Speed of propagation of wind waves. Sea waves
Sea roughness is the oscillation of the water surface up and down from the average level. However, they do not move horizontally during waves. You can verify this by observing the behavior of a float swinging on the waves.
Waves are characterized by the following elements: the lowest part of the wave is called the trough, and the highest part is called the crest. The steepness of a slope is the angle between its slope and the horizontal plane. The vertical distance between the base and the crest is the height of the wave. It can reach 14-25 meters. The distance between two troughs or two crests is called the wavelength. The longest length is about 250 m; waves up to 500 m are extremely rare. The speed of wave movement is characterized by their speed, i.e. the distance covered by the comb usually in a second.
The main reason for wave formation is. At low speeds, ripples appear - a system of small uniform waves. They appear with every gust of wind and instantly fade away. With very strong winds turning into a storm, the waves can be deformed, with the leeward slope being steeper than the windward one, and with very strong winds the wave crests break off and form white foam - “lambs”. When the storm ends, high waves continue to travel across the sea for a long time, but without sharp crests. Long and gentle waves after the wind stops are called swell. A large swell with low steepness and a wave length of up to 300-400 meters in the complete absence of wind is called a wind swell.
The transformation of waves also occurs as they approach the shore. When approaching a gently sloping shore, the lower part of the oncoming wave is slowed down by the ground; the length decreases and the height increases. The top of the wave moves faster than the bottom. The wave overturns, and its crest, falling, crumbles into small, air-saturated, foamy splashes. The waves, breaking up near the shore, form a surf. It is always parallel to the shore. The water splashed onto the shore by the wave slowly flows back down the beach.
When the wave approaches the steep shore, it hits the rocks with all its force. In this case, the wave throws up in the form of a beautiful, foamy shaft, reaching a height of 30-60 meters. Depending on the shape of the rocks and the direction of the waves, the shaft is broken into parts. The impact force of the waves reaches 30 tons per 1 m2. But it should be noted that the main role is played not by the mechanical impacts of masses of water on the rocks, but by the resulting air bubbles and hydraulic changes, which mainly destroy the composing rocks (see Abrasion).
Waves actively destroy coastal land, roll over and abrade debris, and then distribute it along the underwater slope. Near the inland coastline, the impact force of the waves is very high. Sometimes at some distance from the shore there is a shoal in the form of an underwater spit. In this case, the breaking of waves occurs on the shallows, and a breaker is formed.
The shape of the wave changes all the time, giving the impression of running. This occurs due to the fact that each water particle, with a uniform movement, describes circles around the equilibrium level. All these particles move in one direction. At each moment the particles are at different points of the circle; this is the wave system.
The largest wind waves were observed in the Southern Hemisphere, where the ocean is most extensive and where westerly winds are most constant and strong. Here the waves reach 25 meters in height and 400 meters in length. Their movement speed is about 20 m/s. In the seas the waves are smaller - even in the big ones they reach only 5 m.
A 9-point scale is used to assess the degree of sea roughness. It can be used when studying any body of water.
9-point scale for assessing the degree of sea state
| Points | Signs of excitement |
|---|---|
| 0 | Smooth surface |
| 1 | Ripples and small waves |
| 2 | Small wave crests begin to capsize, but there is no white foam yet |
| 3 | In some places “lambs” appear on the crests of the waves |
| 4 | “Lambs” are formed everywhere |
| 5 | High ridges appear, and the wind begins to tear off white foam from them |
| 6 | The crests form the swells of storm waves. The foam begins to stretch completely |
| 7 | Long stripes of foam cover the sides of the waves and in some places reach their base |
| 8 | Foam completely covers the slopes of the waves, the surface becomes white |
| 9 | The entire surface of the wave is covered with a layer of foam, the air is filled with water dust and splashes, visibility is reduced |
To protect port facilities, piers, and coastal areas of the sea from waves, breakwaters are built from stone and concrete blocks to absorb wave energy.
The study of the patterns of wind waves is interesting not only from the standpoint of fundamental science, but also from the standpoint of practical needs, such as navigation, construction of hydraulic structures, port complexes, calculation of technical equipment for oil and gas fields on the shelf. About 80% of proven oil and gas reserves are concentrated on the bottom of the oceans and seas, and the construction of offshore platforms and offshore drilling require reliable data on the wind wave regime. Knowledge of the maximum wave sizes in various waters of the World Ocean is also necessary to ensure the safety of navigation in these places.
Wind waves are a phenomenon that manifests itself on the surface of any body of water. The scale of this phenomenon will be different for different bodies of water. Leonardo da Vinci once wrote: “... a wave runs from the place of its origin, but water does not move from its place. Like the waves formed in the fields in May by the current of the winds, the waves seem to be running across the field, while the fields do not move from their place.” This feature of wind waves
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has enormous practical significance: if along with the form, i.e., the wave, mass, i.e., water, also moved, then not a single ship could move against the waves. Wind waves are usually divided into three types:
Wind waves that are directly under
the action of the wind;
Swell waves that occur after the wind stops
ra or after the waves leave the wind zone;
Mixed waves when wind waves are superimposed on swell waves
Since winds over oceans and seas, especially in temperate latitudes, vary in speed and direction, wind waves are spatially heterogeneous and significantly variable in time. At the same time, wave fields are even more heterogeneous than wind fields, since waves can arrive in one or another region simultaneously from different (differently located) generation zones.
