General information from the theory of wind waves. Methods for calculating the elements of wind waves What is a steady wind wave

Classification of sea waves.

Plan

Lecture number 4. Theme. Sea waves

UDC: 656.62.052.4:551.5 (075) Kuznetsov Yu.M. Ph.D., Associate Professor,

Department "Navigation"

1. Classification of sea waves.

2. Elements of waves.

3. Watching the waves.

As a result of the impact on the waters of the oceans and seas of various natural forces, oscillatory and translational movements of water particles arise.

Under the sea waves understand this form of periodic, continuously changing motion, in which water particles oscillate around their equilibrium position.

Sea waves are classified according to various criteria:

Origin distinguish the following types of waves:

Wind, formed under the influence of wind,

Tidal, arising under the influence of the attraction of the Moon and the Sun,

Anemobaric, formed when the sea surface level deviates from the equilibrium position, which occurs under the influence of wind and changes in atmospheric pressure,

Seismic (tsunami) resulting from underwater earthquakes and eruption of underwater or coastal volcanoes,

Shipborne, 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 the force after the formation of the wave:

Free (force ceased),

Forced (the action of force has not ceased.

By the variability of elements over time:

Settled (do not change their elements),

Unsteady, developing, fading, (changing their elements in time).

By location in the water column:

Surface, arising on the surface of the sea ,

Internal, arising at depth.

By form:

Two-dimensional, representing long parallel shafts following one another,

Three-dimensional, not forming parallel shafts. The length of the crest is commensurate with the wavelength (wind waves),

Solitary (single), having only a domed crest without a wave base.

By the ratio of the wavelength and the depth of the sea:

Short (wavelength is much less than the depth of the sea),

Long (wavelength is much greater than the depth of the sea).

By moving the waveform:

Translational, characterized by a visible movement of the wave profile Water particles move in circular orbits.

Standing (seisha), do not move in space. Water particles move only in the vertical direction. Seiches occur when the water level rises at one end of a body of water and simultaneously drops at the other, usually after the wind stops.

In small basins (in a harbour, a bay, etc.), a seiche may occur during the passage of ships.

Most often in the seas and oceans, navigators have to deal with wind waves, which cause the ship to roll, 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:

wind- this is the excitement that is formed by the wind blowing in a given place at a given moment. With the weakening or complete cessation of the wind, the excitement turns into a swell.

Swell- this is a wave that propagates by inertia in the form of free waves after the weakening or cessation of the wind. A swell that spreads during calm is called a dead swell. Swell waves are usually longer than wind waves, more gentle 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 swell near the coast. Spreading from the deep water of the open sea towards the coast in shallow water, the waves are transformed. 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/m 2 . In the surf zone, overturning and overturning moments occur, which are dangerous for watercraft.

Therefore, navigation in the shallow coastal zone and landing here is very difficult, dangerous, and sometimes impossible.

Underwater warnings can be breakers.

A breaker is a phenomenon when waves capsize and break over shoals, banks, reefs and other bottom elevations.

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 are 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 the 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

Sole - the lowest point of the hollow of the wave;

Height h- vertical distance from the bottom to the top of the wave;

Length λ - horizontal distance between the tops of two adjacent ridges;

Steepness - the ratio of the height of the wave to its length ();

Period τ - the time interval between the passage of two adjacent vertices through the same fixed point;

Front - a line passing along the crest of a given wave; a line perpendicular to the wave front is called a wave beam;

Propagation speed c - the distance traveled by a certain point of the wave per unit of time;

Direction of propagation - the angle measured from the north in the direction of the movement of the waves (or the true rhumb, from where the waves move).

Based on the hydrodynamic theory of waves, formulas are obtained that relate individual elements of waves in deep water (when the sea depth >);

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 waves quickly subside and propagate to depths equal to the wavelength. So, 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, 535 times.

In navigation, it should be borne in mind that large waves occur when a very strong wind of a constant direction blows 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 coast (wind from the coast or from the sea).

