The value of wind waves. General information from the theory of wind 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.
wind waves
Storm waves in the North Pacific Ocean
ocean waves
wind waves are created due to the effect of wind (movement of air masses) on the surface of the water, that is, injection. The reason for the oscillatory movements of the waves becomes easily understood if one notices the effect of the same wind on the surface of a wheat field. The inconsistency of wind flows, which create waves, is clearly visible.
Due to the fact that water is a substance denser than air (about 800 times), the reaction of water to the action of the wind is somewhat “late”, and the ripples turn into waves only after a certain distance and time, provided that the wind is constantly exposed. If we take into account such parameters as the constancy of the wind flow, its direction, speed, area of influence, as well as the previous state of the oscillation of the surface of the water surface, then we get the direction of the wave, the height of the wave, the frequency of the wave, the imposition of several oscillations-directions on the same area water surface. It should be noted that the direction of the wave does not always coincide with the direction of the wind. This is especially noticeable when changing the direction of the wind, mixing different air currents, changing the conditions of the impact environment (open sea, harbor, land, bay or any other large enough body that can change the trend of impact and wave formation) - this means that sometimes the wind dampens the waves.
Vertical movement of waves
Unlike constant flows in rivers that go in almost the same direction, the energy of the waves is contained in their vertical oscillation and partly horizontal at shallow depths. The height of the wave, or rather, its distribution, is regarded as 2/3 above the average surface of the water and only 1/3 in depth. Approximately the same ratio is noted in the speed of the wave up and down. Probably, this difference is caused by the different nature of the forces affecting the movement of the wave: when the water mass rises, it is mainly pressure that acts (the wave is literally squeezed out of the sea by the increased water pressure in this area and the relatively low resistance-air pressure). When the wave moves down, the gravitational force, the viscosity of the liquid, and the wind pressure on the surface mainly act. Counteracting this process are: the inertia of the previous movement of the water, the internal pressure of the sea (the water slowly gives way to the descending wave - moving pressure into nearby areas of water), the density of the water, the likely upward air currents (bubbles) that occur when the wave crest overturns, etc.
Waves as a renewable energy source
It is especially important to note the fact that wind waves are concentrated wind energy. Waves are transmitted over long distances and retain the potential of energy for a long time. So, one can often observe the excitement of the sea after a storm or storm, when the wind has long died down, or the excitement of the sea during calm. This gives waves a great advantage as a renewable energy source due to their relative persistence and predictability, since waves occur with little delay after the onset of the wind and continue to exist long after it, moving over long distances, which makes generating electricity from waves more cost-effective compared to with wind turbines. To this should be added the constancy of sea waves, regardless of the time of day or cloud cover, which makes wave generators more cost-effective compared to solar panels, since solar panels they generate electricity only during the day and preferably in clear summer weather - in winter, the percentage of productivity drops to 5% of the estimated battery power.
Fluctuations in the water surface are the result of solar activity. The sun heats the surface of the planet (and unevenly - the land heats up faster than the sea), an increase in surface temperature leads to an increase in air temperature - and this, in turn, leads to air expansion, which means an increase in pressure. As you know, air with excess pressure flows into an area with less high pressure- that is, wind is created. And the wind blows the waves. It should be noted that this phenomenon also works well in the opposite direction, when the surface of the planet cools unevenly.
If we take into account the possibility of increasing the concentration of energy on square meter surface by reducing the depth of the bottom and (or) creating wave "pens" - vertical barriers, then obtaining electricity from wave oscillations of the water surface becomes a very profitable proposition. It is estimated that when using only 2-5% of the wave energy of the world's oceans, humanity is able to cover all its current needs for electricity at the global level by 5 times.
The complexity of translating wave generators into reality lies in the aquatic environment itself and its volatility. There are known cases of wave heights of 30 meters or more. Waves or high energy concentration of waves are strong in areas closer to the poles (on average 60-70 kV / sq.m.). This fact sets the task for inventors working in northern latitudes to ensure the proper reliability of the device than the level of efficiency. And vice versa - in the Mediterranean Sea and the Black Sea, where the energy intensity of waves is on average about 10 kWh / square meter, designers, in addition to the survivability of the installation in adverse conditions, are forced to look for ways to increase the efficiency of the installation (COP), which will invariably lead the latter to create more cost-effective installations. An example is the Australian project Oceanlinx.
