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20 3.3 Waves on the Shore
Most of the waves discussed in the previous section referred to deep water waves in the open ocean. But what happens when these waves move towards shore and encounter shallow water? Remember that in deep water, a wave’s speed depends on its wavelength, but in shallow water wave speed depends on the depth (section 3.1). When waves approach the shore they will “touch bottom” at a depth equal to half of their wavelength; in other words, when the water depth equals the depth of the wave base (Figure 3.3.1). At this point their behavior will begin to be influenced by the bottom.
When the wave touches the bottom, friction causes the wave to slow down. As one wave slows down, the one behind it catches up to it, thus decreasing the wavelength. However, the wave still contains the same amount of energy, so while the wavelength decreases, the wave height increases. Eventually the wave height exceeds 1/7 of the wavelength, and the wave becomes unstable and forms a breaker. Often breakers will start to curl forwards as they break. This is because the bottom of the wave begins to slow down before the top of the wave, as it is the first part to encounter the seafloor. So the crest of the wave gets “ahead” of the rest of the wave, but has no water underneath it to support it (Figure 3.3.1).
Figure 3.3.1 As waves approach shore they “touch bottom” when the depth equals half of the wavelength, and the wave begins to slow down. As is slows, the wavelength decreases and the wave height increases, until the wave breaks (Steven Earle “Physical Geology”).
There are three main types of breakers: spilling, plunging, and surging. These are related to the steepness of the bottom, and how quickly the wave will slow down and its energy will get dissipated.
Spilling breakers form on gently sloping or flatter beaches, where the energy of the wave is dissipated gradually. The wave slowly increases in height, then slowly collapses on itself (Figure 3.3.2). For surfers, these waves provide a longer ride, but they are less exciting.
Figure 3.3.2 A spilling breaker. The gentle slope of the bottom causes the wave height to slowly increase until the wave collapses on itself (left: JR, right: James St. John, [CC-BY-2.0], https://www.flickr.com/photos/jsjgeology/23769708334).
Plunging breakers form on more steeply-sloped shores, where there is a sudden slowing of the wave and the wave gets higher very quickly. The crest outruns the rest of the wave, curls forwards and breaks with a sudden loss of energy (Figure 3.3.3). These are the “pipeline” waves that surfers seek out.
Figure 3.3.3 A plunging breaker. The steeper slope causes the wave height to increase more rapidly, with the crest of the wave outrunning the base of the wave, causing it to curl as it breaks (left: JR, right: Andrew Schmidt, Public Domain [CC-0], publicdomainpictures.net).
Surging breakers form on the steepest shorelines. The wave energy is compressed very suddenly right at the shoreline, and the wave breaks right onto the beach (Figure 3.3.4). These waves give too short (and potentially painful) a ride for surfers to enjoy.
Figure 3.3.4 A surging breaker. The very steep slope causes the wave height to increase suddenly and break right on the beach (left: JR, right: Tewy, [CC-BY-SA-3.0], via Wikimedia Commons).
Wave Refraction
Swell can be generated anywhere in the ocean and therefore can arrive at a beach from almost any direction. But if you have ever stood at the shore you have probably noticed that the waves usually approach the shore somewhat parallel to the coast. This is due to wave refraction. If a wave front approaches shore at an angle, the end of the wave front closest to shore will touch bottom before the rest of the wave. This will cause that shallower part of the wave to slow down first, while the rest of the wave that is still in deeper water will continue on at its regular speed. As more and more of the wave front encounters shallower water and slows down, the wave font refracts and the waves tend to align themselves nearly parallel to the shoreline (they are refracted towards the region of slower speed). As we will see in section 5.2, the fact that the waves do not arrive perfectly parallel to the beach causes longshore currents and longshore transport that run parallel to the shore.