If you look carefully at the rough surface of the sea, you can come to the conclusion that the waves replace each other without any visible pattern - a large wave may be followed by an even larger one, or perhaps a very small one; sometimes several large waves arrive in a row, and sometimes between the waves there is a section of almost calm surface. The great variability of the configuration of the rough sea surface, especially in the case of mixed waves (and this is the most common situation), gave rise to the famous English physicist Lord Thomson to declare that “... the fundamental law of wind waves is the apparent absence of any law.” And, indeed, until now we cannot predict with certainty the sequence of alternation of individual waves even by any one of the characteristics, for example, height, not to mention other characteristics, such as the shape of crests and troughs, etc.
When two harmonic oscillations are added, the frequencies of which are quite close, a non-harmonic oscillation occurs, called a beat, which is characterized by a periodic change in intensity with a frequency equal to the difference between the interacting oscillations (Fig. 10 2). Something similar is observed in wind waves. Since waves come to any area from different zones and their frequencies can be
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Ch. 10. Waves in the ocean 197
The south-eastern region of the African coast is famous - here there are strong winds that disperse large waves, swell coming from the south, and the North Current - all this creates unusually difficult conditions for swimming. Bartolomeo Dias, whose expedition has already been mentioned, resisted strong waves in this area of the ocean for two weeks and, according to legend, sold his soul to the devil in order to pass this place. That time it was helped. Dias passed this place, called it Cape of Storms, but two years later he died there. The Portuguese king Joan II renamed the Cape of Storms to the Cape of Good Hope, since it offered hope of reaching India by sea. It is with this cape that the origin of the legend of the “Flying Dutchman” is associated. It is here that single rogue waves are observed, formed as a result of the interaction of waves and currents. These waves represent a steep swelling of the water, have a very steep front slope and a fairly flat trough. Their height can exceed 15-20 m, and they often occur in relatively calm seas. The waves in this area also pose a serious danger to modern ships. Waves in tropical hurricanes and typhoons also pose a great danger.
The science of waves arose and developed as one of the branches of classical hydrodynamics until the 50s of the 20th century. practically did not begin to describe such complex waves as wind waves on the surface of reservoirs. The degree of excitement was assessed mainly using the Beaufort scale by eye (Table 10.3).
At the beginning of the 20th century. with the transition from a sailing fleet to a steam one, the number of accidents and ship losses decreased somewhat (from 250-300 ships per year to ~150), and an underestimation of natural forces appeared when determining the safety of navigation. Among the shipbuilders of the early 20th century. There was an opinion that “the forces of the elements surrender before new, strong ships.” This opinion cost the lives of many sailors. Sea waves are a rather formidable phenomenon of nature, and nature does not tolerate disdain and often takes revenge on people, thereby initiating people’s desire to better and more deeply understand its laws.
In table Figure 10.4 shows the number of ships lost due to storms and other adverse hydrometeorological conditions, mainly associated with heavy seas, for the period from 1975 to 1979. This sample applies only to relatively large merchant ships (more than 500 register tons). The number of accidents on smaller ships during the same period is determined by a four-digit number. It became clear that
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Ch. 10. Waves in the ocean 199
To measure waves, accelerometric buoy wave recorders based on the principle of an acoustic echo sounder and hydrostatic wave recorders are usually used. Wavegraphs usually measure the average and maximum height of waves, the average period and length of the wave, and the frequency spectrum of the wave.
In an accelerometer wave recorder, wave elements are determined by double integration of the signal received from the accelerometer sensor. The most common foreign wavegraphs are designed exactly according to this principle. The operating principle of hydrostatic wave recorders is based on the connection between hydrostatic oscillations at a certain depth and the characteristics of oscillations of the wave surface.
Echolocation is used when probing instantaneous elevation values of the water surface from a free-floating or moored buoy (direct echo sounder). Wavegraphs, the operating principle of which is based on reverse echolocation, probe the water-air interface from under the water.
Synthetic aperture radars and altimeters installed on satellites make it possible to measure the main characteristics of wind waves. Remote sensing methods make it possible to obtain characteristics of wind waves over large areas. Based on such measurements, modern wind wave atlases are created. Views of wave data can be obtained from the server http://www.waveclimate.com.
As the history of the development of our fundamental knowledge about waves has shown, a close connection between theoretical, experimental and field research is necessary.
Wind is the most important parameter on which the geometric characteristics of waves depend. However, with a steady and fairly continuous wind, the average characteristics of the waves increase along the path of their propagation while they are under the influence of the wind. This path is called the wind acceleration length, or simply acceleration. The difficulties of observing sea waves and recording them in natural conditions forced scientists to turn to laboratory modeling of wind waves. At the beginning of the study of sea waves, laboratory modeling was almost the only source of quantitative characteristics of waves. However, this source turned out to be very limited - and here's why. The main difficulty in laboratory simulation of waves is to ensure a sufficiently large wave acceleration, i.e., you need to have long trays. The average parameters of waves usually change over time and in
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in this case, each spectral component reaches a maximum, then decreases to a minimum, and finally reaches an equilibrium value. This effect is called the excess effect. It was identified by measurements in field and laboratory conditions. The leading part of the spectrum is formed due to the exponential development of its components and the mechanism of nonlinear redistribution of energy between the spectral components. The wind energy balance equation is discussed in detail in monographs.
