Elements of wind waves. Wind waves and their effects on structures. Wind disturbance. The wave speed is

Each wave is characterized by certain elements. The common elements for waves are: 1. vertex- the highest point of the wave crest; 2. sole- the lowest point of the wave trough; 3. height(h) - exceeding the top of the wave; 4. length() - the horizontal distance between the tops of two adjacent ridges on a wave profile drawn in the general direction of wave propagation; 5. period(T) is the time interval between the passage of two adjacent wave peaks through a fixed vertical; in other words, it is the period of time during which the wave travels a distance equal to its length; 6. steepness(e)- the ratio of the height of a given wave to its length. The steepness of the wave at different points of the wave profile is different. The average wave steepness is determined by the ratio:

7. wave speed(c) is the speed of movement of the wave crest in the direction of its propagation, determined over a short time interval of the order of the period; waves; 8. wave front- a line on the plan of the rough surface, passing along the vertices of the crest of a given wave, which are determined by the blade of the wave profiles drawn parallel to the general direction of propagation.

Figure 1. Basic wave elements

2.2 Wind wave speed

Wind waves are characterized by only minor horizontal movement of water. With increasing depth, horizontal displacement becomes negligibly small even at a depth exceeding the wavelength. As a result, in deep water, waves practically do not interact with the bottom and their behavior does not depend on depth. Therefore, the phase speed of a wave is a function of wavelength only. In deep water

Any system in which the speed of a wave depends on its length is called dispersed. Therefore, the deep ocean is a typical disperse system. When the wave speed becomes independent of (the system ceases to be dispersed). But at the same time it becomes dependent on depth.

In shallow water

All of the above refers to the phase velocity of the wave. Group velocity, i.e. the speed of energy propagation differs from the phase speed in a dispersed medium. For two limiting cases (deep and shallow waves), the following relations are true:

in deep water:

in shallow water:

2.3.Wave height

The wave height depends on:

wave acceleration;

duration of wind action;

wind speed.

Figure 2. Graph of wave height versus wind speed

The maximum recorded wave height was 34 m; its length was 342 m; period 14.8 s.. It had a phase speed of 23.1 m/s and a group speed of about 11.5 m/s

2.4 Wave energy

According to the hydrodynamic theory, the wave energy consists of the kinetic energy E k of the fluid particles participating in the wave motion and the potential energy E p, determined by the position of the fluid mass raised above the level of the calm surface. In waves of small amplitude, the energy per area having a wavelength and unit width:

, (6)

where is the density of the liquid; is the acceleration of gravity;

Ocean waves

Wind waves are created due to the influence 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 easy to understand if you notice the effect of the same wind on the surface of a wheat field. The inconstancy of wind flows, which create waves, is clearly visible.

Due to the fact that water is a substance more dense than air (about 800 times), the reaction of water to the influence of wind is somewhat “delayed”, and ripples turn into waves only after some distance and time, subject to constant exposure to wind. 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 vibration 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 superposition of several vibration 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 the direction of the wind changes, different air currents mix, the conditions of the impact environment change (open sea, harbor, land, bay or any other body large enough to make a change in the tendency of the impact and wave formation) - this means that sometimes the wind dampens the waves. In the deep sea, the size of the waves and the nature of the waves are determined by the wind speed, the duration of its action, the structure of the wind field and the configuration of the coastline, as well as the distance from the lee shore in the wind direction to the observation point.