Refraction can also explain why waves tend to be larger off of points and headlands, and smaller in bays. A wave front approaching shore will touch the bottom off of the point before it touches bottom in a bay. Once again, the shallower part of the wave front will slow down, and cause the rest of the wave front to refract towards the slower region (the point). Now all of the initial wave energy is concentrated in a relatively small area off of the point, creating large, high energy waves (Figure 3.3.6). In the bay, the refraction has caused the wave fronts to refract away from each other, dispersing the wave energy, and leading to calmer water and smaller waves. This makes the large waves of a “point break” ideal for surfing, while water is calmer in a bay, which is where people would launch a boat. This difference in wave energy also explains why there is net erosion on points, while sand and sediments get deposited in bays (see section 5.3).
Figure 3.3.6 Waves approaching shore (blue lines) touch bottom sooner off of points and are refracted towards the points, concentrating their wave energy. Wave energy is spread out in bays, causing smaller waves. Dotted lines represent the bottom contours (PW).
Marine mammals evolved within the last 60 million years from four-legged land ancestors who returned to the sea to increase their access to food. They're most closely related to modern camels and hippos. Next time that you go to the National Aquarium in Baltimore, look up at the whale skeleton and look at the pectoral fins for a hint of the past. As a group, marine mammals share these common features:
a streamlined body shape for more efficient movement through the water
a high metabolic rate that generates a lot of heat and layers of fat and, in some cases, fur, to conserve this heat
modifications to their respiratory system to collect and retain large volumes of oxygen to allow deep and repetitive dives
osmotic adaptations that free them from any requirement for fresh water
Their nostrils have migrated to the top of the head so that the animal doesn't have to come completely out of the water to breathe
Large, deeply convoluted brains
A special skin that "gives" to dampen out irregularities in water flow
Bronchial cartilage that supports their lungs against pressure during deep dives
Their blood is especially rich in hemoglobin to store more oxygen for diving
They can slow their heartbeat while diving
The blood supply can be reduced to all but the vital organs while diving, to conserve oxygen
Whale groups come in two 'flavors' (sub-Orders) – Odontocetes (toothed whales) and Mysticetes (baleen whales)
Odontocetes (toothed whales): The Odontocetes, a parvorder of cetaceans, are the toothed whales and include the sperm whale, killer whale, dolphins and others. They're generally smaller and less evolved than the baleen whales. They have powerful jaws for capturing prey and use echolocation to find their prey (a form of SONAR). This echolocation can be used to find their way around easily, even in murky water, and can be used to stun or even kill their prey. They're considered to be very intelligent.
Sperm whales are the largest of the toothed whales, reaching lengths up to 60 ft
It also possesses the largest brain ever to have evolved on Earth
They can dive to greater depths than any other air-breathing animal – to 3000 ft – and can stay down for over an hour
Their head is filled with up to a ton of clear oil, presumably used to focus sound waves passing to their prey and back
Mysticetes (baleen whales): Also known as baleen whales, the Mysticetes are considered to be more highly evolved than the Odontocetes. Baleen is a bristly, bush, fibrous substance set in the jaws in overlapping plates; it looks like a gigantic comb.
They feed on small planktonic arthropods (krill)
Baleen is a straining mechanism
The whale takes in a big gulp of water, closes its jaws, raises its tongue to expel the water, and the food is caught on the surface of the baleen
The food is swallowed after being licked from the baleen by the whale's giant tongue
Baleen whales include the blue, humpback and gray, among others
Public Domain
Blue whale
The blue whale is probably the largest animal ever to have lived on Earth
They're usually described as up to about 100 feet in length and up to about 200 tons
this compares to three railroad cars in length and about 1600 people in weight
Blue whales feed on krill, which are tiny shrimp-like crustaceans
A mature blue whale consumes about 4 tons of krill per day when it's feeding
For a 7 to 8 month period; it fasts when it is in tropical waters
From December through April, the blue whale gorges on krill around the Antarctic
Humpback whale
Humpbacks are stocky and seldom exceed 50 ft in length
They're generally black above and white below, with extremely long, wing-like flippers
They've become known for their "song", which are sounds with definite patterns and sequences
All the whales in a given population sing the same song, but the song changes every year
Humpbacks are also very acrobatic, at times leaping completely out of the water
It is estimated that there are no more than 10,000 humpbacks surviving today
Gray whale
The Gray whale is the only large whale with a heavily mottled appearance and a knobby ridge down the back
Its 'natural' color is dark gray or black, but it's covered by a profusion of spots, scars, patches, and clusters of barnacles, which gives it a mottled, grayish appearance
The Gray whale makes the longest migration of any mammal, an annual round-trip of some 10,000 miles from the Bering and Chukchi seas in the high Arctic to the warm lagoons of Baja California
They were easily caught by whalers and almost became extinct in the 1940's
Given full protection in 1946, they've made a successful comeback and their population, estimated at about 21,000, is now believed to be inline with the carrying capacity of their range
The Gray whale is the most heavily parasitized of all cetaceans – playing host to three species of lice, some over an inch long – in one case, more than 100,000 of one species of louse were removed from a single whale
Written by Dr. Cristina Cardona.
