Report on the ebb and flow of tides. The influence of the moon on the ebb and flow of tides
Two years ago I was on vacation on the Indian Ocean coast on the wonderful island of Ceylon. My small hotel was only 50 meters from the ocean. Every day I observed with my own eyes all the powerful movement and turbulent life of the ocean. One early morning I stood on the shore, looking at the waves and thinking about what gives strength to such a powerful vibration of the ocean, its daily ebbs and flows.
What gives power to the ebb and flow
Gravity affects the movement of all objects equally. But if gravity causes tides in the oceans, and water causes water in Africa, then why are there no tides in lakes? Hmm, what if we assume that everything we know is wrong. Many intelligent people from the scientific world explain it this way. The Earth's gravity at point A is weaker than at point B. The net effect of the Earth's gravity stretches the ocean. After which it swells on opposite sides.
Yes, indeed the facts are real and there is a difference in the gravitational force of the Moon at points A and B.
The misunderstanding lies in the explanation of the bulges. Maybe they do not appear due to differences in attraction. But the reasons are less obvious, and they get confused. It's more about the cumulative pressure in different places in the water column. And the Moon turns the Earth into a hydraulic pump on a planetary scale, and the water swells, pressing itself towards the center. Therefore, even the slightest impact is enough for the wave movement to begin.
A little more about tides
But I would like to understand why they are not in another accumulation of water:
- in the human body (it consists of 80% water);
- in a filled bath;
- in lakes;
- in cups of coffee, etc.
Most likely due to lower pressure than in the ocean and poor hydraulics. Unlike the ocean, these are all small accumulations of water. The area of the lake, cup and the rest is not enough for the minimum pressure on it to change the water level, creating waves.
Large lakes can create pressure for mini tides. But since winds and splashes create large ripples, we simply do not notice them. Tides form everywhere, they are just very microscopic.
The surface level of oceans and seas changes periodically, approximately twice a day. These fluctuations are called ebb and flow. During high tide, the ocean level gradually rises and reaches its highest position. At low tide the level gradually drops to its lowest level. At high tide, water flows towards the shores, at low tide - away from the shores.
The ebb and flow of the tides are standing. They are formed due to the influence of cosmic bodies such as the Sun. According to the laws of interaction of cosmic bodies, our planet and the Moon mutually attract each other. The lunar gravity is so strong that the surface of the ocean seems to bend towards it. The Moon moves around the Earth, and a tidal wave “runs” behind it across the ocean. When a wave reaches the shore, that’s the tide. A little time will pass, the water will follow the Moon and move away from the shore - that’s the low tide. According to the same universal cosmic laws, ebbs and flows are also formed from the attraction of the Sun. However, the tidal force of the Sun, due to its distance, is significantly less than the lunar one, and if there were no Moon, the tides on Earth would be 2.17 times less. The explanation of tidal forces was first given by Newton.
Tides differ from each other in duration and magnitude. Most often, there are two high tides and two low tides during the day. On the arcs and coasts of Eastern and Central America there is one high tide and one low tide per day.
The magnitude of the tides is even more varied than their period. Theoretically, one lunar tide is equal to 0.53 m, solar - 0.24 m. Thus, the largest tide should have a height of 0.77 m. In the open ocean and near the islands, the tide value is quite close to theoretical: on the Hawaiian Islands - 1 m , on St. Helena Island - 1.1 m; on the islands - 1.7 m. On the continents, the magnitude of the tides ranges from 1.5 to 2 m. In the inland seas, the tides are very insignificant: - 13 cm, - 4.8 cm. It is considered tidalless, but near Venice the tides are up to 1 m. The largest tides are the following, recorded in:
In the Bay of Fundy (), the tide reached a height of 16-17 m. This is the highest tide in the entire globe.
In the north, in Penzhinskaya Bay, the tide height reached 12-14 m. This is the highest tide off the coast of Russia. However, the above tide figures are the exception rather than the rule. At the vast majority of tidal level measurement points, they are small and rarely exceed 2 m.
The importance of tides is very great for maritime navigation and the construction of ports. Each tidal wave carries a huge amount of energy.
There is a rise and fall of water. This is the phenomenon of sea ebbs and flows. Already in ancient times, observers noticed that the tide comes some time after the culmination of the Moon at the place of observation. Moreover, the tides are strongest on new and full moon days, when the centers of the Moon and the Sun are located approximately on the same straight line.
Taking this into account, I. Newton explained the tides by the action of gravity from the Moon and the Sun, namely by the fact that different parts of the Earth are attracted by the Moon in different ways.
The Earth rotates around its axis much faster than the Moon rotates around the Earth. As a result, the tidal hump (the relative position of the Earth and the Moon is shown in Figure 38) moves, a tidal wave runs across the Earth, and tidal currents arise. As the wave approaches the shore, the height of the wave increases as the bottom rises. In inland seas, the height of a tidal wave is only a few centimeters, but in the open ocean it reaches about one meter. In favorably located narrow bays, the height of the tide increases several times more.
The friction of water against the bottom, as well as deformation of the Earth’s solid shell, are accompanied by the release of heat, which leads to the dissipation of energy from the Earth-Moon system. Since the tidal hump is to the east, the maximum tide occurs after the climax of the Moon, the attraction of the hump causes the Moon to accelerate and the Earth's rotation to slow down. The Moon is gradually moving away from the Earth. Indeed, geological data show that in the Jurassic period (190-130 million years ago) the tides were much higher and the days were shorter. It should be noted that when the distance to the Moon decreases by 2 times, the height of the tide increases 8 times. Currently, the day is increasing by 0.00017 s per year. So in about 1.5 billion years their length will increase to 40 modern days. A month will be the same length. As a result, the Earth and the Moon will always face each other with the same side. After this, the Moon will begin to gradually approach the Earth and in another 2-3 billion years it will be torn apart by tidal forces (if, of course, by that time the Solar system still exists).