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, for example, navigation, the construction of hydraulic structures, port complexes, and the 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 limiting wave sizes in various water areas 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 for different reservoirs will be different. Leonardo da Vinci once wrote: “... a wave runs from its place of origin, but water does not Move from its place. Like the waves formed in May on the fields by the course of the winds, the waves seem to be running across the field, meanwhile the fields do not leave their place. This feature of wind waves

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is of tremendous practical importance: if, along with the form, i.e., the wave, the 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 under direct
wind action;

Swell waves that are observed after the cessation of wind
ra or after the exit of waves from the zone of action of the wind;

Mixed swell when wind waves are superimposed on swell waves

Since winds over oceans and seas, especially in temperate latitudes, are variable in speed and direction, wind waves are spatially inhomogeneous and significantly variable in time. In this case, wave fields are even more inhomogeneous than wind fields, since waves can arrive in one or another region simultaneously from different (differently located) generation zones.

If you carefully look at the rough sea surface, then you can come to the conclusion that the waves replace each other without any visible regularity - an even larger one, or maybe a very small wave, can come after a big wave; sometimes several large waves come in a row, and sometimes there is an area of almost calm surface between the waves. 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 basic law of wind waves is the apparent absence of any law." And, indeed, up to the present time we cannot predict with certainty the sequence of alternation of individual waves even by any one of the characteristics, for example, by height, not to mention other characteristics, such as the shape of ridges and troughs, etc.

When two harmonic oscillations are added, the frequencies of which are close enough, 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 the waves come to any area from different zones and their frequencies can be

Ch. 10. Waves in the ocean 197

The southeastern coast of Africa is famous - here strong winds 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, in this region of the ocean resisted strong excitement for two weeks and, according to legend, sold his soul to the devil in order to pass this place. At that time it helped. Dias passed this place, called it the Cape of Storms, but two years later he died there. The Portuguese king Joan II renamed the Cape of Storms into the Cape of Good Hope, since behind it there was a hope to reach India by sea. It is with this cape that the origin of the legend of the "Flying Dutchman" is connected. It is here that single killer waves are observed, which are formed as a result of the interaction of waves and currents. These waves represent a steep heaving of water, have a very steep front slope and a fairly gentle trough. Their height can exceed 15-20 m, while they often occur in relatively calm seas. The waves in this area 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 sections of classical hydrodynamics and until the 50s of the XX century. practically did not begin to describe such a complex disturbance as wind waves on the surface of reservoirs. The degree of excitement was assessed mainly on the Beaufort scale by eye (Table 10.3).

At the beginning of the XX century. with the transition from the sailing fleet to the steam fleet, the number of accidents and loss of ships somewhat decreased (there were 250-300 ships per year, it became ~ 150), and an underestimation of natural forces appeared in determining the safety of navigation. Among the shipbuilders of the early XX century. there was an opinion that "the forces of the elements surrender in front of new durable ships." This opinion cost the lives of many sailors. Sea waves are a rather formidable phenomenon of nature, and nature does not tolerate neglect and often takes revenge on people, thereby initiating the desire of people to better and deeper understand its laws.

In table. Table 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 refers 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

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. Wave recorders usually measure the average and maximum height of the waves, the average period and wavelength, the frequency spectrum of waves.

In an accelerometric wave recorder, the wave elements are determined by double integrating the signal received from the accelerometric sensor. The most common foreign wave recorders are arranged according to this principle. The principle of operation of hydrostatic wave recorders is based on the connection of hydrostatic oscillations at a certain depth with the characteristics of wave surface oscillations.

Echolocation is used when sounding the instantaneous values of the elevation of the water surface from a free-floating or moored buoy (direct echo sounder). Wave recorders, the principle of operation of which is based on reverse echolocation, carry out sounding of the water-air interface from under the water.

Synthetic aperture radars, altimeters installed on satellites, make it possible to measure the main characteristics of wind waves. Remote methods make it possible to obtain the characteristics of wind waves over large areas. Based on such measurements, modern atlases of wind waves are created. Wave data insights can be obtained from http://www.waveclimate.com.

As the history of the development of our fundamental knowledge of waves has shown, a close connection between theoretical, experimental and field studies is necessary.

