Behavior of waves on large bodies of water. Waves on the water

Wave(Wave, surge, sea) - formed due to the adhesion of particles of liquid and air; sliding along the smooth surface of the water, at first the air creates ripples, and only then, acting on its inclined surfaces, gradually develops agitation of the water mass. Experience has shown that water particles do not have forward motion; moves only vertically. Sea waves are the movement of water on the sea surface that occurs at certain intervals.

The highest point of the wave is called comb or the top of the wave, and the lowest point is sole. Height of a wave is the distance from the crest to its base, and length this is the distance between two ridges or soles. The time between two crests or troughs is called period waves.

Main causes

On average, the height of a wave during a storm in the ocean reaches 7-8 meters, usually it can stretch in length - up to 150 meters and up to 250 meters during a storm.

In most cases, sea waves are formed by the wind. The strength and size of such waves depend on the strength of the wind, as well as its duration and “acceleration” - the length of the path along which the wind acts on the water surface. Sometimes the waves that hit the coast can originate thousands of kilometers from the coast. But there are many other factors in the occurrence of sea waves: these are the tidal forces of the Moon and the Sun, fluctuations in atmospheric pressure, eruptions of underwater volcanoes, underwater earthquakes, and the movement of sea vessels.

Waves observed in other water bodies can be of two types:

1) Wind created by the wind, which assume a steady character after the wind ceases to act and are called established waves, or swell; Wind waves are created due to the action 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.

2) Waves of movement, or standing waves, are formed as a result of strong tremors at the bottom during earthquakes or excited, for example, by a sharp change in atmospheric pressure. These waves are also called single waves.

Unlike tides and currents, waves do not move masses of water. The waves move, but the water remains in place. A boat that rocks on the waves does not float away with the wave. She will be able to move slightly along an inclined slope only thanks to the force of earth's gravity. Water particles in a wave move along rings. The further these rings are from the surface, the smaller they become and, finally, disappear completely. Being in a submarine at a depth of 70-80 meters, you will not feel the effect of sea waves even during the most severe storm on the surface.

Types of sea waves

Waves can travel great distances without changing shape and losing virtually no energy, long after the wind that caused them has died down. Breaking on the shore, sea waves release enormous energy accumulated during the journey. The force of continuously breaking waves changes the shape of the shore in different ways. The spreading and rolling waves wash the shore and are therefore called constructive. Waves crashing onto the shore gradually destroy it and wash away the beaches that protect it. That's why they are called destructive.

Low, wide, rounded waves away from the shore are called swells. Waves cause water particles to describe circles and rings. The size of the rings decreases with depth. As the wave approaches the sloping shore, the water particles in it describe increasingly flattened ovals. Approaching the shore, the sea waves can no longer close their ovals, and the wave breaks. In shallow water, the water particles can no longer close their ovals, and the wave breaks. Headlands are formed from harder rock and erode more slowly than adjacent sections of the coast. Steep, high sea waves undermine the rocky cliffs at the base, creating niches. Cliffs sometimes collapse. The terrace, smoothed by the waves, is all that remains of the rocks destroyed by the sea. Sometimes water rises along vertical cracks in the rock to the top and breaks out to the surface, forming a funnel. The destructive force of the waves widens the cracks in the rock, forming caves. When the waves wear away at the rock on both sides until they meet at a break, arches are formed. When the top of the arch falls into the sea, stone pillars remain. Their foundations are undermined and the pillars collapse, forming boulders. The pebbles and sand on the beach are the result of erosion.

Destructive waves gradually erode the coast and carry away sand and pebbles from sea beaches. Bringing the full weight of their water and washed-away material onto slopes and cliffs, the waves destroy their surface. They squeeze water and air into every crack, every crevice, often with explosive energy, gradually separating and weakening the rocks. The broken rock fragments are used for further destruction. Even the hardest rocks are gradually destroyed, and the land on the shore changes under the influence of waves. Waves can destroy the seashore with amazing speed. In Lincolnshire, England, erosion (destruction) is advancing at a rate of 2 m per year. Since 1870, when the largest lighthouse in the United States was built at Cape Hatteras, the sea has washed away beaches 426 m inland.

Tsunami

Tsunami These are waves of enormous destructive power. They are caused by underwater earthquakes or volcanic eruptions and can cross oceans faster than a jet plane: 1000 km/h. In deep waters, they can be less than one meter, but, approaching the shore, they slow down and grow to 30-50 meters before collapsing, flooding the shore and sweeping away everything in their path. 90% of all recorded tsunamis occurred in the Pacific Ocean.

The most common reasons.