The most famous and studied type of long waves are tides. Tides are caused by the gravitational (tide-forming) forces of the Moon and the Sun. In the oceans and seas, tides manifest themselves in the form of periodic fluctuations in water surface levels and currents. Tidal movements also exist in the atmosphere, and tidal deformations exist in the solid Earth, but here they are less pronounced than in the ocean.
In coastal zones, the magnitude of level fluctuations reaches 5-10 m. The maximum values of level fluctuations are achieved in the Bay of Fundy (Canada) - 18 m. Off the coast of Russia, the highest tide is observed in Penzhinskaya Bay - 12.9 m. The speed of tidal currents in the coastal zone reaches 15 km/h. In the open ocean, fluctuations in the level and speed of currents are much smaller.
The tidal force of the Moon is approximately twice that of the Sun. The vertical components of the tidal force are much smaller than the force of gravity, so their effect is negligible. But the horizontal component of the tidal force causes significant movements of water particles, which manifest themselves in the form of tides.
The combined action of the Moon and the Sun leads to the formation of complex forms of level fluctuations. The following main types of tides are distinguished: semidiurnal, diurnal, mixed, anomalous. In a semidiurnal tide, the period of oscillation of the water surface is equal to half a lunar day. The amplitude of the semidiurnal tide varies in accordance with the phases of the Moon. The semi-diurnal tide is the most common in the world's oceans. The period of level fluctuations in the daily tide is equal to a lunar day. The amplitude of the daily tide depends on the declination of the Moon. Mixed tides are divided into irregular semidiurnal and irregular diurnal. Abnormal tides
Ch. 10. Waves in the ocean 209
They have several varieties, but all of them are quite rare in the World Ocean.
For maritime practice, the forecast (or pre-calculation) of tidal levels is of great importance. Tidal prediction is based on harmonic analysis of observational data on level fluctuations. Having identified the main harmonic components based on observational data, the level in the future is calculated. The most complete harmonic expansion of the tidal potential, performed by A. Dudson, contains more than 750 components. Methods for predicting tides are discussed in detail in.
The first theory of tides was developed by I. Newton and is called static. In the static theory, the ocean is considered to cover the entire Earth, which is considered as non-deformable, water is considered inviscid and inertialess. With an ocean covering the entire Earth, the static tide is described to within a constant factor by the tidal potential. The water surface of the ocean is described by the so-called “tidal ellipsoid”, the major axis of which is directed towards the disturbing body (Moon, Sun) and follows it. The Earth rotates around its axis and inside this “tidal ellipsoid”. The static theory, despite the weakness of its basic assumptions, correctly describes the basic properties of tides.
A more advanced dynamic theory of tides, which already considers the movement of waves in the ocean, was built by Laplace. In dynamic theory, the equations of motion and the continuity equation are written in the form of Laplace's tidal equations. Laplace's tidal equations are partial differential equations written in a spherical coordinate system, so their analytical solution can only be obtained for ideal cases, for example, a narrow deep channel encircling the entire Earth (the so-called channel theory of tides). For small water areas, Laplace's tidal equations can be written in a Cartesian coordinate system. The results of calculations of tides in the World Ocean are presented in the form of special maps, on which the position of the tidal wave crest at various times (usually lunar) is plotted. Modern tide maps are constructed using numerical methods taking into account observational data.
210 Ch. 10 Waves in the ocean
The long wave theory is based on the assumption that the depth of the liquid N small compared to wavelength A, i.e. A ^> N. Long wave theory describes tidal phenomena, tsunami waves, and wind waves and swells propagating in shallow water. Long waves also include flood waves and boron waves, which are observed on reservoirs and rivers.
long wave amplitude A much less than their length. And then the description can be carried out using linear theory. If these conditions are not met, then it is necessary to take into account nonlinear effects.
Tsunami literally translated from Japanese means “big wave in the harbor.” Tsunamis are usually understood as gravitational waves that arise in the sea as a result of large-scale, short-term disturbances (underwater earthquakes, the eruption of underwater volcanoes, underwater landslides, meteorites falling into the water, rock fragments, explosions in the water, sudden changes in meteorological conditions, etc.).
The characteristic time duration of a tsunami wave is 10-100 minutes; length - 10-1000 km; propagation speed L™Am,m ..^^h^ t^g,l,„„ based on the long-wave approximation
acceleration of gravity, I am depth 
and the height when rolling onto the shore can reach tens of meters. These waves are very long; as a first approximation, the “shallow water” theory is applicable to them.
In terms of the number of deaths per year as a result of natural disasters on Earth, the tsunami ranks 5th after floods, typhoons, earthquakes, and drought. The distribution of tsunamis across regions is characterized by strong heterogeneity; the majority of tsunamis occur in the seas of the Pacific Ocean.
The distribution of tsunamis in the oceans and seas is characterized as follows:
Pacific Ocean (its periphery) 75%
i Atlantic Ocean 9%
Indian Ocean 3%
Mediterranean Sea 12%
other seas 1%
In order to get an idea of tsunamis, we present the characteristics of the largest tsunamis over a hundred-year interval (1880-1980) in Table. 10 6.