Vertical wave movement

Unlike constant flows in rivers, which flow in almost the same direction, the energy of waves is contained in their vertical oscillations and partially horizontal ones at shallow depths. The height of the wave, or rather its distribution, is regarded as 2/3 above the average water surface and only 1/3 deep. Approximately the same ratio is observed in the speed of the wave moving up and down. This difference is probably caused by the different nature of the forces influencing 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 a given area and the relatively low resistance-air pressure). When a wave moves downward, the main forces acting are gravity, fluid viscosity, and wind pressure on the surface. This process is counteracted by: the inertia of the previous movement of water, the internal pressure of the sea (the water slowly gives way to the descending wave - moving the pressure to nearby areas of water), the density of the water, the probable upward air currents (bubbles) that arise 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. The waves are transmitted over long distances and retain energy potential for a long time. Thus, one can often observe rough seas after a storm or gale, when the wind has long died down, or rough seas during calm periods. This gives waves a great advantage as a renewable energy source due to its relative persistence and predictability, since waves arise with almost little delay after the onset of 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 generators. Here we should add the constancy of sea waves, regardless of the time of day or cloudiness, which makes wave generators more cost-effective compared to solar panels, since solar panels generate electricity only during the day and preferably in clear summer weather - in winter the percentage of productivity drops to 5% of expected 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 the expansion of air, which means an increase in pressure. The difference in air pressure in different areas of the atmosphere, together with the Coriolis force, are the main factors in the formation of wind. And the wind makes 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 per square meter of surface by reducing the depth of the bottom and (or) creating wave “corrals” - vertical barriers, then obtaining electricity from wave oscillations of the water surface becomes a very profitable proposition. It is estimated that by using only 2-5% of the energy of the waves of the world's oceans, humanity is able to cover all its current needs for electricity at the global level by 5 times [ ] .

The difficulty in making wave generators a reality lies in the aquatic environment itself and its variability. There are known cases of wave heights of 30 meters or more. Strong disturbances or high energy concentration of waves in areas closer to the poles (on average 60-70 kW/sq.m.). This fact confronts inventors working in northern latitudes with the task of ensuring 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 averages 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, which will invariably lead the latter to the creation of more cost-effective installations. An example is the Australian Oceanlinx project.

In the Russian Federation, this niche for 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), but Russian companies are already working on their own wave generators capable of extracting electrical energy from waves. An example is OceanRusEnergy from Yekaterinburg.

In addition, in places where waves are converted into electricity, marine life becomes richer due to the fact that the bottom is not subject to destructive influences during a storm.

see also

Notes

Literature

• Sea waves // Great Soviet Encyclopedia: [in 30 volumes] / ch. ed. A. M. Prokhorov. - 3rd ed. - M.: Soviet Encyclopedia, 1969-1978.
• Carr, Michael "Understanding Waves" Sail Oct 1998: 38-45.
• Rousmaniere, John. The Annapolis Book of Seamanship, New York: Simon & Schuster 1989
• G.G. Stokes. On the theory of oscillatory waves (undefined) // Transactions of the Cambridge Philosophical Society. - 1847. - T. 8. - P. 441-455.
  Reprinted in: G.G. Stokes.

Sea roughness is the fluctuation of the water surface up and down from the average level. However, they do not move horizontally during waves. You can verify this by observing the behavior of a float swinging on the waves.

Waves are characterized by the following elements: the lowest part of the wave is called the base, and the highest is called the crest. The steepness of a slope is the angle between its slope and the horizontal plane. The vertical distance between the base and the crest is the height of the wave. It can reach 14-25 meters. The distance between two troughs or two crests is called the wavelength. The longest length is about 250 m; waves up to 500 m are extremely rare. The speed of wave movement is characterized by their speed, i.e. the distance covered by the comb usually in a second.

The main reason for wave formation is. At low speeds, ripples appear - a system of small uniform waves. They appear with every gust of wind and instantly fade away. With very strong winds turning into a storm, the waves can be deformed, with the leeward slope being steeper than the windward one, and with very strong winds the wave crests break off and form white foam - “lambs”. When the storm ends, high waves continue to travel across the sea for a long time, but without sharp crests. Long, gentle waves after the wind stops are called swells. A large swell with low steepness and a wave length of up to 300-400 meters in the complete absence of wind is called a wind swell.

The transformation of waves also occurs as they approach the shore. When approaching a gently sloping shore, the lower part of the oncoming wave is slowed down by the ground; the length decreases and the height increases. The top of the wave moves faster than the bottom. The wave overturns, and its crest, falling, crumbles into small, air-saturated, foamy splashes. The waves, breaking up near the shore, form a surf. It is always parallel to the shore. The water splashed onto the shore slowly flows back down the beach.

