound on the beach, they dissipate an average of 10kW (ten one-bar heaters) per metre of beach or the power of a small car at full throttle, every five metres. (Ref  Douglas L Inman in Oceanography, the last frontier, 1974). Attempts to harness the energy from waves have failed because they require large structures over large areas and these structures should be capable of surviving storm conditions with energies hundreds of times larger than they were designed to capture.

Waves have a direction and speed. Sound waves propagate by compressing the medium. They can travel in water about 4.5 times faster than in air, about 1500m per second (5400km/s, or mach-4.5, depending on temperature and salinity). Such waves can travel in all directions and reach the bottom of the ocean (about 4km) in less than a second. Surface waves, however, are limited by the density of water and the pull of gravity. They can travel only along the surface and their wave lengths can at most be about twice the average depth of the ocean (2 x 4 km). The fastest surface waves observed, are those caused by tsunamis. The 'tidal wave' caused by an under-sea earthquake in Chile in May 1960, covered the 6000 nautical miles (11,000km) to New Zealand in about 12 hours, travelling at a speed of  about 900 km/hr! When it arrived, it caused an oscillation in water level of 0.6m at various places along the coast, 1.4m in Tauranga Harbour and 2.4m in Whitianga harbour. Note that tsunamis reach their minimum at about 6000 km distance. Beyond that, coriolis forces bend the wave fronts to focus them again at a distance of about 12,000 km, where they can still cause considerable damage.
 

The relationship between wave speed (phase velocity) and depth of long surface waves in shallow water is given by the formula  c x c = g x d x (p2 - p1) / p2   or c x c= g x d   for water/air where c= wave speed, g= acceleration of gravity (9.8066 m/s/s), d= wave depth (or upper layer depth, m), p2= density of water (=1) and p1= density of air (= 0.00125). The formula states that wave speed increases with wave depth and the relative difference in density. For an ocean depth of 4000m, a wave's celerity or speed would be about SQR(10 x 4000) = 200 m/s = 720 km/hr. Surface waves could theoretically travel much faster on larger planets, in media denser than water. For deep water, the relationship between speed and wavelength is given by the formula: l = g x t x t / (2 x pi) l = t x c  for all kinds of waves, substitute in above equation: t x c = g x t x t / (2 x pi) c = g x t / (2 x pi)  or  t = c x 2 x pi / g or t = c x 0.641 (s)  where t= wave period (sec), f= wave frequency, l= wave length (m) and pi=3.1415... to calculate c and l from wave period t (in sec):  c = t x 1.56 m/s= t x 5.62 km/hr = t x 3.0 knot l = 1.56 x t x t  (metres) Thus waves with a period of 10 seconds, travel at 56 km/hr with a wave length of about 156m. A 60 knot (110 km/hr) gale can produce in 24 hours waves with periods of 17 seconds and wave lengths of 450m. Such waves travel close to the wind's speed (97 km/hr). A tsunami travelling at 200 m/s has a wave period of 128 s, and a wave length of 25,600 m.

These two diagrams show the relationships between wave speed and period for various depths (left), and wave length and period (right), for periodic, progressive surface waves. (Adapted from Van Dorn, 1974)  Note that the term phase velocity is more precise than wave speed. The period of waves is easy to measure using a stopwatch, whereas wave length and speed are not. In the left picture, the red line gives the linear relationship between wave speed and wave period. A 12 second swell in deep water travels at about 20m/s or 72 km/hr. From the red line in the right diagram, we can see that such swell has a wave length between crests of about 250m. When the 12s swell enters 10m shallow water (follow the green curve for 10m), its speed will halve to 10m/s (left graph) and so will its wave length (right graph). But the height of the wave increases by a similar factor (not shown here).

Waves and wind How wind causes water to form waves is easy to understand although many intricate details still lack a satisfactory theory. On a perfectly calm sea, the wind has practically no grip. As it slides over the water surface film, it makes it move. As the water moves, it forms eddies and small ripples. Ironically, these ripples do not travel exactly in the direction of the wind but as two sets of parallel ripples, at angles 70-80º to the wind direction. The ripples make the water's surface rough, giving the wind a better grip. The ripples, starting at a minimum wave speed of 0.23 m/s, grow to wavelets and start to travel in the direction of the wind. At wind speeds of 4-6 knots (7-11 km/hr), these double wave fronts travel at about 30º from the wind. The surface still looks glassy overall but as the wind speed increases, the wavelets become high enough to interact with the air flow and the surface starts to look rough. The wind becomes turbulent just above the surface and starts transferring energy to the waves. Strong winds are more turbulent and  make waves more easily.

The rougher the water becomes, the easier it is for the wind to transfer its energy. The waves become steep and choppy. Further away from the shore, the water's surface is not only stirred by the wind but also by waves arriving with the wind. These waves influence the motion of the water particles such that opposing movements gradually cancel out, whereas synchronising movements are enhanced. The waves start to become more rounded and harmonious. Depending on duration and distance (fetch), the waves develop into a fully developed sea.