The wind is the most important parameter on which the geometric characteristics of waves depend. However, with a steady and fairly long wind, the average characteristics of the waves increase along the path of their propagation, while they are under the action of the wind. This path is called the length of wind acceleration, or simply acceleration. The difficulties of observing sea waves and registering them in natural conditions forced scientists to turn to laboratory modeling of wind waves. In the early days of the study of sea waves, laboratory modeling was almost the only source of quantitative wave characteristics. However, this source turned out to be very limited - and here's why. The main difficulty in the laboratory modeling of waves is to ensure a sufficiently large wave acceleration, i.e., it is necessary to have long flumes. The average wave parameters usually change with time and

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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 overshoot effect. It was identified by measurements in natural and laboratory conditions. The front section of the spectrum is formed as a result of the exponential development of its components and the mechanism of the nonlinear redistribution of energy between the spectral components. The wind energy balance equation is considered 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 the level of the water surface and currents. Tidal movements also exist in the atmosphere, and tidal deformations 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 reached in the Bay of Fundy (Canada) - 18 m. Off the coast of Russia, the highest tide is observed in Penzhina 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 about 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. There are the following main types of tides: semi-diurnal, 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 according to the phases of the moon. The semidiurnal tide is most common in the oceans. The period of level fluctuations in the daily tide is equal to lunar days. The amplitude of the daily tide depends on the declination of the moon. Mixed tides are divided into irregular semidiurnal and irregular diurnal. anomalous tides

Ch. 10. Waves in the ocean 209

They have several varieties, but they are all quite rare in the oceans.

For marine practice, the forecast (or precalculation) of tidal levels is of great importance. Tide prediction is based on a harmonic analysis of level fluctuation observations. Having singled out the main harmonic components according to the observational data, the level is calculated in the future. The most complete harmonic expansion of the tide-forming 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 by the tidal potential to within a constant factor. The water surface of the ocean is described by the so-called "tidal ellipsoid", the major axis of which is directed to the perturbing luminary (the Moon, the Sun) and follows it. The earth rotates around its axis and inside this "tidal ellipsoid". The static theory, despite the weakness of the basic assumptions, correctly describes the basic properties of tides.

A more perfect 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, such as a narrow deep channel encircling the entire Earth (the so-called channel tide theory). For small water areas, the Laplace tidal equations can be written in the Cartesian coordinate system. The results of tide calculations in the World Ocean are presented in the form of special maps on which the position of the tidal wave crest is plotted at various times (usually lunar). Modern tide charts are built on the basis of 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 H is small compared to the wavelength A, i.e. A ^> N. The theory of long waves describes tidal phenomena, tsunami waves, as well as wind waves and swells propagating in shallow water. Long waves also include flood waves and bora observed on reservoirs and rivers.

long wave amplitude A much smaller than their length A th can be described using linear theory. If these conditions are not met, then nonlinear effects must be taken into account.

Tsunami literally means "big wave in the harbor" in Japanese. Tsunamis are usually understood as gravitational waves arising in the sea as a result of large-scale, short-lived disturbances (underwater earthquakes, underwater volcanoes, underwater landslides, meteorites falling into water, rock fragments, explosions in water, a sharp change in meteorological conditions, etc.).

The characteristic time duration of a tsunami wave is 10–100 min; length - 10-1000 km; propagation velocity L™Am,m ..

acceleration of gravity, I am depth and the height during coasting can reach tens of meters. These waves are very long, in the first approximation, the theory of "shallow water" is applicable to them.

In terms of the number of deaths per year as a result of natural disasters on Earth, tsunamis rank 5th after floods, typhoons, earthquakes, and droughts. The distribution of tsunamis across regions is characterized by strong heterogeneity; the main number of tsunamis occurs 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 the tsunami, 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 tsunami(intensity 4). The average rise in the level on a coast section 400 km long (or more) reaches 8 m. Waves in some places have a height of 20-30 m. All structures on the coast are destroyed. Such tsunamis occur along the entire Pacific coast.

Very strong tsunami(intensity 3). On a shore 200-400 km long, the water rises by 4-8 m, in some places up to 11 m. Such tsunamis are observed in most of the oceans.

Strong tsunamis(intensity 2). On the coast 80-200 km long, the average rise in the water level is 2-4 m, in some places 3-6 m.

moderate tsunamis(intensity 1). In the area of 70-80 km, the water rises by 1-2 m.

Weak tsunamis(intensity 0). Level rise less than 1 m.

212 Ch. 10 Waves in the ocean

Other tsunamis have intensity from -1 to -5.

The stronger the tsunami, the less often they occur. Tsunamis with an intensity of 4 occur once every 10 years, and in the Pacific Ocean; intensity 3 - once every 3 years; intensity 2 - 1 time in 2 years; intensity 1 - 1 time per year; intensity 0 - 4 times a year.