Moon's influence on tide
Let us consider, following Newton, in more detail the tides caused by the attraction of the Moon, since the influence of the Sun is significantly (2.2 times) less.
Let us write down expressions for the accelerations caused by the attraction of the Moon for different points of the Earth, taking into account that for all bodies at a given point in space these accelerations are the same. In the inertial reference system associated with the center of mass of the system, the acceleration values will be:
A A = -GM / (R - r) 2 , a B = GM / (R + r) 2 , a O = -GM / R 2 ,
Where a A, a O, a B— accelerations caused by the attraction of the Moon at points A, O, B(Fig. 37); M— mass of the Moon; r— radius of the Earth; R- the distance between the centers of the Earth and the Moon (for calculations it can be taken equal to 60 r); G— gravitational constant.
But we live on Earth and carry out all observations in a reference system associated with the center of the Earth, and not with the center of mass of the Earth - Moon. To go to this system, it is necessary to subtract the acceleration of the center of the Earth from all accelerations. Then
A’ A = -GM ☾ / (R - r) 2 + GM ☾ / R 2 , a’ B = -GM ☾ / (R + r) 2 + GM / R 2 .
Let's carry out the actions in brackets and take into account that r little compared to R and in sums and differences it can be neglected. Then
A’ A = -GM / (R - r) 2 + GM ☾ / R 2 = GM ☾ (-2Rr + r 2) / R 2 (R - r) 2 = -2GM ☾ r / R 3 .
Acceleration a’A And a’B identical in magnitude, opposite in direction, each directed from the center of the Earth. They're called tidal accelerations. At points C And D tidal accelerations are smaller in magnitude and directed towards the center of the Earth.
Tidal accelerations are accelerations that arise in a reference frame associated with a body due to the fact that, due to the finite dimensions of this body, its different parts are attracted differently by the disturbing body. At points A And B the acceleration of gravity turns out to be less than at points C And D(Fig. 37). Consequently, in order for the pressure at the same depth to be the same (as in communicating vessels) at these points, the water must rise, forming a so-called tidal hump. Calculations show that the rise of water or tide in the open ocean is about 40 cm. In coastal waters it is much greater, and the record is about 18 m. Newton's theory cannot explain this.
On the coasts of many outer seas you can see an interesting picture: fishing nets are stretched along the shore not far from the water. Moreover, these nets were not installed for drying, but for catching fish. If you stay on the shore and watch the sea, everything will become clear. Now the water is beginning to rise, and where there was a sandbank just a few hours ago, waves are splashing. When the water receded, nets appeared, in which tangled fish sparkled with scales. The fishermen went around the nets and removed their catch. Material from the site
This is how an eyewitness describes the onset of the tide: “We reached the sea,” a fellow traveler told me. I looked around in bewilderment. In front of me there really was a shore: a trail of ripples, the half-buried carcass of a seal, rare pieces of driftwood, fragments of shells. And then there was a flat expanse... and no sea. But after about three hours, the motionless line of the horizon began to breathe and became agitated. And now the sea swell began to sparkle behind her. The tide rolled uncontrollably forward along the gray surface. Overtaking each other, the waves ran onto the shore. One after another, the distant rocks sank - and only water is visible all around. She throws salty spray in my face. Instead of a dead plain, the expanse of water lives and breathes in front of me.”
When a tidal wave enters the bay, which has a funnel-shaped plan, the shores of the bay seem to compress it, causing the height of the tide to increase several times. Thus, in the Bay of Fundy off the eastern coast of North America, the tide height reaches 18 m. In Europe, the highest tides (up to 13.5 meters) occur in Brittany near the city of Saint-Malo.
Very often a tidal wave enters the estuaries
Let's continue the conversation about the forces acting on celestial bodies and the effects caused by this. Today I will talk about tides and non-gravitational disturbances.
What does this mean – “non-gravitational disturbances”? Perturbations are usually called small corrections to a large, main force. That is, we will talk about some forces, the influence of which on an object is much less than gravitational ones
What other forces exist in nature besides gravity? Let us leave aside strong and weak nuclear interactions; they are local in nature (act at extremely short distances). But electromagnetism, as we know, is much stronger than gravity and extends just as far - infinitely. But since electric charges of opposite signs are usually balanced, and the gravitational “charge” (the role of which is played by mass) is always of the same sign, then with sufficiently large masses, of course, gravity comes to the fore. So in reality we will be talking about disturbances in the movement of celestial bodies under the influence of an electromagnetic field. There are no more options, although there is still dark energy, but we will talk about it later, when we talk about cosmology.
As I explained on , Newton's simple law of gravity F = G∙M∙m/R² is very convenient to use in astronomy, because most bodies have a close to spherical shape and are sufficiently distant from each other, so that when calculating they can be replaced by points - point objects containing their entire mass. But a body of finite size, comparable to the distance between neighboring bodies, nevertheless experiences different force influences in its different parts, because these parts are located differently from the sources of gravity, and this must be taken into account.
Attraction crushes and tears apart
To feel the tidal effect, let's do a thought experiment popular among physicists: imagine ourselves in a freely falling elevator. We cut off the rope holding the cabin and begin to fall. Before we fall, we can watch what is happening around us. We hang free masses and observe how they behave. At first they fall synchronously, and we say this is weightlessness, because all the objects in this cabin and it itself feel approximately the same acceleration of free fall.