Radiant energy from the sun is important for several major oceanic processes:
Climate, winds, and major ocean currents are ultimately dependent on solar radiation reaching the Earth and heating different areas to different degrees.
Sunlight warms the surface water where much oceanic life lives.
Solar radiation provides light for photosynthesis, which supports the entire ocean ecosystem.
The energy reaching Earth from the sun is a form of electromagnetic radiation, which is represented by the electromagnetic spectrum (Figure 5.9.1). Electromagnetic waves vary in their frequency and wavelength. High frequency waves have very short wavelengths, and are very high energy forms of radiation, such as gamma rays and x-rays. These rays can easily penetrate the bodies of living organisms and interfere with individual atoms and molecules. At the other end of the spectrum are low energy, long wavelength waves such as radio waves, which do not pose a hazard to living organisms.
Most of the solar energy reaching the Earth is in the range of visible light, with wavelengths between about 400-700 nm. Each color of visible light has a unique wavelength, and together they make up white light. The shortest wavelengths are on the violet and ultraviolet end of the spectrum, while the longest wavelengths are at the red and infrared end. In between, the colors of the visible spectrum comprise the familiar "ROYGBIV"; red, orange, yellow, green, blue, indigo, and violet.
Figure 5.9.1 The electromagnetic spectrum. Frequency is expressed in Hertz (Hz), or waves per second, while wavelengths are expressed in meters (Phillip Roman, CC BY-SA 3.0, via Wikimedia Commons).
Water is very effective at absorbing incoming light, so the amount of light penetrating the ocean declines rapidly (is attenuated) with depth (Figure 5.9.2). At 1 m depth, only 45% of the solar energy that falls on the ocean surface remains. At 10 m depth only 16% of the light is still present, and only 1% of the original light is left at 100 m. No light penetrates beyond 1000 m.
In addition to overall attenuation, the oceans absorb the different wavelengths of light at different rates (Figure 5.9.2). The wavelengths at the extreme ends of the visible spectrum are attenuated faster than those wavelengths in the middle. Longer wavelengths are absorbed first; red is absorbed in the upper 10 m, orange by about 40 m, and yellow disappears before 100 m. Shorter wavelengths penetrate further, with blue and green light reaching the deepest depths.
Figure 5.9.2 Light penetration in open ocean and coastal water, showing the different depths to which each color will penetrate (By NOAA - National Oceanic and Atmospheric Administration [Public domain], via Wikimedia Commons).
This explains why everything appears blue under water. The colors we perceive depends on the wavelengths of light that are received by our eyes. If an object appears red to us, that is because the object reflects red light but absorbs all of the other colors. So the only color reaching our eyes is red. Under water, blue is the only color of light still available at depth, so that is the only color that can be reflected back to our eyes, and everything has a blue tinge under water. A red object at depth will not appear red to us because there is no red light available to reflect off of the object. Objects in water will only appear as their real colors near the surface where all wavelengths of light are still available, or if the other wavelengths of light are provided artificially, such as by illuminating the object with a dive light.