The main causes of tsunamis are earthquakes, explosions of volcanic islands and the eruption of underwater volcanoes, landslides and landslides. Let's briefly consider these reasons separately.

About 85% of tsunamis are caused by underwater earthquakes. This is due to the seismicity of many ocean 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 a (average) height of up to 8 m (in some places up to 20-30 m) (intensity 4). A 4-8 m high tsunami (of seismic origin) occurs every 3 years, and a tsunami of 2-4 m high occurs annually.

In the Far East (RF) for 10 years there are 3-4 tsunamis with a height of more than 2 m. 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 collapsed on the city, which receded after a few minutes. The seabed was exposed for several hundred meters, but after about 20 minutes, a wave over 10 meters high hit the city, which destroyed almost everything in its path. After being reflected from the hills surrounding the city, the wave rolled into the lowland, where the city center used to be, and completed the destruction. The tsunami caught the residents of the city by surprise.

There are two zones of earthquake sources on the Earth. One is located in the meridional direction and runs along the eastern and western coasts of the Pacific Ocean. This zone gives the bulk of the tsunami (up to 80%). The second zone of earthquake sources occupies a latitudinal position - the Apennines, the Alps, the Carpathians, the Caucasus, the Tien Shan. Within this zone, tsunamis occur on the shores of the Mediterranean, Adriatic, Arabian, Black Seas, 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 relief of the seabed

Ch. 10 Waves in the ocean 213

(shift), causing deviations of the ocean surface from the equilibrium position. In view of the low compressibility of water, there is a rapid lowering or rise of a significant mass of water in the area of movement. The resulting perturbations propagate in the form of long gravitational waves.

For the quantitative description of earthquakes intensity and magnitude are used. Intensity is evaluated in points (12-point scale MSK-64). (Japan has a 7-point scale). Point - a unit of measurement of ground shaking, soil. The main characteristic that determines the intensity is the reaction of soils to seismic waves. The energy of an earthquake is determined by the magnitude M.

The most important task in the prediction of tsunamis of seismic origin is the establishment of signs of tsunamigenicity of earthquakes. Now it is believed that if the magnitude of an earthquake exceeds a certain threshold value Mn, the source is located under the sea bottom, then the earthquake will be tsunamigenic.

For Japan, empirical formulas are proposed that relate the magnitude of tsunamigenic earthquakes and the depth of the source H(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 orientation depends on the elongation of the focus. The centers of large tsunamis are, as a rule, strongly 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 equal to 1/10-1/15. Separate 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 sufficiently detailed tsunami radiation pattern.

Underwater earthquakes cause not only tsunami waves, they can cause strong perturbations of the water layer in the epicentral region, which can manifest itself as a sharp increase in vertical exchange in the ocean. Vertical

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The exchange leads to the transformation of the fields of temperature, salinity and color of the ocean. The release of deep waters to the surface will lead to the formation of a vast anomaly in ocean surface temperature. The removal of biogens to the surface layer, which is usually depleted in 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 migration of fish, marine animals, etc. are possible. Strong disturbances of the water layer are observed directly above the epicentral region, manifested in water seething, ejections of water columns, and the formation of steep standing waves amplitude up to 10 m. Among sailors, this phenomenon is known as a seaquake. As a result of the analysis of satellite data of ocean surface temperature and seismic data, a decrease in ocean surface temperature and an increase in the concentration of chlorophyll “a” were revealed, which followed a series of strong underwater earthquakes in the area of Sulawesi Island (Indonesia, 2000). A series of laboratory experiments made it possible to establish that oscillations of the basin bottom 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.

During the explosion of the Krakatau volcano on August 26, 1883 in Indonesia, the height of the tsunami wave reached 45 m, 36,000 people died. Tsunami waves swept the whole world. The energy of this catastrophe is equivalent to the energy of an explosion of 250-500 thousand Hiroshima-type atomic bombs.

The explosion of the volcanic island of Tyr in the Aegean Sea 35 centuries ago (the volcano and the island used to be 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 in this way.