But over time, our material points will begin to change their configuration. Why? Because the lower one at the beginning was a little closer to the center of attraction than the upper one, so the lower one, being attracted stronger, begins to outstrip the upper one. And the side points always remain at the same distance from the center of gravity, but as they approach it they begin to approach each other, because accelerations of equal magnitude are not parallel. As a result, the system of unconnected objects is deformed. This is called the tidal effect.
From the point of view of an observer who has scattered grains around him and watches how individual grains move while the entire system falls onto a massive object, one can introduce such a concept as a field of tidal forces. Let us define these forces at each point as the vector difference between the gravitational acceleration at this point and the acceleration of the observer or the center of mass, and if we take only the first term of the expansion in the Taylor series for relative distance, we will get a symmetrical picture: the nearest grains will be ahead of the observer, the distant ones will lag behind him, i.e. the system will stretch along the axis directed towards the gravitating object, and along directions perpendicular to it the particles will be pressed towards the observer.
What do you think will happen when a planet is pulled into a black hole? Those who have not listened to lectures on astronomy usually think that a black hole will tear off matter only from the surface facing itself. They do not know that an almost equally strong effect occurs on the other side of a freely falling body. Those. it is torn in two diametrically opposite directions, not in one at all.
The Dangers of Outer Space
To show how important it is to take into account the tidal effect, let's take the International Space Station. It, like all Earth satellites, falls freely in a gravitational field (if the engines are not turned on). And the field of tidal forces around it is a quite tangible thing, so the astronaut, when working on the outside of the station, must tie himself to it, and, as a rule, with two cables - just in case, you never know what might happen. And if he finds himself untethered in those conditions where tidal forces pull him away from the center of the station, he can easily lose contact with it. This often happens with tools, because you can’t link them all. If something falls out of an astronaut’s hands, then this object goes into the distance and becomes an independent satellite of the Earth.
The work plan for the ISS includes tests in outer space of a personal jetpack. And when his engine fails, tidal forces carry the astronaut away, and we lose him. The names of the missing are classified.
This is, of course, a joke: fortunately, such an incident has not happened yet. But this could very well happen! And maybe someday it will happen.
Planet-ocean
Let's return to Earth. This is the most interesting object for us, and the tidal forces acting on it are felt quite noticeably. From which celestial bodies do they act? The main one is the Moon, because it is close. The next largest impact is the Sun, because it is massive. The other planets also have some influence on the Earth, but it is barely noticeable.
To analyze external gravitational influences on the Earth, it is usually represented as a solid ball covered with a liquid shell. This is a good model, since our planet actually has a mobile shell in the form of ocean and atmosphere, and everything else is quite solid. Although the Earth's crust and inner layers have limited rigidity and are slightly susceptible to tidal influence, their elastic deformation can be neglected when calculating the effect on the ocean.
If we draw tidal force vectors in the Earth’s center of mass system, we get the following picture: the field of tidal forces pulls the ocean along the Earth-Moon axis, and in a plane perpendicular to it presses it to the center of the Earth. Thus, the planet (at least its moving shell) tends to take the shape of an ellipsoid. In this case, two bulges appear (they are called tidal humps) on opposite sides of the globe: one faces the Moon, the other faces away from the Moon, and in the strip between them, a corresponding “bulge” appears (more precisely, the surface of the ocean there has less curvature).
A more interesting thing happens in the gap - where the tidal force vector tries to move the liquid shell along the earth's surface. And this is natural: if you want to raise the sea in one place, and lower it in another place, then you need to move the water from there to here. And between them, tidal forces drive water to the “sublunar point” and to the “anti-lunar point.”
Quantifying the tidal effect is very simple. The Earth's gravity tries to make the ocean spherical, and the tidal part of the lunar and solar influence tries to stretch it along its axis. If we left the Earth alone and allowed it to fall freely onto the Moon, the height of the bulge would reach about half a meter, i.e. The ocean rises only 50 cm above its average level. If you are sailing on a ship on the open sea or ocean, half a meter is not noticeable. This is called static tide.
In almost every exam I come across a student who confidently claims that the tide occurs only on one side of the Earth - the one facing the Moon. As a rule, this is what a girl says. But it happens, although less often, that young men are mistaken in this matter. At the same time, in general, girls have a deeper knowledge of astronomy. It would be interesting to find out the reason for this “tidal-gender” asymmetry.But in order to create a half-meter bulge at the sublunar point, you need to distill a large amount of water here. But the surface of the Earth does not remain motionless, it rotates quickly in relation to the direction of the Moon and the Sun, making a full revolution in a day (and the Moon moves slowly in orbit - one revolution around the Earth in almost a month). Therefore, the tidal hump constantly runs along the surface of the ocean, so that the solid surface of the Earth is under the tidal hump 2 times per day and 2 times under the tidal drop in ocean level. Let's estimate: 40 thousand kilometers (the length of the earth's equator) per day, that's 463 meters per second. This means that this half-meter wave, like a mini-tsunami, hits the eastern coasts of the continents in the equator region at supersonic speed. At our latitudes, the speed reaches 250-300 m/s - also quite a lot: although the wave is not very high, due to inertia it can create a great effect.