When the wave approaches the steep shore, it hits the rocks with all its force. In this case, the wave throws up in the form of a beautiful, foamy shaft, reaching a height of 30-60 meters. Depending on the shape of the rocks and the direction of the waves, the shaft is broken into parts. The impact force of the waves reaches 30 tons per 1 m2. But it should be noted that the main role is played not by the mechanical impacts of masses of water on the rocks, but by the resulting air bubbles and hydraulic changes, which mainly destroy the composing rocks (see Abrasion).

Waves actively destroy coastal land, roll over and abrade debris, and then distribute it along the underwater slope. Near the inland coastline, the impact force of the waves is very high. Sometimes at some distance from the shore there is a shoal in the form of an underwater spit. In this case, the breaking of waves occurs on the shallows, and a breaker is formed.

The shape of the wave changes all the time, giving the impression of running. This occurs due to the fact that each water particle, with a uniform movement, describes circles around the equilibrium level. All these particles move in one direction. At each moment the particles are at different points of the circle; this is the wave system.

The largest wind waves were observed in the Southern Hemisphere, where the ocean is most extensive and where westerly winds are most constant and strong. Here the waves reach 25 meters in height and 400 meters in length. Their movement speed is about 20 m/s. In the seas the waves are smaller - even in the big ones they reach only 5 m.

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

9-point scale for assessing the degree of sea state

Points	Signs of excitement
0	Smooth surface
1	Ripples and small waves
2	Small wave crests begin to capsize, but there is no white foam yet
3	In some places “lambs” appear on the crests of the waves
4	"Lambs" are formed everywhere
5	High ridges appear, and the wind begins to tear off white foam from them
6	The crests form the swells of storm waves. The foam begins to stretch completely
7	Long stripes of foam cover the sides of the waves and in some places reach their base
8	Foam completely covers the slopes of the waves, the surface becomes white
9	The entire surface of the wave is covered with a layer of foam, the air is filled with water dust and splashes, visibility is reduced

To protect port facilities, piers, and coastal areas of the sea from waves, breakwaters are built from stone and concrete blocks to absorb wave energy.

The main reason for the occurrence of waves on the surface of the water is the effect of wind on the water surface. Waves also arise from the movement of ships, and in reservoirs from passages through dams.

Waves and wave motions in the oceans are characterized by an extremely wide range of wavelengths, i.e., distances from crest to crest, and periods, i.e., the time intervals required for two successive crests to pass by an observer. The smallest are capillary surface waves, having lengths of several centimeters and periods of a fraction of a second. The longest waves are tidal, the distance between their crests reaches half the circumference of the Earth, i.e. about 20 thousand km. But the period of tidal waves is not the greatest. Long periods are characterized by slow internal waves that take months to cross the ocean.

Based on the forces causing wave motion, i.e., based on their origin, the following types of waves in the ocean (sea) can be distinguished:

• * wind - caused by the wind and under its influence;
• * tidal - arising under the influence of periodic gravitational forces of the Moon and the Sun;
• * anemobaric - associated with the deviation of the ocean surface from the equilibrium position under the influence of wind and atmospheric pressure;
• * seismic (tsunami) - arising as a result of dynamic processes occurring in the earth's crust and, first of all, underwater earthquakes, as well as volcanic eruptions, both underwater and coastal;
• * ship - created when the ship moves.

Basic elements of a wave.

• Ш The average wave line is a horizontal line that intersects the wave profile so that the total areas above and below this line are equal.
• Ш Crest - part of the wave located above the average wave line.
• Ш The top of the wave is the highest point of the crest.
• Ш Depression (hollow) is a part of a wave located between two adjacent crests below the average wave line.
• Ш The bottom of the wave is the lowest point of the depression.
• Ш The wave front is the line of crest tops in plan.
• Ш The main direction of wave propagation is the direction perpendicular to the wave front.
• Ш Wave height - the excess of the top of the wave above the bottom.
• Ш Wavelength is the distance between adjacent peaks or troughs.
• Ш A wave system is a series of successive waves developing under certain conditions.
• Ш Wave steepness is the ratio of wave height to length.
• Ш The period of a wave is the period of time during which the particles make a full revolution in all orbits, or the period of time between the passage of the tops of two adjacent waves through a fixed point in the reservoir.
• Ш Wave speed is the speed of movement of the wave crest in the main direction of its movement.
• Ш Wave age is the ratio of wave speed to wind speed.