“The great Minoan civilization was distinguished by unsurpassed works of art and artistic crafts, majestic palaces. In the middle of the XV century. BC e. catastrophe struck Crete. Almost all the palaces were destroyed,

Ch 10. Waves in the ocean 215

The settlements were abandoned by their inhabitants. There are two hypotheses of death. According to one, it was destroyed by the barbarians - the Achaean Greeks, according to another, the cause was a natural disaster. Approximately 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 be the real cause of the death of civilization? These questions determined the formulation of the following hydrodynamic problem: “A 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 found under water 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 in the source. Based on the analogue, we assumed that an earthquake of magnitude 8.5 occurred in the area of Santorini Island at a depth of about 300 m. Further, we took the direction of the axis of the source to coincide with the direction of the isobaths in the area of the island of Santorini and parallel to the longitudinal of the island of Crete. Then, as a result of calculations performed according to the original method developed in Soyuzmorniiproekt, it was found 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; in this case, the length of the longitudinal axis of the focus 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 near the northern coast of Crete, its height is 31 m. With the passage into the bays of the island, the wave height increases to 50 m, and after it is reflected from the steep coasts and the continental slope, individual splashes can reach a height of 60-100 m. The Mediterranean wave passes through the straits, weakening due to screening 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 region, its height becomes 4 m.

216 Chapter 10. Waves in the ocean.

(of the order of 5.5 10-5), the wave propagates over a distance of 73 km up to the mouth part on the bedrock, i.e., practically the entire seaward part of the delta is subject to flooding. In the Nile Delta, during a historical period of several thousand years, the rate of alluvium deposition was practically constant and equal to 0.9-1.3 mm per year. The exception is the second millennium BC, when noticeable deposits of alluvium could not 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, probably had serious social consequences. Huge waves, 30-50 m high, were quite capable of destroying the Minoan civilization that existed in Crete. The flooding of the Nile Delta in the period of the end of the 18th - beginning of the 19th dynasty of the pharaohs was primarily the result of a sharp deterioration in the ecological situation associated with the disappearance of the fertile soil layer, salinization and the formation of swamps. The social consequences due to the crisis of agriculture 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 collapse took place on July 10, 1958. An avalanche with a volume of 300 million m relative to the undisturbed level when the wave runs up to the shore).

A tsunami up to 15 m high arose from a piece of rock falling from a height of 200 m (Madeira Island, 1930). In Norway in 1934, a tsunami 37 m high arose from the fall of a rock weighing 3 million tons from a height of 500 m.

Landslides on the slope of the ocean trench (Puerto Rico) in December 1951 caused a tsunami wave. Landslides and turbidity flows are often observed on the continental slope of the ocean, while the role of indicators of the formation and passage of landslides or turbidity flows is played by breaks in cables and pipelines.

On October 6, 1979, a 3 m high tsunami hit the Cote d'Azur near Nice. Careful seismic analysis

Ch. 10. Waves in the ocean 217

The situation and weather conditions made it possible to conclude that underwater landslides were the cause of the tsunami. Engineering work on the shelf can provoke the formation of landslides and, as a result, the occurrence of a tsunami.

Explosions in the water of atomic and hydrogen bombs can cause a wave like a tsunami. 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 only a small part of the explosion energy is converted into wave energy during the formation of a tsunami, and the directivity of the tsunami wave is low, the energy costs for 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) wave propagation in the open ocean of great depth; 3) transformation, reflection and destruction of waves on the shelf, their run-up to the shore, resonant phenomena in bays and on the shelf. The research-ness of 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. These data can be obtained by direct measurement of tsunamis in the ocean or indirectly by analyzing the characteristics of the processes that generate tsunamis. The first registrations of tsunamis in the open ocean were carried out by S.L. Soloviev et al. in 1980 near the South Kuril Islands. There is a fundamental possibility of determining the parameters in the source based on the solution of the inverse problem - based on the few manifestations of a tsunami on the coast, determine its parameters in the source. However, as a rule, there are very few field data for the 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. Rays (orthogonal to the position of the fronts) are drawn on the same map. Assuming that the energy flow between two orthogonals is preserved, we can estimate the change in wave height. The intersection of the rays leads to an unlimited increase in the height of the wave. Power carried

220 Chapter 10. Waves in the ocean

Rising breaker - a wave rolls without breaking on steep slopes.

Sea swell is the movement of the water surface up and down from the mean level. However, they do not move in the horizontal direction during waves. This can be seen by observing the behavior of a float swaying on the waves.