About 80% of tsunami generation cases are underwater earthquakes. During an earthquake under water, a mutual vertical displacement of the bottom occurs: part of the bottom sinks, and part rises. Oscillatory movements occur vertically on the surface of the water, tending to return to the original level - the average sea level - and generate a series of waves. Not every underwater earthquake is accompanied by a tsunami. Tsunamigenic (that is, generating a tsunami wave) is usually an earthquake with a shallow source. The problem of recognizing the tsunamigenicity of an earthquake has not yet been solved, and warning services are guided by the magnitude of the earthquake. The most powerful tsunamis are generated in subduction zones. Also, it is necessary for the underwater shock to resonate with the wave oscillations.

Landslides. Tsunamis of this type occur more frequently than estimated in the 20th century (about 7% of all tsunamis). Often an earthquake causes a landslide and it also generates a wave. On July 9, 1958, an earthquake in Alaska caused a landslide in Lituya Bay. A mass of ice and earth rocks collapsed from a height of 1100 m. A wave was formed that reached a height of more than 524 m on the opposite shore of the bay. Cases of this kind are quite rare and are not considered as a standard. But underwater landslides occur much more often in river deltas, which are no less dangerous. An earthquake can cause a landslide and, for example, in Indonesia, where shelf sedimentation is very large, landslide tsunamis are especially dangerous, as they occur regularly, causing local waves more than 20 meters high.

Volcanic eruptions account for approximately 5% of all tsunami events. Large underwater eruptions have the same effect as earthquakes. In large volcanic explosions, not only are waves generated from the explosion, but water also fills the cavities of the erupted material or even the caldera, resulting in a long wave. A classic example is the tsunami generated after the eruption of Krakatoa in 1883. Huge tsunamis from the Krakatoa volcano were observed in harbors around the world and destroyed a total of more than 5,000 ships and killed about 36,000 people.

Signs of a tsunami.

• Sudden fast the withdrawal of water from the shore over a considerable distance and the drying of the bottom. The further the sea recedes, the higher the tsunami waves can be. People who are on the shore and do not know about dangers, may stay out of curiosity or to collect fish and shells. In this case, it is necessary to leave the shore as soon as possible and move as far away from it as possible - this rule should be followed when, for example, in Japan, on the Indian Ocean coast of Indonesia, or Kamchatka. In the case of a teletsunami, the wave usually approaches without the water receding.
• Earthquake. The epicenter of an earthquake is usually in the ocean. On the coast, the earthquake is usually much weaker, and often there is no earthquake at all. In tsunami-prone regions, there is a rule that if an earthquake is felt, it is better to move further from the coast and at the same time climb a hill, thus preparing in advance for the arrival of the wave.
• Unusual drift ice and other floating objects, formation of cracks in fast ice.
• Huge reverse faults at the edges of stationary ice and reefs, the formation of crowds and currents.

rogue waves

rogue waves(Roaming waves, monster waves, freak waves - anomalous waves) - giant waves that arise in the ocean, more than 30 meters high, have behavior unusual for sea waves.

Just 10-15 years ago, scientists considered sailors’ stories about gigantic killer waves that appear out of nowhere and sink ships as just maritime folklore. For a long time wandering waves were considered fiction, since they did not fit into any mathematical model that existed at that time for calculating the occurrence and their behavior, because waves with a height of more than 21 meters cannot exist in the oceans of planet Earth.

One of the first descriptions of a monster wave dates back to 1826. Its height was more than 25 meters and it was noticed in the Atlantic Ocean near the Bay of Biscay. Nobody believed this message. And in 1840, the navigator Dumont d'Urville risked appearing at a meeting of the French Geographical Society and declaring that he had seen a 35-meter wave with his own eyes. Those present laughed at him. But there were stories about huge ghost waves that suddenly appeared in the middle of the ocean even with little storm, and their steepness resembled sheer walls of water, it became more and more.

Historical evidence of rogue waves

So, in 1933, the US Navy ship Ramapo was caught in a storm in the Pacific Ocean. For seven days the ship was tossed about by the waves. And on the morning of February 7, a shaft of incredible height suddenly crept up from behind. First, the ship was thrown into a deep abyss, and then lifted almost vertically onto a mountain of foaming water. The crew, who were lucky enough to survive, recorded a wave height of 34 meters. It moved at a speed of 23 m/sec, or 85 km/h. So far, this is considered the highest rogue wave ever measured.

During World War II, in 1942, the Queen Mary liner carried 16 thousand American military personnel from New York to the UK (by the way, a record for the number of people transported on one ship). Suddenly a 28-meter wave appeared. “The upper deck was at its usual height, and suddenly - suddenly! - it suddenly went down,” recalled Dr. Norval Carter, who was on board the ill-fated ship. The ship tilted at an angle of 53 degrees - if the angle had been even three degrees more, death would have been inevitable. The story of "Queen Mary" formed the basis of the Hollywood film "Poseidon".