Wind waves.

Acting on the surface of the water, the wind, due to friction with the water, creates tangential stresses and drag forces, and also causes local fluctuations in air pressure. As a result, on the surface of the water, even with a wind speed of 1 m/s, small waves are formed with a height measured in millimeters and a length in centimeters. These barely born waves have the appearance of ripples. Since the existence of such waves is associated with surface tension, they are called capillary. Standing early in the morning on a high bank above a calm lake, we can see how the first weak breeze gives way to calm and spots of light ripples, sometimes called “cat’s paws,” suddenly appear and disappear on the surface of the water. These are the areas of development of capillary waves with a wavelength of only 2-5 cm. Friction with air wrinkles the water surface into a series of small waves, and the surface tension of water constantly strives to return the surface to its original smoothness, characterized by minimal energy. This is how capillary waves lose their energy of motion, which, thanks to the molecular viscosity of water, is converted directly into heat.

The growth of waves leads to their joining into groups and lengthening up to several meters. The waves become gravitational. The length of the surface wave increases to 5 - 30 cm, the force of gravity begins to have an increasing influence on its shape and movement, leaving the surface tension force an important role only in the steeply curved part of the waves near the crest. With a period of 1 second, these waves travel very slowly—much slower than typical surface waves. Accordingly, such waves are observed on the slopes and crests of faster wind waves and swell.

Wind waves depend on the size of the water space open for wave acceleration, wind speed and time of action in one direction, as well as depth. As the depth decreases, the wave becomes steeper. A weak wind blowing for a long time over a large expanse of water can cause more significant waves than a strong short-term wind on a small water surface.

Wind waves are asymmetrical, their windward slope is gentle, and their leeward slope is steep. Since the wind acts more strongly on the upper part of the wave than on the lower part, the wave crest crumbles, forming “lambs”.

Wind waves contain more energy than any other type of ocean wave. Such energy, however, is distributed unevenly across the World Ocean. These surface waves are caused by winds; therefore, we can expect that waves with the greatest amount of energy arise in the same belts where near-surface westerly and eastern winds blow.

Most often (almost always) wind and tidal waves are observed on the surface of the seas and oceans, while wind waves cause the greatest trouble to seafarers: they cause the ship to rock, flood the deck, reduce the speed, deviate it from the given course, can cause damage, and sometimes cause the destruction of the vessel, destruction of the shores and coastal structures.

The waves that we are used to seeing on the surface of the sea are formed mainly under the influence of wind. However, waves can also arise for other reasons, then they are called;

Tidal, formed under the influence of the tidal forces of the Moon and the Sun;

Baric pressure, which occurs during sudden changes in atmospheric pressure;

Seismic (tsunami) formed as a result of an earthquake or volcanic eruption;

Ship related problems that arise when the ship is moving.

Wind waves are predominant on the surface of seas and oceans. Tidal, seismic, pressure and ship waves do not have a significant effect on the navigation of ships in the open ocean, so we will not dwell on their description. Wind waves are one of the main hydrometeorological factors that determine the safety and economic efficiency of navigation, since the wave, running onto the ship, hits it, rocks it, hits the side, floods the decks and superstructures, and reduces the speed. The motion creates dangerous lists, makes it difficult to determine the position of the vessel and greatly exhausts the crew. In addition to the loss of speed, waves cause the vessel to yaw and deviate from the given course, and to maintain it, constant shifting of the rudder is required.