Water in the open ocean appears clear and blue because it contains much less particulate matter, such as phytoplankton or other suspended particles, and the clearer the water, the deeper the light penetration. Blue light penetrates deeply and is scattered by the water molecules, while all other colors are absorbed; thus the water appears blue. On the other hand, coastal water often appears greenish (Figure 5.9.2). Coastal water contains much more suspended silt and algae and microscopic organisms than the open ocean. Many of these organisms, such as phytoplankton, absorb light in the blue and red range through their photosynthetic pigments, leaving green as the dominant wavelength of reflected light. Therefore the higher the phytoplankton concentration in water, the greener it appears. Small silt particles may also absorb blue light, further shifting the color of water away from blue when there are high concentrations of suspended particles.
The ocean can be divided into depth layers depending on the amount of light penetration, as discussed in section 1.3 (Figure 5.9.3). The upper 200 m is referred to as the photic or euphotic zone. This represents the region where enough light can penetrate to support photosynthesis, and it corresponds to the epipelagic zone. From 200-1000 m lies the dysphotic zone, or the twilight zone (corresponding with the mesopelagic zone). There is still some light at these depths, but not enough to support photosynthesis. Below 1000 m is the aphotic (or midnight) zone, where no light penetrates. This region includes the majority of the ocean volume, which exists in complete darkness.
Figure 5.9.3 The zones of the water column as defined by the amount of light penetration (PW).
Radiant energy from the sun is important for several major oceanic processes:
Climate, winds, and major ocean currents are ultimately dependent on solar radiation reaching the Earth and heating different areas to different degrees.
Sunlight warms the surface water where much oceanic life lives.
Solar radiation provides light for photosynthesis, which supports the entire ocean ecosystem.
The energy reaching Earth from the sun is a form of electromagnetic radiation, which is represented by the electromagnetic spectrum (Figure 5.9.1). Electromagnetic waves vary in their frequency and wavelength. High frequency waves have very short wavelengths, and are very high energy forms of radiation, such as gamma rays and x-rays. These rays can easily penetrate the bodies of living organisms and interfere with individual atoms and molecules. At the other end of the spectrum are low energy, long wavelength waves such as radio waves, which do not pose a hazard to living organisms.
Most of the solar energy reaching the Earth is in the range of visible light, with wavelengths between about 400-700 nm. Each color of visible light has a unique wavelength, and together they make up white light. The shortest wavelengths are on the violet and ultraviolet end of the spectrum, while the longest wavelengths are at the red and infrared end. In between, the colors of the visible spectrum comprise the familiar "ROYGBIV"; red, orange, yellow, green, blue, indigo, and violet.
Water is very effective at absorbing incoming light, so the amount of light penetrating the ocean declines rapidly (is attenuated) with depth (Figure 5.9.2). At 1 m depth, only 45% of the solar energy that falls on the ocean surface remains. At 10 m depth only 16% of the light is still present, and only 1% of the original light is left at 100 m. No light penetrates beyond 1000 m.
In addition to overall attenuation, the oceans absorb the different wavelengths of light at different rates (Figure 5.9.2). The wavelengths at the extreme ends of the visible spectrum are attenuated faster than those wavelengths in the middle. Longer wavelengths are absorbed first; red is absorbed in the upper 10 m, orange by about 40 m, and yellow disappears before 100 m. Shorter wavelengths penetrate further, with blue and green light reaching the deepest depths.
Figure 5.9.2 Light penetration in open ocean and coastal water, showing the different depths to which each color will penetrate (By NOAA - National Oceanic and Atmospheric Administration [Public domain], via Wikimedia Commons).
This explains why everything appears blue under water. The colors we perceive depends on the wavelengths of light that are received by our eyes. If an object appears red to us, that is because the object reflects red light but absorbs all of the other colors. So the only color reaching our eyes is red. Under water, blue is the only color of light still available at depth, so that is the only color that can be reflected back to our eyes, and everything has a blue tinge under water. A red object at depth will not appear red to us because there is no red light available to reflect off of the object. Objects in water will only appear as their real colors near the surface where all wavelengths of light are still available, or if the other wavelengths of light are provided artificially, such as by illuminating the object with a dive light.