In the Russian Federation, this niche of electricity production has not yet been filled, despite the practically unlimited water expanses of different energy intensity, starting from Baikal, the Caspian, Black Seas and ending with the Pacific Ocean and other northern water expanses (for the period of non-freezing).
In addition, where waves are converted into electricity, marine life becomes richer due to the fact that the bottom is not exposed to destructive effects during a storm.
Notes
- Carr, Michael "Understanding Waves" Sail Oct 1998: 38-45.
- Rousmaniere, John. The Annapolis Book of Seamanship, New York: Simon & Schuster 1989
- G.G. Stokes (1847). "On the theory of oscillatory waves". Transactions of the Cambridge Philosophical Society 8
: 441–455.
Reprinted in: G.G. Stokes Mathematical and Physical Papers, Volume I. - Cambridge University Press, 1880. - P. 197–229. - Phillips, O.M. (1977) "The dynamics of the upper ocean"(2nd ed.) ISBN 0 521 29801 6
- Holthuisen, L.H. (2007) "Waves in oceanic and coastal waters" Cambridge University Press, ISBN 0521860288
- Falkovich, Gregory (2011), "Fluid Mechanics (A short course for physicists)", Cambridge University Press, ISBN 978-1-107-00575-4
Links
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 bottoms. |
| 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.
Excitement is accompanied by the movement of water masses. The movement of water particles during waves occurs along non-closed orbits and is a random disordered process that is difficult for a theoretical description and depends on many factors.
The main elements of sea wind waves are as follows: height h is the vertical distance from the wave trough to the crest; length X - the horizontal distance between two consecutive ridges or troughs; period T, - the time interval between the passage of the tops of two consecutive waves through a fixed vertical.
The height of offshore wind waves decreases as it moves from the surface to the bottom of the sea. According to the classical trochoidal theory of waves, their height decreases with depth according to the exponential law
h 2 \u003d he -2ir / ^ (3.1)
where z is the depth from the sea surface; h z and h - wave height at depth z and on the sea surface, respectively.
In reality, the attenuation of waves with depth occurs somewhat faster than it follows from the classical theory of waves. 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, it is more correct to estimate by the expression
h z \u003d he -5.5 (z / X) 0.8. (3.2)
However, for engineering calculations, such refinements are not essential. In these water areas, it is possible to approximately calculate the wave height h z at depth z, based on a simple rule: if the depth increases in arithmetic progression, then the wave height decreases exponentially (Table 3.1).
Wind waves are divided into forced, arising and under the influence of wind pressure, and free, occurring after the cessation of the wind or gone beyond its zone of action. Free waves are otherwise 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 subjected to hydrodynamic loads. According to modern concepts of hydrodynamics, the main components of the total force of wave pressure on any cylindrical barrier are the drag force, inertial force, and the force of water impact on the barrier.
The drag force is proportional to the square linear speed orbital movement. Its maximum value is reached when the top of the wave crest passes near the monosupport. The force of frontal resistance is due to the fact that on the surface of the obstacle, when a viscous fluid flows around it, a boundary layer of the vortex structure arises, and under certain conditions periodically detaches. Energy,
Table 3.1
Decrease in wave height with sea depth (in relative units)
Table 3.2
Scales of the degree of wind waves (numerator) and swell (denominator)
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||||||||||
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Moderate |
|
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 the technical equipment of 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
194_______________________ Ch 10 Waves in the ocean _________________________
has a colossal practical value: 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 excitement. 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
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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 merchant ships with respect to big size(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. 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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208_______________________ Ch. 10. Waves in the ocean _____________________________
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 commonly understood as gravitational waves arising in the sea due to 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, a 2-4 m high - 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
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(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 assessed 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 tons. atomic bombs Hiroshima type.
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,
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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 reason was 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.
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(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
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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
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Rising breaker - a wave rolls without breaking on steep slopes.