Wind waves are the process of formation, development and propagation of wind-induced waves on the sea surface. Wind waves have two main features. The first feature is irregularity: disorder in the sizes and shapes of waves. One wave does not repeat another; a large one may be followed by a small one, or perhaps an even larger one; Each individual wave continuously changes its shape. Wave crests move not only in the direction of the wind, but also in other directions. Such a complex structure of the disturbed sea surface is explained by the vortex, turbulent nature of the wind that forms waves. The second feature of waves is the rapid variability of its elements in time and space and is also associated with the wind. However, the size of the waves depends not only on the wind speed; the duration of its action, the area and configuration of the water surface are of significant importance. From a practical point of view, there is no need to know the elements of each individual wave or each wave vibration. Therefore, the study of waves ultimately comes down to identifying statistical patterns that are numerically expressed by the dependencies between wave elements and the factors that determine them.

3.1.1. Wave elements

Each wave is characterized by certain elements,

The common elements for waves are (Fig. 25):

Apex - the highest point of the wave crest;

The bottom is the lowest point of the wave trough;

Height (h) - exceeding the top of the wave;

Length (L) is the horizontal distance between the tops of two adjacent ridges on a wave profile drawn in the general direction of wave propagation;

Period (t) - the time interval between the passage of two adjacent wave peaks through a fixed vertical; in other words, it is the period of time during which the wave travels a distance equal to its length;

Slope (e) is the ratio of the height of a given wave to its length. The steepness of the wave at different points of the wave profile is different. The average wave steepness is determined by the ratio:

Rice. 25. Basic elements of waves.

For practice, the greatest slope is important, which is approximately equal to the ratio of the wave height h to its half-length λ/2

- wave speed c - the speed of movement of the wave crest in the direction of its propagation, determined over a short time interval of the order of the wave period;

Wave front is a line on the plan of a rough surface, passing along the vertices of the crest of a given wave, which are determined by a set of wave profiles drawn parallel to the general direction of wave propagation.

For navigation, wave elements such as height, period, length, steepness and general direction of wave movement are of greatest importance. All of them depend on the parameters of the wind flow (wind speed and direction), its length (acceleration) over the sea and the duration of its action.

Depending on the conditions of formation and propagation, wind waves can be divided into four types.

Wind - a system of waves that, at the moment of observation, is under the influence of the wind by which it is caused. The directions of propagation of wind waves and wind in deep water usually coincide or differ by no more than four points (45°).

Wind waves are characterized by the fact that their leeward slope is steeper than the windward one, so the tops of the crests usually collapse, forming foam, or are even torn off by strong winds. When waves enter shallow water and approach the shore, the directions of wave and wind propagation can differ by more than 45°.

Swell - wind-induced waves that propagate in the wave-forming area after the wind weakens and/or changes its direction, or wind-induced waves that come from the wave-forming area to another area where the wind is blowing at a different speed and/or a different direction. A special case of swell that propagates in the absence of wind is called a dead swell.

Mixed - waves formed as a result of the interaction of wind waves and swell.

Transformation of wind waves - changes in the structure of wind waves with changes in depth. In this case, the shape of the waves is distorted, they become steeper and shorter, and at a shallow depth, not exceeding the height of the wave, the crests of the latter overturn and the waves are destroyed.

In their appearance, wind waves are characterized by different shapes.

Ripple is the initial form of wind wave development that occurs under the influence of a weak wind; The crests of the waves resemble scales when they ripple.

Three-dimensional waves are a set of waves whose average crest length is several times greater than the average wavelength.

Regular waves are waves in which the shape and elements of all waves are the same.

Crowd is a chaotic disturbance that arises as a result of the interaction of waves traveling in different directions.

Waves breaking over banks, reefs or rocks are called breakers. Waves crashing in the coastal area are called surf. Near steep shores and near port facilities, the surf has the form of a reverse surge.

Waves on the surface of the sea are divided into free, when the force that caused them ceases to act and the waves move freely, and forced, when the force that caused the formation of the waves does not stop.

Based on the variability of wave elements over time, they are divided into steady waves, i.e., wind waves, in which the statistical characteristics of waves do not change over time, and developing or attenuating waves, which change their elements over time.