Water in the open ocean appears clear and blue because it contains much less particulate matter, such as phytoplankton or other suspended particles, and the clearer the water, the deeper the light penetration. Blue light penetrates deeply and is scattered by the water molecules, while all other colors are absorbed; thus the water appears blue. On the other hand, coastal water often appears greenish (Figure 5.9.2). Coastal water contains much more suspended silt and algae and microscopic organisms than the open ocean. Many of these organisms, such as phytoplankton, absorb light in the blue and red range through their photosynthetic pigments, leaving green as the dominant wavelength of reflected light. Therefore the higher the phytoplankton concentration in water, the greener it appears. Small silt particles may also absorb blue light, further shifting the color of water away from blue when there are high concentrations of suspended particles.
The ocean can be divided into depth layers depending on the amount of light penetration, as discussed in section 1.3 (Figure 5.9.3). The upper 200 m is referred to as the photic or euphotic zone. This represents the region where enough light can penetrate to support photosynthesis, and it corresponds to the epipelagic zone. From 200-1000 m lies the dysphotic zone, or the twilight zone (corresponding with the mesopelagic zone). There is still some light at these depths, but not enough to support photosynthesis. Below 1000 m is the aphotic (or midnight) zone, where no light penetrates. This region includes the majority of the ocean volume, which exists in complete darkness.
Figure 5.9.3 The zones of the water column as defined by the amount of light penetration (PW).
Estuaries are partially enclosed bodies of water where the salt water is diluted by fresh water input from land, creating brackish water with a salinity somewhere between fresh water and normal seawater. Estuaries include many bays, inlets, and sounds, and are often subject to large temperature and salinity variations due to their enclosed nature and smaller size compared to the open ocean.
Estuaries can be classified geologically into four basic categories based on their method of origin. In all cases they are a result of rising sea level over the last 18,000 years, beginning with the end of the last ice age; a period that has seen a rise of about 130 m. The rise in sea level has flooded coastal areas that were previously above water, and prevented the estuaries from being filled in by all of the sediments that have been emptied into them.
The first type is a coastal plain estuary, or drowned river valley. These estuaries are formed as sea level rises and floods an existing river valley, mixing salt and fresh water to create the brackish conditions where the river meets the sea. These types of estuaries are common along the east coast of the United States, including major bodies such as the Chesapeake Bay, Delaware Bay, and Narragansett Bay (Figure 4.6.1). Coastal plain estuaries are usually shallow, and since there is a lot of sediment input from the rivers, there are often a number of depositional features associated with them such as spits and barrier islands.
Figure 4.6.1 A coastal plain estuary. Sea level has risen and flooded what was once a river valley. The satellite image shows Chesapeake Bay and Delaware Bay, two coastal plain estuaries (left: JR, right: NASA, Public Domain via Wikimedia Commons).
The presence of sand bars, spits, and barrier islands can lead to bar-built estuaries, where a barrier is created between the mainland and the ocean. The water that remains inside the sand bar is cut off from complete mixing with the ocean, and receives freshwater input from the mainland, creating estuarine conditions (Figure 4.6.2).
Figure 4.6.2 A bar-built estuary. Sand bars and barrier islands have partially isolated a lagoon from the rest of the ocean. Freshwater input into the lagoon from the mainland creates brackish conditions in the estuary. At right is a satellite image of Pamlico Sound, North Carolina, a bar-built estuary surrounded by spits and barrier islands (left: JR, right: NASA, Public Domain via Wikimedia Commons).
Fjords are estuaries formed in deep, U-shaped basins that were carved out by advancing glaciers. When the glaciers melted and retreated, sea level rose and filled these troughs, creating deep, steep-walled fjords (Figure 4.6.3). Fjords are common in Norway, Alaska, Canada, and New Zealand, where there are mountainous coastlines once covered by glaciers.