To classify tsunamis, Academician S.L. Soloviev proposed a semi-quantitative scale (based on the analysis of historical tsunamis), which is based on the height of the level rise.
Catastrophic tsunamis(intensity 4). The average rise in level on a section of the coast 400 km long (or more) reaches 8 m. In some places the waves are 20-30 m high. All structures on the coast are destroyed. Such tsunamis occur along the entire Pacific coast.
Very strong tsunami(intensity 3). On a coast 200-400 km long, the water rises by 4-8 m, in some places up to 11 m. Such tsunamis are observed throughout most of the World Ocean.
Strong tsunami(intensity 2). On a coast 80-200 km long, the average rise in water level is 2-4 m, in some places 3-6 m.
Moderate tsunamis(intensity 1). In a section of 70-80 km, the water rises by 1-2 m.
Weak tsunamis(intensity 0). The level rise is less than 1 m.
212 Ch. 10 Waves in the ocean
Other tsunamis have intensities from -1 to -5.
The stronger the tsunami, the less often they occur. Tsunamis with intensity 4 occur once every 10 years, and in the Pacific Ocean; intensity 3 - once every 3 years; intensity 2 - 1 time every 2 years; intensity 1 - 1 time per year; intensity 0 - 4 times a year.
The main causes of tsunamis: earthquakes, explosions of volcanic islands and the eruption of underwater volcanoes, landslides and landslides. Let us briefly consider these reasons separately.
About 85% of tsunamis are caused by underwater earthquakes. This is due to the seismicity of many oceanic areas. On average, 100,000 earthquakes occur annually, of which 100 are catastrophic. On average, once every 10 years, an earthquake causes a tsunami in the Pacific Ocean with an average height of up to 8 m (at some points up to 20-30 m) (intensity 4). A tsunami with a height of 4-8 m (of seismic origin) occurs once every 3 years, with a height of 2-4 m - annually.
In the Far East (RF), 3-4 tsunamis with a height of more than 2 m occur in 10 years. The most tragic tsunami in Russia occurred on November 4, 1952 in Severo-Kurilsk. The city was almost completely destroyed. An earthquake began at night, about 40 minutes after it ended, a water shaft fell on the city, which retreated after a few minutes. The seabed was exposed for several hundred meters, but after about 20 minutes a wave more than 10 m high hit the city, destroying almost everything in its path. After being reflected from the hills surrounding the city, the wave rolled into the lowland where the city center had previously been, and completed the destruction. The tsunami took the city's residents by surprise.
There are two zones of earthquake foci on Earth. One is located in the meridional direction and runs along the eastern and western shores of the Pacific Ocean. This zone produces the bulk of the tsunami (up to 80%). The second zone of earthquake sources occupies a latitudinal position - the Apennines, Alps, Carpathians, Caucasus, Tien Shan. Within this zone, tsunamis occur on the shores of the Mediterranean, Adriatic, Arabian, Black Seas, and in the northern part of the Indian Ocean. Less than 20% of all tsunamis occur within this zone.
The mechanism of tsunami generation during earthquakes is as follows. The main reason is the rapid change in the topography of the seabed
Ch. 10 Waves in the ocean 213
(slip), causing deviations of the ocean surface from its equilibrium position. Due to the low compressibility of water, a rapid descent or rise of a significant mass of water occurs in the area of movement. The resulting disturbances propagate in the form of long gravitational waves.
Intensity and magnitude are used to describe earthquakes quantitatively. Intensity is assessed in points (12-point MSK-64 scale). (In Japan, there is a 7-point scale.) Point is a unit of measurement of ground or soil shaking. The main characteristic that determines the intensity is the reaction of soils to seismic waves. The energy of an earthquake is determined by its magnitude M.
The most important task in forecasting tsunamis of seismic origin is to establish signs of tsunamigenicity of earthquakes. It is now believed that if the earthquake magnitude exceeds a certain threshold value Mn, the source is located under the seabed, then the earthquake will be tsunamigenic.
For Japan, empirical formulas have been proposed that relate the magnitude of tsunamigenic earthquakes and the depth of the source N(in kilometers): 
No more than 0.1 of the energy released during an earthquake is converted into tsunami energy.
As a result of the analysis of field data, the following properties of the source of tsunamigenic earthquakes were established. The energy propagates mainly along the normal to the main axis of the source. The degree of directionality depends on the elongation of the lesion. The sources of large tsunamis, as a rule, are very elongated. Their axes are oriented parallel to the nearest coast, depression or island arc, so the main source of energy is directed towards the sea. The ratio of the wave amplitude along the fault and the wave amplitude in the direction perpendicular to the fault is approximately 1/10-1/15. Individual measurements confirm this, for example, the tsunami caused by the 1964 Alaska earthquake, the waves from which were recorded at several seismic stations in the Pacific Ocean. This made it possible to construct a fairly detailed tsunami radiation pattern.