Anyone familiar with the sea, knows that waves never assume a uniform, harmonious shape. Even when the wind has blown strictly from one direction only, the resulting water movement is made up of various waves, each with a different speed and height. Although some waves are small, most waves have a certain height and sometimes a wave occurs which is much higher.
 

When trying to be more precise about waves, difficulties arise: how do we measure waves objectively? When is a wave a wave and should be counted? Scientists do this by introducing a value E which is derived from the energy component of the compound wave. In the left part of the drawing is shown how the value E is derived entirely mathematically from the shape of the wave. Instruments can also measure it precisely and objectively. The wave height is now proportional to the square root of E. The sea state E is two times the average of the sum of the squared amplitudes of all wave samples. The right part of the diagram illustrates the probability of waves exceeding a certain height.  The vertical axis gives height relative to the square root of the average energy state of the sea: h / SQR( E ) . For understanding the graph, one can take the average wave height at 50% probability as reference. Fifty percent of all waves exceed the average wave height, and an equal number are smaller. The highest one-tenth of all waves are twice as high as the average wave height (and four times more powerful). Towards the left, the probability curve keeps rising off the scale: one in 5000 waves is three times higher and so on. The significant wave height H3 is twice the most probable height and occurs about 15% or once in seven waves, hence the saying "Every seventh wave is highest".

When the wind blows sufficiently long from the same direction, the waves it creates, reach maximum size, speed and period beyond a certain distance (fetch) from the shore. This is called a fully developed sea. Because the waves travel at speeds close to that of the wind, the wind is no longer able to transfer energy to them and the sea state has reached its maximum. In the picture the wave spectra of three different fully developed seas are shown. The bell curve for a 20 knot wind (green) is flat and low and has many high frequency components (wave periods 1-10 seconds). As the wind speed increases, the wave spectrum grows rapidly while also expanding to the low frequencies (to the right). Note how the bell curve rapidly cuts off for long wave periods, to the right. Compare the size of the red bell, produced by 40 knot winds, with that of the green bell, produced by winds of half that speed. The energy in the red bell is 16 times larger! Important to remember is that the energy of the sea (maximum sea condition) increases very rapidly with wind speed, proportional to its fourth power. The amplitude of the waves increases to the third power of wind speed. This property makes storms so unexpectedly destructive.

The biggest waves on the planet are found where strong winds consistently blow in a constant direction. Such a place is found south of the Indian Ocean, at latitudes of -40º to -60º, as shown by the yellow and red colours on this satellite map. Waves here average 7m, with the occasional waves twice that height! Directly south of New Zealand, wave heights exceeding 5m are also normal. The lowest waves occur where wind speeds are lowest, around the equator, particularly where the wind's fetch is limited by islands, indicated by the pink colour on this map. However, in these places, the sea water warms up, causing the birth of tropical cyclones, typhoons or hurricanes, which may send large waves in all directions, particularly in the direction they are travelling.

Waves entering shallow water As waves enter shallow water, they slow down, grow taller and change shape. At a depth of half its wave length, the rounded waves start to rise and their crests become shorter while their troughs lengthen. Although their period (frequency) stays the same, the waves slow down and their overall wave length shortens. The 'bumps' gradually steepen and finally break in the surf when depth becomes less than 1.3 times their height. Note that waves change shape in depths depending on their wave length, but break in shallows relating to their height! How high a wave will rise, depends on its wave length (period) and the beach slope. It has been observed that a swell of 6-7m height in open sea, with a period of 21 seconds, rose to 16m height off Manihiki Atoll, Cooks Islands, on 2 June, 1967. Such swell could have arisen from a 60 knot storm.

The photo shows waves entering shallow water at Piha, New Zealand. Notice how the wave crests rise from an almost invisible swell in the far distance. As they enter shallow water, they also change shape and are no longer sinus-like. Although their period remain the same, their distance between crests and their speed, diminish. Not quite visible on this scale are the many surfies in the water near the centre of the picture. They favour this spot because as the waves bend around the rocks, and gradually break in a 'peeling' motion, they can ride them almost all the way back to the beach.

Going back to the 'wave motion and depth' diagram showing how water particles move, we can see that all particles make a circular movement in the same direction. They move up on the wave's leading edge, forward on its crest, down on its trailing slope and backward on its trough. In shallow water, the particles close to the bottom will be restricted in their up and downward movements and move along the bottom instead. As the diagram shows, the particle's amplitude of movement does not decrease with depth. The forward/backward movement over the sand creates ripples and disturbs it.
Since shallow long waves have short crests and long troughs, the sand's forward movement is much more brisk than its backward movement, resulting in sand being dragged towards the shore. This is important for sandy beaches.
 