Figure 4.6.3 A fjord is a deep estuary that was carved out by glacial movements. At right is Geirangerfjord, Norway (left: JR, right: Fgmedia, [CC-BY-SA-3.0], via Wikimedia Commons).
Tectonic estuaries are the result of tectonic movements, where faulting causes some sections of the crust to subside, and those lower elevation sections then get flooded with seawater. San Francisco Bay is an example of a tectonic estuary (Figure 4.6.4).
Figure 4.6.4 A tectonic estuary, formed from the subsidence of crust along fault lines, and the subsequent filling by seawater. San Francisco Bay is a tectonic estuary, shown at right (left: JR, right: USGS, Public Domain, via Wikimedia Commons).
Estuaries are also classified based on their salinity and mixing patterns. The amount of mixing of fresh and salt water in an estuary depends on the rate at which fresh water enters the head of the estuary from river input, and the amount of seawater that enters the estuary mouth as a result of tidal movements. The input of fresh water is reflected in the flushing time of the estuary. This refers to the time it would take for the in-flowing fresh water to completely replace all the fresh water currently in the estuary. Seawater input is measured by the tidal volume, or tidalprism, which is the average volume of sea water entering and leaving the estuary during each tidal cycle. In other words, it is the volume difference between high and low tides. The interaction between the flushing time, tidal volume, and the shape of the estuary will determine the extent and type of water mixing within the estuary.
In a vertically mixed, or well-mixed estuary there is complete mixing of fresh and salt water from the surface to the bottom. In a particular location the salinity is constant at all depths, but across the estuary the salinity is lowest at the head where the fresh water enters, and is highest at the mouth, where the seawater comes in. This type of salinity profile usually occurs in shallower estuaries, where the shallow depths allow complete mixing from the surface to the bottom.
Figure 4.6.5 A well-mixed estuary. The shallow basin allows nearly complete mixing or fresh and seawater from top to bottom. Salinities are in ppt (JR).
Slightly stratified or partially mixed estuaries have similar salinity profiles to vertically mixed estuaries, where salinity increases from the head to the mouth, but there is also a slight increase in salinity with depth at any point. This usually occurs in deeper estuaries than those that are well-mixed, where waves and currents mix the surface water, but the mixing may not extend all the way to the bottom.
Figure 4.6.6 A slightly-stratified estuary. Generally deeper than a well-mixed estuary, the inflow of seawater (dark blue arrow) and fresh water (light blue arrow) create an estuary where salinity increases with depth, and at the surface when moving from the head to the mouth of the estuary. Salinities are in ppt (JR).
A salt wedge estuary occurs where the outflow of fresh water is strong enough to prevent the denser ocean water to enter through the surface, and where the estuary is deep enough that surface waves and turbulence have little mixing effect on the deeper water. Fresh water flows out along surface, salt water flows in at depth, creating a wedge shaped lens of seawater moving along the bottom. The surface water may remain mostly fresh throughout the estuary if there is no mixing, or it can become brackish depending on the level of mixing that occurs.
Figure 4.6.7 A salt wedge estuary. Strong river outflow (light blue arrows) creates a layer of mostly fresh water that sits on top of a wedge of encroaching seawater along the bottom (dark blue arrow). Salinities are in ppt (JR).
Highly stratified profiles are found in very deep estuaries, such as in fjords. Because of the depth, mixing of fresh and salt water only occurs near the surface, so in the upper layers salinity increases from the head to the mouth, but the deeper water is of standard ocean salinity.
Figure 4.6.8 A highly stratified estuary. Strong river outflow and a deep basin prevent mixing between surface and bottom water, creating an estuary that is vertically stratified. Salinities are represented in ppt (JR).