Underwater earthquakes not only cause tsunami waves, they are capable of causing strong disturbances of the water layer in the epicentral region, which can manifest itself in the form of a sharp increase in vertical exchange in the ocean. Vertical
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The exchange leads to transformation of the fields of temperature, salinity and color of the ocean. The release of deep water to the surface will lead to the formation of a widespread ocean surface temperature anomaly. The removal of nutrients into the surface layer, which is usually depleted of these substances, leads to an increase in the concentration of phytoplankton. Since phytoplankton is the primary link in the trophic chain and determines the bioproductivity of waters, phenomena such as the migration of fish, marine animals, etc. are possible. Directly above the epicentral region, strong disturbances of the water layer are observed, manifested in the boiling water, emissions of water columns, and the formation of steep standing waves with an amplitude of up to 10 m. Among sailors, this phenomenon is known as a seaquake. An analysis of satellite ocean surface temperature and seismic data revealed a decrease in ocean surface temperature and an increase in chlorophyll a concentrations that followed a series of large undersea earthquakes off the island of Sulawesi (Indonesia, 2000). A series of laboratory experiments made it possible to establish that fluctuations in the bottom of the basin can lead to the generation of vertical flows that can destroy the existing stable stratification and lead to the release of cold and nutrient-rich deep waters to the surface, which will lead to the formation of an anomaly in ocean surface temperature and chlorophyll concentration.
There are about 520 active volcanoes on earth, two-thirds of which are located on the shores and islands of the Pacific Ocean. Their eruptions often lead to tsunamis. Let's give some examples.
When the Krakatoa volcano exploded on August 26, 1883 in Indonesia, the height of the tsunami wave reached 45 m, killing 36,000 people. Tsunami waves swept across the world. The energy of this catastrophe is equivalent to the energy of the explosion of 250-500 thousand Hiroshima-type atomic bombs.
The explosion of the volcanic island of Tire in the Aegean Sea 35 centuries ago (the volcano and the island were previously called Santorini) caused the death of the Minoan civilization. This event probably served as a prototype for Atlantis. Employees of the Soyuzmornia project S. Strekalov and B. Duginov describe the death of the Minoan civilization as follows.
“The great Minoan civilization was distinguished by unsurpassed works of art and artistic crafts, majestic palaces. In the middle of the 15th century. BC e. disaster struck Crete. Almost all the palaces were destroyed,
Chapter 10. Waves in the ocean 215
The settlements were abandoned by their inhabitants. There are two hypotheses for the death. According to one, it was destroyed by barbarians - the Achaean Greeks; according to another, the cause was a natural disaster. About 3.5 thousand years ago, the volcanic island of Santorini exploded in the Aegean Sea. As a result of the disaster, giant waves were formed that hit the island of Crete and spread to Egypt, flooding the Nile Delta. Was it so? Could it really become the cause of the death of civilization? These questions determined the formulation of the following hydrodynamic problem: “Catastrophic tsunami on the coast of Crete and in Egypt in the 15th-14th centuries. BC"
In the coastal zone of Crete, ceramic products were discovered underwater at depths of 8 to 30 m, and building blocks dating back to ancient times were found at depths of 30-35 m. Based on the fact that the ebb wave is equal to the tidal wave, the first one also had a height of 30-35 m. In search of analogues of such a wave in approximately the corresponding underwater and surface terrain, we turned to the most powerful natural disaster of recent centuries - the explosion of the Krakatoa volcano (at the end of the 19th century .). There, the tsunami wave, according to available data, reached a height of 40 m at the source. Based on the analogue, we assumed that an earthquake with a magnitude of 8.5 occurred in the area of the island of Santorini at a depth of about 300 m. Further, we took the direction of the source axis to coincide with the direction of the isobaths in the area of the island of Santorini and parallel to the longitudinal direction of the island of Crete. Then, as a result of calculations performed using the original methodology developed in Soyuzmorniiproekt, it was established that, in accordance with the initial data, a single soliton-type tsunami wave with a height of 44 m and a length of about 100 km should have arisen; the length of the longitudinal axis of the source is 220 km, and its width is 50 km. The propagation of such a wave makes it possible to assume the following.
To the south of the source, the wave decreases, and off the northern coast of Crete its height is 31 m. As it passes into the bays of the island, the height of the wave increases to 50 m, and after its reflection from the steep shores and the continental slope, individual splashes can reach a height of 60-100 m. The Mediterranean Sea wave passes through the straits, weakening due to shielding by the islands. Upon exiting the Kasos Strait off the southern coast of Crete, the wave height is 9.3 m. After crossing the Mediterranean Sea and the interaction of the wave with the continental slope and shelf in the Nile Delta area, its height becomes 4 m. Along the Nile Delta, which has a low surface slope
216 Chapter 10. Waves in the ocean.
(about 5.5 10~ 5), the wave propagates over a distance of 73 km up to the mouth on the main shore, i.e., almost the entire seaward part of the delta is subject to flooding. In the Nile Delta, over a historical period of several thousand years, the rate of alluvium deposition was almost constant and equal to 0.9-1.3 mm per year. The exception is the second millennium BC, when no noticeable alluvium deposits could be found for reasons that are not entirely clear. It can be assumed that the tsunami wave that flooded the delta during this period of time washed away and carried the entire surface alluvial layer into the sea.
The disaster that occurred on the island of Santorini, along with environmental ones, probably also had serious social consequences. Huge waves, 30-50 m high, were quite capable of destroying the Minoan civilization that existed on Crete. The flooding of the Nile Delta during the period of the late XVIII - early XIX dynasty of the pharaohs was primarily the result of a sharp deterioration of the ecological situation associated with the disappearance of the fertile soil layer, salinization and the formation of swamps. The social consequences due to the agricultural crisis in the delta may ultimately have contributed to the beginning of the decline of the Egyptian kingdom."