However, on January 1, 1995, on the Dropner oil platform in the North Sea off the coast of Norway, a wave 25.6 meters high, called the Dropner wave, was first recorded by instruments. The Maximum Wave project allowed us to take a fresh look at the causes of the death of dry cargo ships that transported containers and other important cargo. Further research recorded over three weeks around the globe more than 10 single giant waves, the height of which exceeded 20 meters. The new project is called Wave Atlas, which provides for the compilation of a worldwide map of observed monster waves and its subsequent processing and addition.

Causes

There are several hypotheses about the causes of extreme waves. Many of them lack common sense. The simplest explanations are based on the analysis of a simple superposition of waves of different lengths. Estimates, however, show that the probability of extreme waves in such a scheme is too small. Another noteworthy hypothesis suggests the possibility of focusing wave energy in some surface current structures. These structures, however, are too specific for an energy focusing mechanism to explain the systematic occurrence of extreme waves. The most reliable explanation for the occurrence of extreme waves should be based on the internal mechanisms of nonlinear surface waves without involving external factors.

Interestingly, such waves can be both crests and troughs, which is confirmed by eyewitnesses. Further research involves the effects of nonlinearity in wind waves, which can lead to the formation of small groups of waves (packets) or individual waves (solitons) that can travel long distances without significantly changing their structure. Similar packages have also been observed many times in practice. The characteristic features of such groups of waves, confirming this theory, are that they move independently of other waves and have a small width (less than 1 km), with heights decreasing sharply at the edges.

However, it has not yet been possible to completely clarify the nature of the anomalous waves.

Try to count how many colors there are in a rainbow. This task cannot be completed. There are no sharp boundaries between the stripes of red and orange, blue and cyan, as well as between any neighboring stripes: there are many transitional tones between them. Not all shades of colors can be distinguished by the eye. It is often difficult to determine whether a color is “closer to blue” or “closer to blue.”

Is it not possible, in this case, for each ray to find a characteristic more accurate than its color? Physicists have found such a characteristic - and a very accurate one.

This happened due to the discovery of the wave properties of light.

What are waves and what are their properties?

For the sake of clarity, we will first get acquainted with waves on the surface of the water.

Everyone knows that water waves are different. A barely noticeable ripple sweeps across the pond, gently shaking the fisherman's plug; in the expanses of the sea, huge water shafts rock ocean-going steamers. How do waves differ from each other? To answer this question, let's look at how water waves arise.

As a water wave exciter, we will take the device shown in Fig. 3. When motor A rotates eccentric B, rod B moves rhythmically up and down, plunging into the water to different depths. Waves spread out from it in the form of circles with one center (Fig. 4). They are a series of alternating ridges and depressions.

The distance between adjacent crests or troughs is called the wavelength and is usually denoted by the Greek letter X (lambda). Let's increase the number of revolutions of the motor, and therefore the frequency of oscillations of the rod, by half. Then the number of waves appearing during the same time will be twice as large. But the wavelength will now be half as long. The number of waves produced in one second is called the wave frequency. It is usually denoted by the Greek letter V (nu).

Let a cork float on the water. Under the influence of a traveling wave, it will oscillate. The ridge that approaches the cork will lift it up, and the subsequent depression will lower it down. In a second, the cork will raise as many crests (and lower as many troughs) as waves are formed during this time. And this number is the frequency of the wave V. This means that the plug will oscillate with the frequency V. Thus, by detecting the action of the waves, we can establish their frequency at any point in their propagation.

For the sake of simplicity, we will assume that the waves do not decay. The frequency and length of undamped waves are related to each other by a simple law. V waves are formed per second. All these waves will fit within a certain segment. The first wave formed at the beginning of the second will reach the end of this segment; it is separated from the source at a distance equal to the wavelength times the frequency. But the distance traveled by the wave per second is the wave speed V. So, = If the wavelength and the speed of wave propagation are known, then

You can determine the frequency V, namely: V - y.

Frequency and wavelength are their essential characteristics; These characteristics distinguish some waves from others.

In addition to frequency (or wavelength), the blocks also differ in the height of the crests (or the depth of the troughs). The height of the wave is measured from the horizontal level of the resting surface of the water. It's called amplitude.

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• Friction waves:
  
  
  • wind, formed as a result of the action of wind
  
  
  • deep
  
  


• Tidal waves.