Estuaries are very important commercially, as they are home to the majority of the world’s metropolitan areas, they serve as ports for industrial activity, and a large percentage of the world's population lives near estuaries. Estuaries are also very important biologically, especially in their role as the breeding grounds for many species of fish, birds, and invertebrates.
Most ocean waves are generated by wind. Wind blowing across the water's surface creates little disturbances called capillary waves, or ripples that start from gentle breezes (Figure 3.2.1). Capillary waves have a rounded crest with a V-shaped trough, and wavelengths less than 1.7 cm. These small ripples give the wind something to "grip" onto to generate larger waves when the wind energy increases, and once the wavelength exceeds 1.7 cm the wave transitions from a capillary wave to a wind wave. As waves are produced, they are opposed by a restoring force that attempts to return the water to its calm, equilibrium condition. The restoring force of the small capillary waves is surface tension, but for larger wind-generated waves gravity becomes the restoring force.
Figure 3.2.1 Small capillary waves or ripples caused by winds blowing over the surface of calm water (By Blue Elf (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0], via Wikimedia Commons).
As the energy of the wind increases, so does the size, length and speed of the resulting waves. There are three important factors determining how much energy is transferred from wind to waves, and thus how large the waves will get:
Wind speed.
The duration of the wind, or how long the wind blows continuously over the water.
The distance over which the wind blows across the water in the same direction, also known as the fetch.
Increasing any of these factors increases the energy of wind waves, and therefore their size and speed. But there is an upper limit to how large wind-generated waves can get. As wind energy increases, the waves receive more energy and they get both larger and steeper (recall from section 3.1 that wave steepness = height/wavelength). When the wave height exceeds 1/7 of the wavelength, the wave becomes unstable and collapses, forming whitecaps.
The ocean surface represents an irregular mixture of hundreds of waves of different speeds and sizes, all coming from different directions and interacting with each other. A histogram of wave heights within this mixture reveals a bell-shaped curve (Figure 3.2.2). In addition to basic statistics such as mode (most probable), median and mean wave height, wave heights are also reported in other ways. Marine weather forecasts and ship and buoy data often report significant wave height (Hs), which is the mean height of the largest one-third of the waves. Mean wave height is approximately equal to two-thirds of the significant wave height. Finally, there is the minimum height of the highest 10% of waves (the 90th percentile of wave heights), often expressed as H1/10.
Figure 3.2.2 Histogram of typical wave height distribution at sea, showing common statistical measurements (NOAA, Public Domain via Wikimedia Commons).
Under strong wind conditions, the ocean surface becomes a chaotic mixture of choppy, whitecapped wind-generated waves. The term sea state describes the size and extent of the wind-generated waves in a particular area. When the waves are at their maximum size for the existing wind speed, duration, and fetch, it is referred to as a fully developed sea. The sea state is often reported on the Beaufort scale, ranging from 0-12, where 0 means calm, windless and waveless conditions, while Beaufort 12 is a hurricane (see box below).
The Beaufort Scale
The Beaufort scale is used to describe the wind and sea state conditions on the ocean. It is an observational scale based on the judgement of the observer, rather than one dictated by accurate measurements of wave height. Beaufort 0 represents calm, flat conditions, while Beaufort 12 represents a hurricane.
(Images by United States National Weather Service (http://www.crh.noaa.gov/mkx/marinefcst.php) [Public domain], via Wikimedia Commons).
A fully developed sea often occurs under stormy conditions, where high winds create a chaotic, random pattern of waves and whitecaps of varying sizes. The waves will propagate outwards from the center of the storm, powered by the strong winds. However, as the storm subsides and the winds weaken, these irregular seas will sort themselves out into more ordered patterns. Recall that open ocean waves will usually be deep water waves, and their speed will depend on their wavelength (section 3.1). As the waves move away from the storm center, they sort themselves out based on speed, with longer wavelength waves traveling faster than shorter wavelength waves. This means that eventually all of the waves in a particular area will be traveling with the same wavelength, creating regular, long period waves called swell (Figure 3.2.3). We experience swell as the slow up and down or rocking motion we feel on a boat, or with the regular arrival of waves on shore. Swell can travel very long distances without losing much energy, so we can observe large swells arriving at the shore even where there is no local wind; the waves were produced by a storm far offshore, and were sorted into swell as they traveled towards the coast.