The second object in terms of influence on the Earth is the Sun. It is 400 times farther from us than the Moon, but 27 million times more massive. Therefore, the effects from the Moon and from the Sun are comparable in magnitude, although the Moon still acts a little stronger: the gravitational tidal effect from the Sun is about half as weak as from the Moon. Sometimes their influence is combined: this happens on a new moon, when the Moon passes against the background of the Sun, and on a full moon, when the Moon is on the opposite side from the Sun. On these days - when the Earth, Moon and Sun line up, and this happens every two weeks - the total tidal effect is one and a half times greater than from the Moon alone. And after a week, the Moon passes a quarter of its orbit and finds itself in quadrature with the Sun (a right angle between the directions on them), and then their influence weakens each other. On average, the height of tides in the open sea varies from a quarter of a meter to 75 centimeters.
Sailors have known tides for a long time. What does the captain do when the ship runs aground? If you have read sea adventure novels, then you know that he immediately looks at what phase the Moon is in and waits for the next full moon or new moon. Then the maximum tide can lift the ship and refloat it.
Coastal problems and features
Tides are especially important for port workers and for sailors who are about to bring their ship into or out of port. As a rule, the problem of shallow water arises near the coast, and to prevent it from interfering with the movement of ships, underwater channels - artificial fairways - are dug to enter the bay. Their depth should take into account the height of the maximum low tide.
If we look at the height of the tides at some point in time and draw lines of equal heights of water on the map, we will get concentric circles with centers at two points (sublunar and anti-lunar), in which the tide is maximum. If the orbital plane of the Moon coincided with the plane of the Earth’s equator, then these points would always move along the equator and would make a full revolution per day (more precisely, in 24ʰ 50ᵐ 28ˢ). However, the Moon does not move in this plane, but near the ecliptic plane, in relation to which the equator is inclined by 23.5 degrees. Therefore, the sublunar point also “walks” along latitude. Thus, in the same port (i.e., at the same latitude), the height of the maximum tide, which repeats every 12.5 hours, changes during the day depending on the orientation of the Moon relative to the Earth's equator.
This “trifle” is important for the theory of tides. Let's look again: the Earth rotates around its axis, and the plane of the lunar orbit is inclined towards it. Therefore, each seaport “runs” around the Earth’s pole during the day, once falling into the region of the highest tide, and after 12.5 hours - again into the region of the tide, but less high. Those. two tides during the day are not equivalent in height. One is always larger than the other, because the plane of the lunar orbit does not lie in the plane of the earth's equator.
For coastal residents, the tidal effect is vital. For example, in France there is one that is connected to the mainland by an asphalt road laid along the bottom of the strait. There are many people living on the island, but they cannot use this road while the sea level is high. This road can only be driven twice a day. People drive up and wait for low tide, when the water level drops and the road becomes accessible. People travel to and from work on the coast using a special tide table that is published for each coastal settlement. If this phenomenon is not taken into account, water may overwhelm a pedestrian along the way. Tourists simply come there and walk around to look at the bottom of the sea when there is no water. And local residents collect something from the bottom, sometimes even for food, i.e. in essence, this effect feeds people.
Life came out of the ocean thanks to the ebb and flow of the tides. As a result of the low tide, some coastal animals found themselves on the sand and were forced to learn to breathe oxygen directly from the atmosphere. If there were no Moon, then life might not have come out of the ocean so actively, because it is good there in all respects - a thermostatic environment, weightlessness. But if you suddenly found yourself on the shore, you had to somehow survive.
The coast, especially if it is flat, is greatly exposed at low tide. And for some time people lose the opportunity to use their watercraft, lying helplessly like whales on the shore. But there is something useful in this, because the low tide period can be used to repair ships, especially in some bay: the ships sailed, then the water went away, and they can be repaired at this time.
For example, there is the Bay of Fundy on the east coast of Canada, which is said to have the highest tides in the world: the water level drop can reach 16 meters, which is considered a record for a sea tide on Earth. Sailors have adapted to this property: during high tide they bring the ship to the shore, strengthen it, and when the water goes away, the ship hangs, and the bottom can be caulked.
People have long begun to monitor and regularly record the moments and characteristics of high tides in order to learn how to predict this phenomenon. Soon invented tide gauge- a device in which a float moves up and down depending on sea level, and the readings are automatically drawn on paper in the form of a graph. By the way, the means of measurement have hardly changed since the first observations to the present day.
Based on a large number of hydrograph records, mathematicians are trying to create a theory of tides. If you have a long-term record of a periodic process, you can decompose it into elementary harmonics - sinusoids of different amplitudes with multiple periods. And then, having determined the parameters of the harmonics, extend the total curve into the future and make tide tables on this basis. Now such tables are published for every port on Earth, and any captain about to enter a port takes a table for him and looks at when there will be sufficient water level for his ship.
The most famous story related to predictive calculations took place during the Second World War: in 1944, our allies - the British and Americans - were going to open a second front against Nazi Germany, for this it was necessary to land on the French coast. The northern coast of France is very unpleasant in this regard: the coast is steep, 25-30 meters high, and the ocean bottom is quite shallow, so ships can only approach the coast at times of maximum tide. If they ran aground, they would simply be shot from cannons. To avoid this, a special mechanical (there were no electronic ones yet) computer was created. She performed Fourier analysis of sea-level time series using drums rotating at their own speed, through which a metal cable passed, which summed up all the terms of the Fourier series, and a feather connected to the cable plotted a graph of tide height versus time. This was top secret work that greatly advanced the theory of tides because it was possible to predict with sufficient accuracy the moment of the highest tide, thanks to which heavy military transport ships swam across the English Channel and landed troops ashore. This is how mathematicians and geophysicists saved the lives of many people.