• Gravitational waves:
  
  
  • gravitational waves in shallow water
  
  
  • gravitational waves in deep water
  
  
  • seismic waves (tsunamis) that arise in the oceans as a result of an earthquake (or volcanic activity) and reach a height of 10-30 m off the coast.
  
  
  • ship waves
  
  

Wind waves arise with the wind; when the wind stops, these waves in the form of a dead swell, gradually fading, continue to move in the same direction. 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.
Wind waves are asymmetrical, their windward slope is gentle, 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”. In the open sea, "lamblets" are formed in a wind that is called "fresh" (wind force 5 and a speed of 8.0-10.7 m/s, or 33 km/h).
Swell- excitement that continues after the wind has already died down, weakened or changed direction. A disturbance that spreads by inertia in complete calm is called a dead swell.
When waves from different directions meet in a certain area, a crush. The chaotic accumulation of waves formed when direct waves meet reflected ones is also crush.
When waves pass over banks, reefs and rocks, breakers.
The approach of waves onto the shore with an increase in height and steepness and subsequent capsizing is called surf.

The surf takes on a different character depending on which shore: shallow (having small angles of inclination and a large width of the underwater slope) or deep (having significant slopes of the underwater slope).

The overturning of the crest of a moving wave onto a steep bank forms reverse faults having great destructive power.

© Yuri Danilevsky: November storm. Sevastopol

When the surf occurs near a deep shore that rises steeply from the water, the wave breaks up only when it hits the shore. In this case, a reverse wave is formed, meeting the next one and reducing its impact force, and then a new wave comes in and hits the shore again.
Such wave impacts in the case of a large swell or strong waves are often accompanied by surges of waves to a considerable height.

© Storm in Sevastopol, November 11, 2007

On the shores of the Black Sea, the wave impact force can reach 25 tons per 1 m 2.
When upturning, the wave gains enormous force. On the Shetland Islands, north of Scotland, there are fragments of gneiss rocks weighing up to 6-13 tons, thrown by the surf to a height of up to 20 m above sea level.

The rapid movement of waves and swell onto the shore is called roll forward.

Waves are regular when their crests are clearly visible, and irregular when the waves do not have clearly defined crests and are formed without any visible pattern.
Wave crests perpendicular to the wind direction in the open sea, lake, reservoir, but near the shore they take a position parallel to the coastline, running onto the banks.
The direction of wave propagation in the open sea is indicated on the surface of the water by a family of parallel stripes of foam - the traces of collapsing wave crests.

> Water waves

Explore waves on the water and moving elements in a circle. Find out what phase and group velocity is, a plane wave, an example of circular motion.

Usually water waves(lateral and longitudinal movements) can be considered in real life.

Learning Objective

• Describe the movement of particles in water waves.

Main points

• Particles in water waves move in a circle.
• If the waves move slower than the wind above them, then energy is transferred from the wind to the waves.
• On the surface, vibrations gain maximum strength and lose it as they dive.

Terms

• Phase velocity is the rate of propagation of a pure sine wave of infinite length and tiny amplitude.
• Group velocity is the rate of propagation of the modulated wave envelope. It is considered as the speed of information or energy transmission.
• Plane wave - wave photons act as infinite parallel planes of constant amplitude from peak to peak, located perpendicular to the phase velocity vector.

Example

The easiest way is to go to the sea, lake, or even go to the bathroom. Simply blow into a cup of water and notice that you create waves.

Water waves provide a rich area for physicists to study. Moreover, their description goes far beyond the scope of the introductory course. We often look at waves in 2D, but here we will discuss 1D.

Surface waves in water

The uniqueness of these phenomena lies in the fact that they manage to include transverse and longitudinal movements. Because of this, the particles make circular movements (clockwise). The oscillatory movement is at its highest on the surface and weakens with depth.

Waves are generated by wind passing over the sea surface. If the speed of wave propagation is inferior to the wind, then energy is transferred from the wind to the waves.

If we encounter monochromatic linear plane waves at depth, then particles near the surface move in a circle, forming longitudinal (back and forth) and transverse (up and down) wave movements. When wave propagation occurs in shallow water, the particle trajectories are compressed into ellipses. The higher the amplitude, the weaker the closed orbit. After passing along the ridges, the particles are displaced from the previous position and form a Stokes drift.

In front of you is a wave propagating towards the phase velocity

Water waves transport energy, so they use physical movement to generate it. The power of the wave depends on the size, length and density of the water. A deep wave corresponds to a water depth greater than half the wavelength. The deeper the wave, the faster it spreads. In shallow water the group velocity reaches the phase velocity. Currently they do not provide a sustainable form to be used as stable renewable energy sources.