According to their shape, waves are divided into two-dimensional - a set of waves whose average crest length is many times greater than the average wavelength, three-dimensional - a set of waves whose average crest length is several times greater than the wave length, and solitary, having only a dome-shaped crest without a sole.

Depending on the ratio of the wavelength to the depth of the sea, waves are divided into short, the length of which is significantly less than the depth of the sea, and long, the length of which is greater than the depth of the sea.

According to the nature of the movement of the waveform, they can be translational, in which there is visible movement of the waveform, and standing - having no movement. Based on how the waves are located, they are divided into surface and internal. Internal waves are formed at one or another depth at the interface between layers of water of different densities.

3.1.2. Methods for calculating wave elements

When studying sea waves, certain theoretical principles are used to explain certain aspects of this phenomenon. The general laws of the structure of waves and the nature of the movement of their individual particles are considered by the trochoidal theory of waves. According to this theory, individual water particles in surface waves move in closed ellipsoidal orbits, making a full revolution in a time equal to the wave period t.

The rotational motion of successively located water particles, shifted by a phase angle at the initial moment of movement, creates the appearance of translational motion: individual particles move in closed orbits, while the wave profile moves translationally in the direction of the wind. The trochoidal wave theory made it possible to mathematically substantiate the structure of individual waves and relate their elements to each other. Formulas were obtained that made it possible to calculate individual wave elements

where g is the acceleration of gravity, the wavelength K, the speed of its propagation C and the period t are related to each other by the dependence K = Cx.

It should be noted that the trochoidal wave theory is valid only for regular two-dimensional waves, which are observed in the case of free wind waves - swell. In three-dimensional wind waves, the orbital paths of particles are not closed circular orbits, since under the influence of wind, horizontal transfer of water occurs on the sea surface in the direction of wave propagation.

The trochoidal theory of sea waves does not reveal the process of their development and attenuation, as well as the mechanism of energy transfer from wind to wave. Meanwhile, solving precisely these issues is necessary in order to obtain reliable dependencies for calculating the elements of wind waves.

Therefore, the development of the theory of sea waves took the path of developing theoretical and empirical connections between wind and waves, taking into account the diversity of real sea wind waves and the non-stationary nature of the phenomenon, i.e., taking into account their development and attenuation.

In general, formulas for calculating wind wave elements can be expressed as a function of several variables

H, t, L,C=f(W , D t, H),

Where W is wind speed; D - acceleration, t - duration of wind action; H - depth of the sea.

For shallow sea areas, the dependences can be used to calculate wave height and length

Coefficients a and z are variable and depend on the depth of the sea

A = 0.0151H 0.342; z = 0.104H 0.573 .

For open sea areas, the elements of waves, the probability of heights of which is 5%, and the average wavelengths are calculated according to the dependencies:

H = 0.45 W 0.56 D 0.54 A,

L = 0.3lW 0.66 D 0.64 A.

Coefficient A is calculated using the formula

For open ocean areas, wave elements are calculated using the following formulas:

where e is the steepness of the wave at low accelerations, D PR is the maximum acceleration, km. The maximum height of storm waves can be calculated using the formula

where hmax is the maximum wave height, m, D is the acceleration length, miles.

At the State Oceanographic Institute, based on the spectral statistical theory of waves, graphical connections were obtained between wave elements and wind speed, duration of its action and acceleration length. These dependencies should be considered the most reliable, giving acceptable results, on the basis of which nomograms for calculating wave heights were constructed at the Hydrometeorological Center of the USSR (V.S. Krasyuk). The nomogram (Fig. 26) is divided into four quadrants (I-IV) and consists of a series of graphs arranged in a certain sequence.