Some mathematicians are trying to generalize the data on a planetary scale, trying to create a unified theory of tides, but comparing records made in different places is difficult because the Earth is so irregular. It is only in the zero approximation that a single ocean covers the entire surface of the planet, but in reality there are continents and several weakly connected oceans, and each ocean has its own frequency of natural oscillations.
Previous discussions about sea level fluctuations under the influence of the Moon and the Sun concerned open ocean spaces, where tidal acceleration varies greatly from one coast to another. And in local bodies of water - for example, lakes - can the tide create a noticeable effect?
It would seem that it should not be, because at all points of the lake the tidal acceleration is approximately the same, the difference is small. For example, in the center of Europe there is Lake Geneva, it is only about 70 km long and is in no way connected with the oceans, but people have long noticed that there are significant daily fluctuations in water there. Why do they arise?
Yes, the tidal force is extremely small. But the main thing is that it is regular, i.e. operates periodically. All physicists know the effect that, when a force is applied periodically, sometimes causes an increased amplitude of oscillations. For example, you take a bowl of soup from the cafeteria and... This means that the frequency of your steps is in resonance with the natural vibrations of the liquid in the plate. Noticing this, we sharply change the pace of walking - and the soup “calms down.” Each body of water has its own basic resonant frequency. And the larger the size of the reservoir, the lower the frequency of natural vibrations of the liquid in it. So, Lake Geneva’s own resonant frequency turned out to be a multiple of the frequency of the tides, and a small tidal influence “looses” Lake Geneva so that the level on its shores changes quite noticeably. These long-period standing waves that occur in closed bodies of water are called seiches.
Tidal energy
Nowadays, they are trying to connect one of the alternative energy sources with the tidal effect. As I said, the main effect of tides is not that the water rises and falls. The main effect is a tidal current that moves water around the entire planet in a day.
In shallow places this effect is very important. In the New Zealand area, captains do not even risk guiding ships through some straits. Sailboats have never been able to get through there, and even modern ships have difficulty getting through there, because the bottom is shallow and tidal currents have enormous speed.
But since the water is flowing, this kinetic energy can be used. And power plants have already been built, in which turbines rotate back and forth due to tidal currents. They are quite functional. The first tidal power plant (TPP) was made in France, it is still the largest in the world, with a capacity of 240 MW. Compared to a hydroelectric power station, it’s not so great, of course, but it serves the nearest rural areas.
The closer to the pole, the lower the speed of the tidal wave, therefore in Russia there are no coasts that would have very powerful tides. In general, we have few outlets to the sea, and the coast of the Arctic Ocean is not particularly profitable for using tidal energy, also because the tide drives water from east to west. But there are still places suitable for PES, for example, Kislaya Bay.
The fact is that in bays the tide always creates a greater effect: the wave runs up, rushes into the bay, and it narrows, narrows - and the amplitude increases. A similar process occurs as if a whip was cracked: at first the long wave travels slowly along the whip, but then the mass of the part of the whip involved in the movement decreases, so the speed increases (impulse mv is preserved!) and reaches supersonic at the narrow end, as a result of which we hear a click.
By creating the experimental Kislogubskaya TPP of low power, power engineers tried to understand how effectively tides at circumpolar latitudes can be used to produce electricity. It doesn't make much economic sense. However, now there is a project for a very powerful Russian TPP (Mezenskaya) – for 8 gigawatts. In order to achieve this colossal power, it is necessary to block off a large bay, separating the White Sea from the Barents Sea with a dam. True, it is highly doubtful that this will be done as long as we have oil and gas.
The past and future of tides
By the way, where does tidal energy come from? The turbine spins, electricity is generated, and what object loses energy?
Since the source of tidal energy is the rotation of the Earth, if we draw from it, it means that the rotation must slow down. It would seem that the Earth has internal sources of energy (heat from the depths comes from geochemical processes and the decay of radioactive elements), and there is something to compensate for the loss of kinetic energy. This is true, but the energy flow, spreading on average almost evenly in all directions, can hardly significantly affect the angular momentum and change the rotation.
If the Earth did not rotate, the tidal humps would point exactly in the direction of the Moon and the opposite direction. But, as it rotates, the Earth’s body carries them forward in the direction of its rotation - and a constant divergence of the tidal peak and the sublunar point of 3-4 degrees arises. What does this lead to? The hump that is closer to the Moon is attracted to it more strongly. This gravitational force tends to slow down the Earth's rotation. And the opposite hump is further from the Moon, it tries to speed up the rotation, but is attracted weaker, so the resultant moment of force has a braking effect on the rotation of the Earth.
So, our planet is constantly decreasing its rotation speed (though not quite regularly, in jumps, which is due to the peculiarities of mass transfer in the oceans and atmosphere). What effect do Earth's tides have on the Moon? The near tidal bulge pulls the Moon along with it, while the distant one, on the contrary, slows it down. The first force is greater, as a result the Moon accelerates. Now remember from the previous lecture, what happens to a satellite that is forcibly pulled forward in motion? As its energy increases, it moves away from the planet and its angular velocity decreases because the orbital radius increases. By the way, an increase in the period of revolution of the Moon around the Earth was noticed back in the time of Newton.
Speaking in numbers, the Moon moves away from us by about 3.5 cm per year, and the length of the Earth’s day increases by a hundredth of a second every hundred years. It seems like nonsense, but remember that the Earth has existed for billions of years. It is easy to calculate that in the time of dinosaurs there were about 18 hours in a day (the current hours, of course).