Figure 3.2.3 Ocean swell, the regular pattern of waves of equal wavelength (Phillip Capper [CC BY 2.0], via Wikimedia Commons).
Because swell travels such long distances, eventually swells coming from different directions will run into each other, and when they do they create interference patterns. The interference pattern is created by adding the features of the waves together, and the type of interference that is created depends on how the waves interact with each other (Figure 3.2.4). Constructive interference occurs when the two waves are completely in phase; the crest of one wave lines up exactly with the crest of the other wave, as do the troughs of the two waves. Adding the two crest together creates a crest that is higher than in either of the source waves, and adding the troughs creates a deeper trough than in the original waves. The result of constructive interference is therefore to create waves that are larger than the original source waves. In destructive interference, the waves interact completely out of phase, where the crest of one wave aligns with the trough of the other wave. In this case, the crest and the trough work to cancel each other out, creating a wave that is smaller than either of the source waves. In reality, it is rare to find perfect constructive or destructive interference as displayed in Figure 3.2.4. Most interference by swells at sea is mixed interference, which contains a mix of both constructive and destructive interference. The interacting swells do not have the same wavelength, so some points show constructive interference, and some points show destructive interference, to varying degrees. This results in an irregular pattern of both small and large waves, called surf beat.
It is important to point out that these interference patterns are only temporary disturbances, and do not affect the properties of the source waves. Moving swells interact and create interference where they meet, but each wave continues on unaffected after the swells pass each other.
Figure 3.2.4 Wave interference patterns. In constructive interference the source waves (red) are completely in phase, and when added together produce waves that are larger than the original waves (blue). In destructive interference the source waves are out of phase, so they cancel each other out and produce waves that are smaller than the originals. In mixed interference, constructive and destructive interference occur at various point, creating an irregular wave pattern. (Modified by PW from original version: Haade; vectorization: Wjh31, Quibik (Vecorized from File:Interference of two waves.png) [CC BY-SA 3.0 or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons).
About half of the waves in the open sea are less than 2 m high, and only 10-15% exceed 6 m. But the ocean can produce some extremely large waves. The largest wind wave reliably measured at sea occurred in the Pacific Ocean in 1935, and was measured by the navy tanker the USS Ramapo. Its crew measured a wave of 34 m or about 112 ft high! Occasionally constructive interference will produce waves that are exceptionally large, even when all of the surrounding waves are of normal height. These random, large waves are called rogue waves (Figure 3.2.5). A rogue wave is usually defined as a wave that is at least twice the size of the significant wave height, which is the average height of the highest one-third of waves in the region. It is not uncommon for rogue waves to reach heights of 20 m or more.
Figure 3.2.5 A rogue wave in the Bay of Biscay, off of the French coast, ca. 1940 (NOAA, [Public domain], via Wikimedia Commons).
Rogue waves are particularly common off of the southeast coast of South Africa, a region referred to as the "wild coast." Here, Antarctic storm waves move north into the oncoming Agulhas Current, and the wave energy gets focused over a narrow area, leading to constructive interference. This area may be responsible for sinking more ships than anywhere else on Earth. On average about 100 ships are lost every year across the globe, and many of these losses are probably due to rogue waves.
Waves in the Southern Ocean are generally fairly large (the red areas in Figure 3.2.6) because of the strong winds and the lack of landmasses, which provide the winds with a very long fetch, allowing them to blow unimpeded over the ocean for very long distances. These latitudes have been termed the “Roaring Forties”, “Furious Fifties”, and “Screaming Sixties” due to the high winds.
Figure 3.2.6 Wind speed and wave height data for a 9-day period in 1992. The Southern Ocean is notorious for its high winds and large waves (NASA, Public Domain via Wikimedia Commons).