Waves are characterized by the following elements: the lowest part of the wave is called the bottom, and the highest part is called the crest. The steepness of slopes is the angle between its slope and the horizontal plane. The vertical distance between the bottom and the crest is the height of the wave. It can reach 14-25 meters. The distance between two soles or two crests is called the wavelength. The greatest length is about 250 m, waves up to 500 m are extremely rare. The speed of wave advance is characterized by their speed, i.e. the distance traveled by the ridge, usually per second.

The main cause of wave formation is . At low speeds, ripples appear - a system of small uniform waves. They appear with every gust of wind and fade instantly. With a very strong wind turning into a storm, the waves can be deformed, while the leeward slope turns out to be steeper than the windward one, and with very strong winds, the wave crests break off and form white foam - “lambs”. When the storm is over, high waves still roam the sea for a long time, but without sharp crests. Long and gently sloping waves after the cessation of the wind are called swell. A large swell with a small steepness and a wavelength of up to 300-400 meters in the absence of wind is called a wind swell.

The transformation of waves also occurs when they approach the shore. When approaching a gently sloping coast, the lower part of the oncoming wave slows down on the ground; length decreases and 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. Waves breaking near the shore form surf. It is always parallel to the shore. The water splashed by the wave on the shore slowly flows back along the beach.

When a wave approaches a steep shore, it hits the rocks with all its might. In this case, the wave is thrown 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 divided 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 mechanical impacts of water masses on rocks, but by the resulting air bubbles and hydraulic drops, which basically destroy the constituent rocks (see Abrasion).

The waves actively destroy the coastal land, dove and abrade the clastic material, and then distribute it along the underwater slope. At the depths of the coast, the force of the impact of the waves is very high. Sometimes at some distance from the coast there is a shallow in the form of an underwater spit. In this case, the overturning of the 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 is due to the fact that each water particle describes circles around the equilibrium level with uniform motion. All these particles move in the same direction. At each moment, the particles are at different points on 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 the westerly winds are most constant and strong. Here the waves reach 25 meters in height and 400 meters in length. Their speed of movement is about 20 m / s. In the seas, the waves are smaller - even in large ones they reach only 5 m.

A 9-point scale is used to assess the degree of sea roughness. It can be used in the study of any body of water.

9-point scale for assessing the degree of sea disturbance

Points	Signs of the degree of excitement
0	Smooth surface
1	Ripples and small waves
2	Small wave crests begin to capsize, but no white foam yet
3	In some places, "lambs" appear on the crests of the waves
4	"Lambs" are formed everywhere
5	Ridges of great height appear, and the wind begins to tear white foam from them.
6	The crests form shafts of storm waves. Foam begins to stretch completely
7	Long strips of foam cover the slopes of the waves and in places reach their soles.
8	The 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 mist and spray, visibility is reduced

To protect port facilities, berths, coastal areas of the sea from stone and concrete blocks, breakwaters are built to dampen the energy of waves to protect them from waves.

With prolonged action of wind on the surface of the water, waves develop, in which water particles perform a complex rotational-translational motion. During waves, water produces additional pressure on the structure (in excess of hydrostatic, corresponding to the calculated level), called wave pressure.

The type of waves and the value of their parameters (height h, period, wavelength, - fig. 2.6) depend on wave-forming factors - wind speed W, the duration of its action t, depth of the reservoir H and wave acceleration length D.

Rice. 2.6 Wave parameters

The wave height is determined by the most unfavorable combination of wind speeds during the design storm and the length of the acceleration. The length of the acceleration is equal to the distance in a straight line from the coast to the structure, and the magnitude of the wind speed in this direction is determined by the wind rose (Fig. 2.7).

Rice. 2.7 Wind rose ( A) and the length of the wave acceleration ( b)

Waves whose periods and height change randomly from one wave to another are called irregular; if the periods and heights of individual waves are the same, they are classified as regular.

The wave field of the reservoir is divided into zones along the length of the wave acceleration (Fig. 2.8): I- deep sea (), where practically the bottom does not affect the parameters of the waves; II- shallow ( ), in which, as the depth decreases, the length and speed of the waves decrease and the steepness of the front and the gentleness of the rear slopes increase (when the waves are destroyed and converted into breaking waves); III- a zone of surf waves overturning when moving (); IV- near-shore, where the waves finally break up and then roll onto the shore.
The wind speed determined at any height is reduced to a height of 10 m above the water level. Design storm probability for structures I And II class - 2%, III And IV - 4%.