As the Moon moves away, tidal forces become smaller. But it was always moving away, and if we look into the past, we will see that before the Moon was closer to the Earth, which means the tides were higher. You can appreciate, for example, that in the Archean era, 3 billion years ago, the tides were kilometer high.
Tidal phenomena on other planets
Of course, the same phenomena occur in the systems of other planets with satellites. Jupiter, for example, is a very massive planet with a large number of satellites. Its four largest satellites (they are called Galilean because Galileo discovered them) are quite significantly influenced by Jupiter. The nearest of them, Io, is entirely covered with volcanoes, among which there are more than fifty active ones, and they emit “extra” matter 250-300 km upward. This discovery was quite unexpected: there are no such powerful volcanoes on Earth, but here is a small body the size of the Moon, which should have cooled down long ago, but instead it is bursting with heat in all directions. Where is the source of this energy?
Io's volcanic activity was not a surprise to everyone: six months before the first probe approached Jupiter, two American geophysicists published a paper in which they calculated Jupiter's tidal influence on this moon. It turned out to be so large that it could deform the satellite’s body. And during deformation, heat is always released. When we take a piece of cold plasticine and begin to knead it in our hands, after several compressions it becomes soft and pliable. This happens not because the hand heated it with its heat (the same thing will happen if you squish it in a cold vice), but because the deformation put mechanical energy into it, which was converted into thermal energy.
But why on earth does the shape of the satellite change under the influence of tides from Jupiter? It would seem that, moving in a circular orbit and rotating synchronously, like our Moon, it once became an ellipsoid - and there is no reason for subsequent distortions of the shape? However, there are also other satellites near Io; all of them cause its (Io) orbit to shift slightly back and forth: it either approaches Jupiter or moves away. This means that the tidal influence either weakens or intensifies, and the shape of the body changes all the time. By the way, I have not yet talked about tides in the solid body of the Earth: of course, they also exist, they are not so high, on the order of a decimeter. If you sit in your place for six hours, then, thanks to the tides, you will “walk” about twenty centimeters relative to the center of the Earth. This vibration is imperceptible to humans, of course, but geophysical instruments register it.
Unlike the solid earth, the surface of Io fluctuates with an amplitude of many kilometers during each orbital period. A large amount of deformation energy is dissipated as heat and heats the subsurface. By the way, meteorite craters are not visible on it, because volcanoes constantly bombard the entire surface with fresh matter. As soon as an impact crater is formed, a hundred years later it is covered with products of eruptions of neighboring volcanoes. They work continuously and very powerfully, and to this are added fractures in the planet’s crust, through which a melt of various minerals, mainly sulfur, flows from the depths. At high temperatures it darkens, so the stream from the crater looks black. And the light rim of the volcano is the cooled substance that falls around the volcano. On our planet, matter ejected from a volcano is usually decelerated by air and falls close to the vent, forming a cone, but on Io there is no atmosphere, and it flies along a ballistic trajectory far in all directions. Perhaps this is an example of the most powerful tidal effect in the solar system.
The second satellite of Jupiter, Europa, all looks like our Antarctica, it is covered with a continuous ice crust, cracked in some places, because something is constantly deforming it too. Since this satellite is further away from Jupiter, the tidal effect here is not so strong, but still quite noticeable. Beneath this icy crust is a liquid ocean: the photographs show fountains gushing out of some of the cracks that have opened up. Under the influence of tidal forces, the ocean rages, and ice fields float and collide on its surface, much like we have in the Arctic Ocean and off the coast of Antarctica. The measured electrical conductivity of Europa's ocean fluid indicates that it is salt water. Why shouldn't there be life there? It would be tempting to lower a device into one of the cracks and see who lives there.
In fact, not all planets meet ends meet. For example, Enceladus, a moon of Saturn, also has an icy crust and an ocean underneath. But calculations show that tidal energy is not enough to maintain the subglacial ocean in a liquid state. Of course, in addition to tides, any celestial body has other sources of energy - for example, decaying radioactive elements (uranium, thorium, potassium), but on small planets they can hardly play a significant role. This means there is something we don’t understand yet.
The tidal effect is extremely important for stars. Why - more on this in the next lecture.
October 15th, 2012
British photographer Michael Marten created a series of original photographs capturing the coast of Britain from the same angles, but at different times. One shot at high tide and one at low tide.
It turned out to be quite unusual, and positive reviews of the project literally forced the author to start publishing the book. The book, called "Sea Change", was published in August this year and was released in two languages. It took Michael Marten about eight years to create his impressive series of photographs. The time between high and low water averages just over six hours. Therefore, Michael has to linger in each place for longer than just the time of a few shutter clicks. The author had been nurturing the idea of creating a series of such works for a long time. He was looking for how to realize changes in nature on film, without human influence. And I found it by chance, in one of the coastal Scottish villages, where I spent the whole day and caught the time of high and low tide.
Periodic fluctuations in water levels (rises and falls) in water areas on Earth are called tides.
The highest water level observed in a day or half a day during high tide is called high water, the lowest level during low tide is called low water, and the moment of reaching these maximum level marks is called the standing (or stage) of high tide or low tide, respectively. Average sea level is a conditional value, above which the level marks are located during high tides, and below which during low tides. This is the result of averaging large series of urgent observations.
Vertical fluctuations in water level during high and low tides are associated with horizontal movements of water masses in relation to the shore. These processes are complicated by wind surge, river runoff and other factors. Horizontal movements of water masses in the coastal zone are called tidal (or tidal) currents, while vertical fluctuations in water levels are called ebbs and flows. All phenomena associated with ebbs and flows are characterized by periodicity. Tidal currents periodically change direction to the opposite, in contrast, ocean currents, moving continuously and unidirectionally, are caused by the general circulation of the atmosphere and cover large areas of the open ocean.