In quadrant I (counting from the lower right corner) of the nomogram, a degree grid is given, each division of which (horizontally) corresponds to 1° of the meridian at a given latitude (from 70 to 20° N) for maps at a scale of 1:15 000000 polar stereographic projections. The degree grid is necessary to convert the distance between the isobars n and the radius of curvature of the isobars R, measured on maps of a different scale, to a scale of 1:15 000000. In this case, we determine the distance between the isobars n and the radius of curvature of the isobars R in meridian degrees at a given latitude. The radius of curvature of isobars R is the radius of the circle with which the section of the isobar passing through the point for which the calculation is being carried out, or near it, has the greatest contact. It is determined using a meter by selecting it in such a way that an arc drawn from the found center coincides with a given section of the isobar. Then, on a degree grid, we plot the measured values ​​at a given latitude, expressed in degrees of the meridian, and using a compass we determine the radius of curvature of the isobars and the distance between the isobars, corresponding to a scale of 1:15,000,000.

Quadrant II of the nomogram shows curves expressing the dependence of wind speed on the pressure gradient and geographic latitude of the place (each curve corresponds to a certain latitude - from 70 to 20° N). To transition from the calculated gradient wind to the wind blowing near the sea surface (at an altitude of 10 m), a correction was derived that takes into account the stratification of the surface layer of the atmosphere. When calculating for the cold part of the year (stable stratification t w 2°C), the coefficient is 0.6.

Rice. 26. Nomogram for calculating wave elements and wind speed from surface pressure field maps, where isobars are drawn at intervals of 5 mbar (a) and 8 mbar (b). 1 - winter, 2 - summer.

In quadrant III, the influence of isobar curvature on the geostrophic wind speed is taken into account. Curves corresponding to different values ​​of the radius of curvature (1, 2, 5, etc.) are given by solid (winter) and dashed (summer) lines. The sign oo means that the isobars are straight. Typically, when the radius of curvature exceeds 15°, it is not necessary to take curvature into account in calculations. Along the abscissa axis separating keys III and IV, the wind speed W for a given point is determined.

In quadrant IV there are curves that make it possible to determine the height of the so-called significant waves (h 3H), which have a probability of 12.5%, based on wind speed, acceleration or duration of wind action.

If it is possible, when determining wave height, to use not only data on wind speed, but also on the acceleration and duration of the wind, the calculation is performed using the acceleration and duration of the wind (in hours). To do this, from quadrant III of the nomogram we lower the perpendicular not to the acceleration curve, but to the wind duration curve (6 or 12 hours). From the results obtained (in terms of acceleration and duration), the smaller value of the wave height is taken.

Calculation using the proposed nomogram can be made only for areas of the “deep sea”, i.e. for areas where the sea depth is not less than half the wavelength. When acceleration exceeds 500 km or wind duration exceeds 12 hours, the dependence of wave heights on wind corresponding to ocean conditions is used (thickened curve in quadrant IV).

Thus, to determine the height of the waves at a given point, it is necessary to perform the following operations:

A) find the radius of curvature of the isobar R passing through a given point or near it (using a compass by selection). The radius of curvature of isobars is determined only in the case of cyclonic curvature (in cyclones and troughs) and is expressed in meridian degrees;

B) determine the pressure difference n by measuring the distance between adjacent isobars in the area of ​​the selected point;

C) using the found values ​​of R and n, depending on the time of year, we find the wind speed W;

D) knowing the wind speed W and acceleration D or the duration of the wind (6 or 12 hours), we find the height of significant waves (h 3H).

Acceleration is found as follows. From each point for which the wave height is calculated, a streamline is drawn in the direction against the wind until its direction changes relative to the initial one by an angle of 45° or reaches the shore or the ice edge. Approximately this will be the acceleration or path of the wind, along which waves should be formed, arriving at a given point.

The duration of wind action is defined as the time during which the wind direction remains unchanged or deviates from the original by no more than ±22.5°.

According to the nomogram in Fig. 26a, you can determine the wave height from a map of the surface pressure field, on which isobars are drawn through 5 mbar. If the isobars are drawn through 8 mbar, then the nomogram shown in Fig. 26 b.

The wave period and length can be calculated from wind speed and wave height data. An approximate calculation of the wave period can be made using the graph (Fig. 27), which shows the relationship between the periods and the height of wind waves at different wind speeds (W). The wave length is determined by its period and sea depth at a given point according to the graph (Fig. 28).