Recently (01/08/1933), a volcanic explosion on the island of Kharimkatan led to the formation of a tsunami, with waves reaching 9 m (Kuril ridge).
The most impressive example of the formation of a tsunami wave during a landslide took place on July 10, 1958. The descent of an avalanche with rock volume of 300 million m 3 from the slopes of Mount Fairweather (Alaska) into Lituya Bay created a tsunami 60 m high with a maximum splash of 524 m (splash is the height of the water rise relative to the undisturbed level when the wave rolls onto the shore).
A tsunami up to 15 m high was caused by rock fragments falling from a height of 200 m (Madeira Island, 1930). In Norway in 1934, a tsunami 37 m high was caused by the fall of a rock weighing 3 million tons from a height of 500 m.
Landslides on the slope of the oceanic trench (Puerto Rico) in December 1951 caused a tsunami wave. Landslides and turbidity currents are often observed on the continental slope of the ocean, while the role of indicators of the formation and passage of landslides or turbidity currents is played by ruptures of cables and pipelines.
On October 6, 1979, a 3 m high tsunami hit the Côte d'Azur near Nice. Thorough seismic analysis
Ch. 10. Waves in the ocean 217
The situation and weather conditions allowed us to conclude that the tsunami was caused by underwater landslides. Engineering work on the shelf can trigger the formation of landslides and, as a result, the occurrence of a tsunami.
Explosions in water from atomic and hydrogen bombs can cause a tsunami-type wave. For example, on Bikini Atoll, the Baker explosion created waves about 28 m high at a distance of 300 m from the epicenter. The military considered the issue of artificially creating a tsunami. But since during the formation of a tsunami only a small part of the explosion energy is converted into wave energy, and the direction of the tsunami wave is low, the energy costs of creating an artificial tsunami (a powerful wave run-up in a certain part of the coast) are very high.
In the development of a tsunami, 3 stages are usually distinguished: 1) the formation of waves and their propagation near the source; 2) propagation of waves in the open ocean of great depth; 3) transformation, reflection and destruction of waves on the shelf, their run-up to the shore, resonance phenomena in bays and on the shelf. The research on these stages is significantly different.
To solve the hydrodynamic problem of calculating waves, it is necessary to set the initial conditions - the fields of displacements and velocities in the source. This data can be obtained by directly measuring a tsunami in the ocean or indirectly by analyzing the characteristics of the processes that generate a tsunami. The first tsunami registrations in the open ocean were carried out by S.L. Solovyov et al. in 1980 near the South Kuril Islands. There is a fundamental possibility of determining the parameters in the source based on solving the inverse problem - based on the few manifestations of the tsunami on the shore, determine its parameters in the source. However, as a rule, there is very little natural data for a correct solution of such an inverse problem.
To predict the manifestation of a tsunami in the coastal zone and solve other engineering problems, it is necessary to know the change in height, period, and direction of the wave front due to refraction. This purpose is served by refraction diagrams, which indicate the position of wave crests (fronts) at different distances at the same time, or the positions of the crest of the same wave at different times. The rays (orthogonal to the position of the fronts) are drawn on the same map. Assuming that the energy flow between two orthogonals is conserved, we can estimate the change in wave height. The intersection of the rays leads to an unlimited increase in wave height. Power transferred
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220 Chapter 10. Waves in the ocean
A rising breaker - a wave rolls without breaking on steep slopes.
The disturbance is accompanied by the movement of water masses. The movement of water particles during waves occurs in open orbits and is a random, disordered process that is difficult to theoretically describe and depends on many factors.
The main elements of sea wind waves are as follows: height h - vertical distance from the wave trough to the crest; length X - horizontal distance between two successive ridges or depressions; period T, is the time interval between the passage of the tops of two successive waves through a fixed vertical.
The height of sea wind waves decreases as they move from the surface to the seabed. According to the classical trochoidal theory of waves, their height decreases with depth according to the exponential law
h 2 = he -2r/ ^ (3.1)
where z is the depth from the sea surface; h z and h are the height of waves at depth z and on the sea surface, respectively.
In fact, the attenuation of waves with depth occurs somewhat faster than it follows from the classical wave theory. The results of field studies show that the decrease in the height of surface waves with depth for aquatic
thorium, the depth of which is 2 times or more greater than the wavelength, is more correctly estimated by the expression
h z = he -5.5(z/X)0.8. (3.2)
However, for engineering calculations such clarifications are not significant. In the indicated water areas, the wave height h z at depth z can be approximately calculated based on a simple rule: if the depth increases in an arithmetic progression, then the wave height decreases in a geometric progression (Table 3.1).
Wind waves are divided into forced waves, which arise and are under the influence of wind pressure, and free waves, which occur after the wind stops or go beyond the zone of its action. Free waves are also called swell waves. The results of numerous observations of waves in natural conditions show that for deep-water areas, where the bottom does not affect the shape and size of wind waves, we can assume that X « 20h for wind waves and X « 30h for swell waves (Table 3.2). Obstacles encountered in the path of waves are subject to hydrodynamic loads. According to modern concepts of hydrodynamics, the main components of the total force of wave pressure on any cylindrical obstacle are the drag force, the inertial force and the force of the impact of water on the obstacle.