High and low tides alternate cyclically in accordance with changing astronomical, hydrological and meteorological conditions. The sequence of tidal phases is determined by two maxima and two minima in the daily cycle.
Although the Sun plays a significant role in tidal processes, the decisive factor in their development is the gravitational pull of the Moon. The degree of influence of tidal forces on each particle of water, regardless of its location on the earth's surface, is determined by Newton's law of universal gravitation.
This law states that two material particles attract each other with a force directly proportional to the product of the masses of both particles and inversely proportional to the square of the distance between them. It is understood that the greater the mass of the bodies, the greater the force of mutual attraction that arises between them (with the same density, a smaller body will create less attraction than a larger one).
The law also means that the greater the distance between two bodies, the less attraction between them. Since this force is inversely proportional to the square of the distance between two bodies, the distance factor plays a much larger role in determining the magnitude of the tidal force than the masses of the bodies.
The gravitational attraction of the Earth, acting on the Moon and keeping it in near-Earth orbit, is opposite to the force of attraction of the Earth by the Moon, which tends to move the Earth towards the Moon and “lifts” all objects located on the Earth in the direction of the Moon.
The point on the earth's surface located directly below the Moon is only 6,400 km from the center of the Earth and on average 386,063 km from the center of the Moon. In addition, the mass of the Earth is 81.3 times the mass of the Moon. Thus, at this point on the earth’s surface, the Earth’s gravity acting on any object is approximately 300 thousand times greater than the Moon’s gravity.
It is a common idea that water on Earth directly below the Moon rises in the direction of the Moon, causing water to flow away from other places on the Earth's surface, but since the Moon's gravity is so small compared to the Earth's, it would not be enough to lift so much water. huge weight.
However, the oceans, seas and large lakes on Earth, being large liquid bodies, are free to move under the influence of lateral displacement forces, and any slight tendency to move horizontally sets them in motion. All waters that are not directly under the Moon are subject to the action of the component of the Moon's gravitational force directed tangentially (tangentially) to the earth's surface, as well as its component directed outward, and are subject to horizontal displacement relative to the solid earth's crust.
As a result, water flows from adjacent areas of the earth's surface towards a place located under the Moon. The resulting accumulation of water at a point under the Moon forms a tide there. The tidal wave itself in the open ocean has a height of only 30-60 cm, but it increases significantly when approaching the shores of continents or islands.
Due to the movement of water from neighboring areas towards a point under the Moon, corresponding ebbs of water occur at two other points removed from it at a distance equal to a quarter of the Earth’s circumference. It is interesting to note that the decrease in sea level at these two points is accompanied by a rise in sea level not only on the side of the Earth facing the Moon, but also on the opposite side.
This fact is also explained by Newton's law. Two or more objects located at different distances from the same source of gravity and, therefore, subjected to the acceleration of gravity of different magnitudes, move relative to each other, since the object closest to the center of gravity is most strongly attracted to it.
Water at the sublunar point experiences a stronger pull towards the Moon than the Earth below it, but the Earth in turn has a stronger pull towards the Moon than water on the opposite side of the planet. Thus, a tidal wave arises, which on the side of the Earth facing the Moon is called direct, and on the opposite side - reverse. The first of them is only 5% higher than the second.
Due to the rotation of the Moon in its orbit around the Earth, approximately 12 hours and 25 minutes pass between two successive high tides or two low tides in a given place. The interval between the climaxes of successive high and low tides is approx. 6 hours 12 minutes The period of 24 hours 50 minutes between two successive tides is called a tidal (or lunar) day.
Tide inequalities. Tidal processes are very complex and many factors must be taken into account to understand them. In any case, the main features will be determined:
1) the stage of development of the tide relative to the passage of the Moon;
2) tidal amplitude and
3) the type of tidal fluctuations, or the shape of the water level curve.
Numerous variations in the direction and magnitude of tidal forces give rise to differences in the magnitude of morning and evening tides in a given port, as well as between the same tides in different ports. These differences are called tide inequalities.
Semi-diurnal effect. Usually within a day, due to the main tidal force - the rotation of the Earth around its axis - two complete tidal cycles are formed.
When viewed from the North Pole of the ecliptic, it is obvious that the Moon rotates around the Earth in the same direction in which the Earth rotates around its axis - counterclockwise. With each subsequent revolution, a given point on the earth's surface again takes a position directly under the Moon somewhat later than during the previous revolution. For this reason, both the ebb and flow of the tides are delayed by approximately 50 minutes every day. This value is called lunar delay.
Half-month inequality. This main type of variation is characterized by a periodicity of approximately 143/4 days, which is associated with the rotation of the Moon around the Earth and its passage through successive phases, in particular syzygies (new moons and full moons), i.e. moments when the Sun, Earth and Moon are located on the same straight line.
So far we have touched only on the tidal influence of the Moon. The gravitational field of the Sun also affects the tides, however, although the mass of the Sun is much greater than the mass of the Moon, the distance from the Earth to the Sun is so greater than the distance to the Moon that the tidal force of the Sun is less than half that of the Moon.
However, when the Sun and Moon are on the same straight line, either on the same side of the Earth or on opposite sides (during the new moon or full moon), their gravitational forces add up, acting along the same axis, and the solar tide overlaps with the lunar tide.