Due to the low accuracy of determining wave-forming factors, in particular wind speed, the accuracy of calculating wave elements is low. It is not possible to estimate the wind speed with sufficient accuracy from direct observations due to the fact that only after the creation of the reservoir does the corresponding situation develop, which determines the formation of the air flow during the transition from the mainland to the water surface. Obtaining the calculated wave height with an accuracy of about 10% requires an accuracy of about 5% of the wind speed entered into the calculation, which is still unattainable. As a result of the approximate determination of the wave height, an approximate value of the wave load is obtained.

The system of waves formed during the design storm is characterized by average values and , to determine which are calculated from the given W, H And D dimensionless parameters , , and further along the nomogram in Fig. 2.9 (SNiP I-57-75) are being sought , , defining and .
The upper envelope of the nomogram corresponds to the deep-water zone, for which the calculation and are carried out according to the initial parameters and ; in the absence of actual data, it is accepted t= 6 hours

Having defined and , their smallest values are used to find the average wave height and period.
The field below the envelope curve corresponds to a shallow water zone with a bottom slope of 0.001 or less. Calculation and lead by parameters

Rice. 2.8 Division of the water area into zones by depth:
I- deep water; II- shallow; III- surf; IV- near-water; 1 – alignment of the first wave breaking; 2 - last collapse

Rice. 2.9 Graphs for determining the average values of wind wave elements in deep water I and shallow (with bottom slope) II zones

And . With a bottom slope of more than 0.001, the calculation of the wave height h produce [SNiP 11-57-75, App. I, p. 17] taking into account the transformation of waves. i.e., changes in wave parameters due to a decrease in depth, taking into account refraction - the curvature of the wave crest line during an oblique wave approach - and taking into account energy losses.

The average wavelength in the deep water zone is determined by the formula

(2.10)

wave height R The % of coverage in the wave system of the deep-water zone is determined by multiplying the average wave height by a coefficient that depends on the wave-forming factors and has a value equal to or slightly less than that indicated below.

Critical depth value N cr(wave breaking depth) depends on many simultaneously acting factors. Can be taken N cr = (1,25-1,8)h i.

The wave height is counted from the calculated level, which, at a given water level mark in the upper pool, can change due to wind surge by the value

(2.11)

Where is the angle between the longitudinal axis of the reservoir and the direction of the wind.

sea waves

periodic oscillations of the surface of the sea or ocean, due to reciprocating or circular movements of water. Depending on the causes of movement, wind waves, tidal waves ( tides And low tide), baric (seiches) and seismic ( tsunami). The waves are characterized height, equal to the vertical distance between the crest and the bottom of the wave, length– horizontal distance between two adjacent ridges, propagation speed And period. At wind waves, it lasts approx. 30 s, for baric and seismic ones - from several minutes to several hours, for tidal ones it is measured in hours.

Most common in water wind waves. They are formed and developed due to the energy of the wind transferred to the water due to friction and by the pressure of the air flow on the slopes of the wave crests. They always exist in the open ocean and can have a wide variety of sizes, reaching lengths. up to 400 m, h. 12–13 m and propagation speed 14–15 m/s. Max. registered high. wind waves is 25–26 m, higher waves are possible. At the initial stage of development, wind waves run in parallel rows, which then break up into separate crests. In deep water, the size and nature of the waves are determined by the speed of the wind, the duration of its action and the distance from the leeward space; shallow depths limit wave growth. If the wind that caused the excitement subsides, then the wind waves turn into the so-called. swell. It is often observed simultaneously with wind waves, while not always coinciding with them in direction and height.

In the surf zone, so-called. surf beats- periodic rises in the water level during the approach of a group of high waves. High rise can be from 10 cm to 2 m, rarely up to 2.5 m. Seiches are usually observed in limited water bodies (seas, bays, straits, lakes) and are standing waves, most often caused by a rapid change in the atmosphere. pressure, less often by other reasons (sudden inflow of flood waters, heavy rains, etc.). Once caused, the deformation of the water level leads to gradually damped oscillations in it. At the same time, at some points the water level remains constant - this is the so-called. standing wave nodes. High such waves is insignificant - usually several tens of centimeters, rarely up to 1–2 m.

Geography. Modern illustrated encyclopedia. - M.: Rosman. Under the editorship of prof. A. P. Gorkina. 2006 .

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