The drag force is proportional to the square of the linear speed of orbital motion. Its maximum value is achieved when the top of the wave crest passes at the monosupport. The force of drag is due to the fact that on the surface of an obstacle, when a viscous fluid flows around it, a boundary layer of a vortex structure appears, and under certain conditions periodically breaks off. Energy,
Table 3.1
Decrease in wave height with sea depth (in relative units)
Table 3.2
Scales for the degree of wind waves (numerator) and swell (denominator)
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Moderate |
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The main reason for the occurrence of waves on the surface of the water is the effect of wind on the water surface. Waves also arise from the movement of ships, and in reservoirs from passages through dams.
Waves and wave motions in the oceans are characterized by an extremely wide range of wavelengths, i.e., distances from crest to crest, and periods, i.e., the time intervals required for two successive crests to pass by an observer. The smallest are capillary surface waves, having lengths of several centimeters and periods of a fraction of a second. The longest waves are tidal, the distance between their crests reaches half the circumference of the Earth, i.e. about 20 thousand km. But the period of tidal waves is not the greatest. Long periods are characterized by slow internal waves that take months to cross the ocean.
Based on the forces causing wave motion, i.e., based on their origin, the following types of waves in the ocean (sea) can be distinguished:
- * wind - caused by the wind and under its influence;
- * tidal - arising under the influence of periodic gravitational forces of the Moon and the Sun;
- * anemobaric - associated with the deviation of the ocean surface from the equilibrium position under the influence of wind and atmospheric pressure;
- * seismic (tsunami) - arising as a result of dynamic processes occurring in the earth's crust and, first of all, underwater earthquakes, as well as volcanic eruptions, both underwater and coastal;
- * ship - created when the ship moves.
Basic elements of a wave.
- Ш The average wave line is a horizontal line that intersects the wave profile so that the total areas above and below this line are equal.
- Ш Crest - part of the wave located above the average wave line.
- Ш The top of the wave is the highest point of the crest.
- Ш Depression (hollow) is a part of a wave located between two adjacent crests below the average wave line.
- Ш The bottom of the wave is the lowest point of the depression.
- Ш The wave front is the line of crest tops in plan.
- Ш The main direction of wave propagation is the direction perpendicular to the wave front.
- Ш Wave height - the excess of the top of the wave above the bottom.
- Ш Wavelength is the distance between adjacent peaks or troughs.
- Ш A wave system is a series of successive waves developing under certain conditions.
- Ш Wave steepness is the ratio of wave height to length.
- Ш The period of a wave is the period of time during which the particles make a full revolution in all orbits, or the period of time between the passage of the tops of two adjacent waves through a fixed point in the reservoir.
- Ш Wave speed is the speed of movement of the wave crest in the main direction of its movement.
- Ш Wave age is the ratio of wave speed to wind speed.
Wind waves.
Acting on the surface of the water, the wind, due to friction with the water, creates tangential stresses and drag forces, and also causes local fluctuations in air pressure. As a result, on the surface of the water, even with a wind speed of 1 m/s, small waves are formed with a height measured in millimeters and a length measured in centimeters. These barely born waves have the appearance of ripples. Since the existence of such waves is associated with surface tension, they are called capillary. Standing early in the morning on a high bank above a calm lake, we can see how the first weak breeze gives way to calm and spots of light ripples, sometimes called “cat’s paws,” suddenly appear and disappear on the surface of the water. These are the areas of development of capillary waves with a wavelength of only 2-5 cm. Friction with the air wrinkles the water surface into a series of small waves, and the surface tension of the water constantly strives to return the surface to its original smoothness, characterized by minimal energy. This is how capillary waves lose their energy of motion, which, thanks to the molecular viscosity of water, is converted directly into heat.
The growth of waves leads to their joining into groups and lengthening up to several meters. The waves become gravitational. The length of the surface wave increases to 5 - 30 cm, the force of gravity begins to have an increasing influence on its shape and movement, leaving the force of surface tension an important role only in the steeply curved part of the waves near the crest. With a period of 1 second, these waves travel very slowly—much slower than typical surface waves. Accordingly, such waves are observed on the slopes and crests of faster wind waves and swell.
Wind waves depend on the size of the water space open for wave acceleration, wind speed and time of action in one direction, as well as depth. As the depth decreases, the wave becomes steeper. A weak wind blowing for a long time over a large expanse of water can cause more significant waves than a strong short-term wind on a small water surface.
Wind waves are asymmetrical, their windward slope is gentle, and their leeward slope is steep. Since the wind acts more strongly on the upper part of the wave than on the lower part, the wave crest crumbles, forming “lambs”.
Wind waves contain more energy than any other type of ocean wave. Such energy, however, is distributed unevenly across the World Ocean. These surface waves are caused by winds; therefore, we can expect that waves with the greatest amount of energy arise in the same belts where near-surface westerly and eastern winds blow.
Most often (almost always) wind and tidal waves are observed on the surface of the seas and oceans, while wind waves cause the greatest trouble to sailors: they cause the ship to rock, flood the deck, reduce the speed of the ship, deviate it from the given course, can cause damage, and sometimes cause the destruction of the vessel, destruction of the shores and coastal structures.