Likewise, the attraction of the Sun increases the ebb caused by the influence of the Moon. As a result, the tides become higher and the tides lower than if they were caused only by the Moon's gravity. Such tides are called spring tides.
When the gravitational force vectors of the Sun and the Moon are mutually perpendicular (during quadratures, i.e. when the Moon is in the first or last quarter), their tidal forces oppose, since the tide caused by the attraction of the Sun is superimposed on the ebb caused by the Moon.
Under such conditions, the tides are not as high and the tides are not as low as if they were due only to the gravitational force of the Moon. Such intermediate ebbs and flows are called quadrature.
The range of high and low water marks in this case is reduced by approximately three times compared to the spring tide.
Lunar parallactic inequality. The period of fluctuations in tidal heights, which occurs due to lunar parallax, is 271/2 days. The reason for this inequality is the change in the distance of the Moon from the Earth during the latter’s rotation. Due to the elliptical shape of the lunar orbit, the tidal force of the Moon at perigee is 40% higher than at apogee.
Daily inequality. The period of this inequality is 24 hours 50 minutes. The reasons for its occurrence are the rotation of the Earth around its axis and a change in the declination of the Moon. When the Moon is near the celestial equator, the two high tides on a given day (as well as the two low tides) differ slightly, and the heights of morning and evening high and low waters are very close. However, as the Moon's north or south declination increases, morning and evening tides of the same type differ in height, and when the Moon reaches its greatest north or south declination, this difference is greatest.
Tropical tides are also known, so called because the Moon is almost above the Northern or Southern tropics.
The diurnal inequality does not significantly affect the heights of two successive low tides in the Atlantic Ocean, and even its effect on the heights of the tides is small compared to the overall amplitude of the fluctuations. However, in the Pacific Ocean, diurnal variability is three times greater in low tide levels than in high tide levels.
Semiannual inequality. Its cause is the revolution of the Earth around the Sun and the corresponding change in the declination of the Sun. Twice a year for several days during the equinoxes, the Sun is near the celestial equator, i.e. its declination is close to 0. The Moon is also located near the celestial equator for approximately one day every half month. Thus, during the equinoxes, there are periods when the declinations of both the Sun and the Moon are approximately equal to 0. The total tidal effect of the attraction of these two bodies at such moments is most noticeable in areas located near the earth's equator. If at the same time the Moon is in the new moon or full moon phase, the so-called. equinoctial spring tides.
Solar parallax inequality. The period of manifestation of this inequality is one year. Its cause is the change in the distance from the Earth to the Sun during the orbital movement of the Earth. Once for each revolution around the Earth, the Moon is at its shortest distance from it at perigee. Once a year, around January 2, the Earth, moving in its orbit, also reaches the point of closest approach to the Sun (perihelion). When these two moments of closest approach coincide, causing the greatest net tidal force, higher tidal levels and lower tidal levels can be expected. Likewise, if the passage of aphelion coincides with apogee, lower tides and shallower tides occur.
Greatest tidal amplitudes. The world's highest tide is generated by strong currents in Minas Bay in the Bay of Fundy. Tidal fluctuations here are characterized by a normal course with a semi-diurnal period. The water level at high tide often rises by more than 12 m in six hours, and then drops by the same amount over the next six hours. When the effect of spring tide, the position of the Moon at perigee and the maximum declination of the Moon occur on the same day, the tide level can reach 15 m. This exceptionally large amplitude of tidal fluctuations is partly due to the funnel-shaped shape of the Bay of Fundy, where the depths decrease and the shores move closer together towards top of the bay. The causes of tides, which have been the subject of constant study for many centuries, are among those problems that have given rise to many controversial theories even in relatively recent times
Charles Darwin wrote in 1911: “There is no need to look for ancient literature for the sake of grotesque theories of tides.” However, sailors manage to measure their height and take advantage of the tides without having any idea of the actual causes of their occurrence.
I think that we don’t have to worry too much about the causes of the tides. Based on long-term observations, special tables are calculated for any point in the earth’s waters, which indicate the times of high and low water for each day. I’m planning my trip, for example, to Egypt, which is famous for its shallow lagoons, but try to plan in advance so that the full water occurs in the first half of the day, which will allow you to fully ride most of the daylight hours.
Another question related to tides that is interesting for kiters is the relationship between wind and water level fluctuations.
A folk superstition states that at high tide the wind intensifies, but at low tide it turns sour.
The influence of wind on tidal phenomena is more understandable. The wind from the sea pushes the water towards the coast, the height of the tide increases above normal, and at low tide the water level also exceeds the average. On the contrary, when the wind blows from land, water is driven away from the coast, and sea level drops.
The second mechanism operates by increasing atmospheric pressure over a vast area of water; the water level decreases as the superimposed weight of the atmosphere is added. When atmospheric pressure increases by 25 mmHg. Art., the water level drops by approximately 33 cm. A high pressure zone or anticyclone is usually called good weather, but not for kiters. There is calm in the center of the anticyclone. A decrease in atmospheric pressure causes a corresponding increase in water levels. Consequently, a sharp drop in atmospheric pressure combined with hurricane-force winds can cause a noticeable rise in water levels. Such waves, although called tidal, are in fact not associated with the influence of tidal forces and do not have the periodicity characteristic of tidal phenomena.
But it is quite possible that low tides can also influence the wind, for example, a decrease in the water level in coastal lagoons leads to greater warming of the water, and as a result to a decrease in the temperature difference between the cold sea and the heated land, which weakens the breeze effect.
Photo by Michael Marten