Surf breakers are classified in three types:

• Spilling breakers: result from waves of low steepness (long period swell) over gentle slopes. They cause rows of breakers, rolling towards the beach. Such breakers gradually transport water towards the beach during groups of high waves. Rips running back to sea, transport this water away from the beach during groups of low waves. When caught swimming in a rip, do not attempt to swim back to shore because such rips can be very strong (up to 8 km/hr). Swim parallel to the beach towards where the waves are highest. This is where water moves towards the beach. The next group of tall waves should assist you to swim back to shore. However, when launching (rescue) boats, this is best done in a rip zone.
• Plunging breakers: result from steeper waves over moderate slopes. The slope of a beach is not constant but may change with the tide. Some beaches are steep toward high tide, others toward low tide. A plunging breaker is dangerous for swimmers because its intensity is greatly augmented by backwash from its predecessor. This strong backwash precludes easy exit from the breaker zone, particularly for divers. Often a steep bank of loose sand prevents one from standing upright. In order to exit safely, wait for a group of low waves.
• Surging breakers: occur where the beach slope exceeds wave steepness. The wave does not really curl and break but runs up against the shore while producing foam and large surges of water. Such places are dangerous for swimmers because the rapidly moving water can drag swimmers over the rocks.

Spilling breakers are a familiar sight on most beaches. They arise from long waves breaking on gently sloping beaches. There are several rows of breakers.

Plunging breakers can occur on steeply sloping beaches. There is only one row of breakers.

Surging breakers surge over steeply sloping (but not vertical) beaches or rocks. Waves break one at a time. Photos Van Dorn, 1974

When waves break, their energy is absorbed and converted to heat. The gentler the slope of the beach, the more energy is converted. Steep slopes such as rocky shores do not break waves as much but reflect them back to sea.

When approaching a gently sloping shore, waves are slowed down and bent towards the shore.

When approaching a steep rocky shore, waves are bounced back, creating a 'confused sea' of interfering waves with twice the height and steepness. Such places may become hazardous to shipping in otherwise acceptable sea conditions.
 

When wave fronts approach a gently sloping beach on an angle, they slow down in the shallows, causing them to bend towards the beach. If the beach slopes gently enough, all breakers will eventually line up parallel to the beach.

When a beach is steep, the wave fronts get bent and then reflected back. Sometimes part of the energy is absorbed and the remaining energy reflected.

This drawing shows how waves are bent around an island which should be at least 2-3 wave lengths wide in order to offer some shelter. It causes immediately in the lee of the island (A) a wave shadow zone but further out to sea a confusing sea (B) of interfering but weakened waves which at some point (C) focuses the almost full wave energy from two directions, resulting in unpredictable and dangerous seas. When seeking shelter, avoid navigating through this area. Recent research has shown that underwater sand banks can act as wave lenses, refracting the waves and focussing them some distance farther. It may suddenly accelerate coastal erosion in localised places along the coast. Drawings from Van Dorn, 1974.

• The amplitude of a tsunami depends on the size of the original disturbance and distance travelled. A tsunami wave behaves much the same as the widening circle radiating out from a pebble's plunge. As the circle widens, the wave's crest lengthens and its height decreases proportionally to the square root of distance travelled. After about 6700 nautical miles (12,000 km) it reaches minimum amplitude, after which it starts focusing again under the influence of coriolis forces and the curvature of Earth. At sea a tsunami is hardly noticeable even though it travels so fast, typically rising less than a metre over a period of 10-30 seconds. Such movement is easily concealed by local waves.
• The speed of a tsunami wave is limited by the depth of the sea, to about 450 knots (830 km/hr) in the Pacific Ocean.
• A tsunami of 4000m deep, bounces off the continental shelf, producing a variety of wave forms. The continental shelf of 100m is a very shallow area for these waves and they rise, form steep crests and very large horizontal water movements, which over-run low lying areas, rip boats from their moorings and may bare the sea to a depth of 5m or splash against the coast to a height of 20-30m. The first tsunami wave is not necessarily the worst.

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.

Dr 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.

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.

Earthquakes 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

Also read Tsunami by Frank I Gonzalez. Scientific American, May 1999. (Available from the Seafriends library)
Visit Dr George Pararas-Carayannis pages on earthquakes and tsunamis.
 

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 (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 disproof  Simon Days' findings, common sense evaluation of the situation makes 40-50m tall waves swamping America and Britain, highly unlikely.
 

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, g = acceleration of gravity (9.8), d = thickness of the upper layer p1 = density of top layer, p2 = density of deep layer. 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.

Although 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 When 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 (Lithothamnia sp) thrive, protecting the rock. What are the forces of the waves that carve these shapes?

When 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 disappearingdue 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, flea mussels, greenlipped mussels. Plants: various matting algae, pink paint (Lithothamnia 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.
 

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 entering 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.

Close-up of a polished paua shell. Notice that the rock is covered by a rock-hard pink alga, affectionately called 'pink paint' (Lithothamnia 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.

Close-up of pink paint (Lithothamnia 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.

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.