Classification of sea waves.
Plan
Lecture No. 4. Topic. Sea waves
UDC: 656.62.052.4:551.5 (075) Kuznetsov Yu.M. Ph.D., Associate Professor,
Department of Navigation
1. Classification of sea waves.
2. Elements of waves.
3. Watching the waves.
As a result of the influence of various natural forces on the waters of the oceans and seas, oscillatory and translational movements of water particles arise.
Sea waves mean a form of periodic, continuously changing movement in which water particles oscillate around their equilibrium position.
Sea waves are classified according to various criteria:
By origin The following types of waves are distinguished:
Wind, formed under the influence of wind,
Tidal waves, which arise under the influence of the attraction of the Moon and the Sun,
Anemobaric, formed when the sea surface level deviates from the equilibrium position, occurring under the influence of wind and changes in atmospheric pressure,
Seismic (tsunamis) resulting from underwater earthquakes and eruptions of underwater or coastal volcanoes,
Ship damage, formed during the movement of the vessel.
According to the forces tending to return the water particle to the equilibrium position:
Capillary waves (ripples),
Gravitational.
According to the action of force after the formation of a wave:
Free (the force has ceased),
Forced (the action of force has not stopped.
According to the variability of elements over time:
Steady (do not change their elements),
Unsteady, developing, fading, (changing their elements over time).
By location in the water column:
Superficial, arising on the surface of the sea ,
Internal, arising at depth.
By form:
Two-dimensional, representing long parallel shafts following each other,
Three-dimensional, not forming parallel shafts. The length of the crest is commensurate with the wavelength (wind waves),
Solitary (single), having only a dome-shaped crest without a wave base.
According to the ratio of wavelength and sea depth:
Short (wavelength is significantly less than the depth of the sea),
Long (the wavelength is much greater than the depth of the sea).
By moving the waveform:
Translational, characterized by visible movement of the wave profile. Water particles move in circular orbits.
Standing (seiche), do not move in space. Water particles move only in the vertical direction. Seiches occur when the water level rises at one edge of a body of water and simultaneously falls at the other, usually after the wind stops.
In small basins (harbours, bays, etc.), a seiche can occur when ships pass.
Most often in the seas and oceans, navigators have to encounter wind waves, which cause the ship to rock, flood the deck, reduce the speed, and in a strong storm cause damage that leads to the death of the ship.
Wind waves are divided into three main types:
Vetrovoe- this is the excitement that is formed by the wind blowing in a given place at a given moment. When the wind weakens or completely stops, the waves turn into swells.
Swell is a wave that propagates by inertia in the form of free waves after the wind weakens or stops. A swell that spreads during calm conditions is called dead. Swell waves are usually longer than wind waves, flatter and have an almost symmetrical shape. The direction of the swell may differ from the direction of the wind and often the swell propagates towards the wind or at right angles to it.
Surf- These are waves formed by wind waves or swells near the coast. Propagating from the deep water of the open sea towards the shore in shallow water, the waves transform. Three-dimensional waves turn into two-dimensional ones, having the form of long crests parallel to each other. Their height, steepness and destructive force increase. The impact force of a breaking wave can reach 90 t/m2. In the surf zone, capsizing and turning over moments occur, which are dangerous for watercraft.
Therefore, swimming in the shallow coastal zone and landing on the shore here is very difficult, dangerous, and sometimes impossible.
Warnings about underwater obstacles can be breakers.
A breaker is a phenomenon where waves overturn and break over shoals, banks, reefs and other rises in the bottom.
One type of wave is crowd - This is the meeting of waves from different directions, as a result of which they lose a certain direction of movement and represent random standing waves.
Each wave is characterized by certain elements, such as:
Crest waves - the part of the wave located above the calm level.
Vertex waves - the highest point of a wave crest.
Hollow waves - the part of the wave located below the calm level.
Waves are characterized by the following elements (Fig. 1):
Rice. 1 Wave elements
The bottom is the lowest point of the wave trough;
Height h- vertical distance from the base to the top of the wave;
Length λ - horizontal distance between the tops of two adjacent ridges;
Slope – the ratio of wave height to its length ();
Period τ – the time interval between the passage of two adjacent vertices through the same fixed point;
Front – a line running along the crest of a given wave; the line perpendicular to the wave front is called a wave ray;
Spread speed c - the distance traveled by a certain point of the wave per unit time;
The direction of propagation is the angle measured from the north in the direction of wave movement (or the true direction from which the waves are moving).
Based on the hydrodynamic theory of waves, formulas were obtained that connect the individual elements of waves in deep water (when the sea depth is >);
With= 1.56 τ,
λ = 0.64 With 2 ,
τ = 0.64 With,
The wave height is measured directly or determined approximately using a special nomogram.
It has been established that with depth the disturbance quickly subsides and spreads to depths equal to the wavelength. Thus, at a depth equal to half the wavelength, the wave height is 23 times less than on the surface, and at a depth equal to the wavelength it is 535 times less.
In navigation, it should be taken into account that large waves arise when there is a very strong wind of a constant direction, blowing for a long time
(more than a day), in basins of significant size and depth, and that in the coastal zone, wave formation, in addition to depth, is greatly influenced by the configuration of the coastline and the direction of the wind relative to the shore (wind from the shore or from the sea).