The movement of water causes particles to travel in a circular path (clockwise). The thing is that the wave has both transverse and longitudinal properties

The formulas derived above are only suitable for waves in deep water. They are still quite accurate if the water depth is equal to half the wavelength. At shallower depths, water particles on the surface of the wave describe not circular trajectories, but elliptical ones, and the derived relationships are incorrect and actually take on a more complex form. However, for waves in very shallow water, as well as for very long waves in medium water, the relationship between the length and speed of wave propagation again takes a simpler form. In both of these cases, the vertical movements of water particles on the free surface are very small compared to the horizontal movements. Therefore, again we can assume that the waves have an approximately sinusoidal shape. Since the particle trajectories are very flattened ellipses, the effect of vertical acceleration on the pressure distribution can be neglected. Then at each vertical the pressure will change according to a static law.

Let a “shaft” of water of width b spread at a speed c from right to left on the water surface above a flat bottom, increasing the water level from h 1 to h 2 (Figure 4.4). Before the arrival of the swell, the water was at rest. The speed of her movement after increasing the level of shield. This speed does not coincide with the speed of the shaft; it is necessary in order to cause a lateral movement of the volume of water in the transition zone of width b to the right and thereby raise the water level.

Fig 4.4 n

The inclination of the shaft over its entire width is assumed to be constant and equal. Provided that the speed u is small enough that it can be neglected in comparison with the speed c of the propagation of the shaft, the vertical speed of water in the area of ​​the shaft will be equal to (Figure 4.5)

Continuity condition 3.4, applied to a single layer of water (in the direction perpendicular to the plane of Figure 4.4), has the form

u 1 l 1 = u 2 l 2 , (the integral disappeared due to the linearity of the areas under consideration),

here u 1 and u 2 are the average velocities in the cross sections l 1 and l 2 of the flow, respectively. l 1 and l 2 - linear quantities (lengths).

This equation, applied to this case, leads to the relation

h 2 u = bV, or h 2 u = c (h 2 -h 1). (4.9)

From 4.9 it is clear that the relationship between the speeds u and c does not depend on the width of the shaft.

Equation 4.9 remains true for a shaft with a non-rectilinear profile (provided that the angle b is small). This is easy to show by dividing such a shaft into a number of narrow shafts with straight profiles and adding up the continuity equations compiled for each individual shaft:

Where, provided that the difference h 2 - h 1 can be neglected and instead of h 2i in each case, substitute h 2, it turns out. This condition is valid under the already accepted assumption that the velocity u is small (see 4.9).

To the kinematic relation 4.9, a dynamic relation should be added, derived from the following considerations:

A volume of water with width b in the area of ​​the shaft is in accelerated motion, since the particles that make up this volume begin their movement on the right edge with zero speed, and on the left edge they have speeds w (Figure 4.4). An arbitrary particle of water is taken from the area inside the shaft. The time it takes for the shaft to pass over this particle is

therefore the particle acceleration

Next, the width of the shaft (its linear dimension in a plane perpendicular to the figure) is taken equal to one (Figure 4.6). This allows us to write the expression for the mass of the volume of water located in the shaft area as follows:

Where h m is the average water level in the shaft area. (4.11)

The pressure difference on both sides of the shaft at the same height is (according to the hydrostatic formula) , where is a constant for a given substance (water).

Therefore, the total pressure force acting on the considered volume of water in the horizontal direction is equal. Newton's second law (the basic equation of dynamics), taking into account 4.10 and 4.11, will be written as:

Where. (4.12)

So the shaft width was taken out of the equation. In the same way as was done for equation 4.9, it is proven that equation 4.12 is also applicable for a shaft with a different profile, provided that the difference h 2 - h 1 is small compared to h 2 and h 1 themselves.

So, there is a system of equations 4.9 and 4.12. Next, on the left side of equation 4.9, h 2 is replaced by h m (which, with a low shaft and, as a consequence, a small difference h 2 - h 1, is quite acceptable) and equation 4.12 is divided into equation 4.9:

After the reductions it turns out

The alternation of shafts with symmetrical angles of inclination (the so-called positive and negative shafts) leads to the formation of waves. The speed of propagation of such waves does not depend on their shape.

Long waves in shallow water travel at a speed called the critical speed.

If several low shafts follow each other on the water, each of which slightly increases the water level, then the speed of each subsequent shaft is slightly greater than the speed of the previous shaft, since the latter has already caused a slight increase in the depth h. In addition, each subsequent shaft no longer propagates in still water, but in water already moving in the direction of movement of the shaft at a speed of All this leads to the fact that subsequent shafts catch up with the previous ones, resulting in a steep shaft of finite height.