Ebb and flow

high tide and low tide- periodic vertical fluctuations in the level of the ocean or sea, which are the result of changes in the positions of the Moon and the Sun relative to the Earth, coupled with the effects of the Earth's rotation and the features of this relief, and manifested in a periodic horizontal displacement of water masses. Tides cause changes in sea level and periodic currents, known as tidal currents, making tide prediction important for coastal navigation.

The intensity of these phenomena depends on many factors, but the most important of them is the degree of connection of water bodies with the oceans. The more closed the reservoir, the less the degree of manifestation of tidal phenomena.

The yearly recurring tidal cycle remains unchanged due to the exact compensation of the forces of attraction between the Sun and the center of mass of the planetary pair and the forces of inertia applied to this center.

Since the position of the Moon and the Sun in relation to the Earth periodically changes, the intensity of the resulting tidal phenomena also changes.

Low tide at Saint Malo

Story

Ebb tides played a significant role in supplying the coastal population with seafood, allowing food suitable for food to be collected on the exposed seabed.

Terminology

major tidal ports.

Tide component M2

If we connect points on the map with the same tide phases, we get the so-called cotidal lines radiating from the amphidromic point. Typically, cotidal lines characterize the position of the crest of the tidal wave for each hour. In fact, the cotidal lines reflect the speed of propagation of the tidal wave in 1 hour. Maps that show lines of equal amplitudes and phases of tidal waves are called cotidal cards.

high tide- the difference between the highest water level at high tide (high tide) and its lowest level at low tide (low tide). The height of the tide is a variable value, however, its average indicator is given when characterizing each section of the coast.

Depending on the relative position of the Moon and the Sun, small and large tidal waves can reinforce each other. For such tides, special names have historically developed:

Quadrature tide- the smallest tide, when the tide-forming forces of the Moon and the Sun act at right angles to each other (this position of the luminaries is called quadrature).
spring tide- the greatest tide, when the tide-forming forces of the Moon and the Sun act along the same direction (this position of the luminaries is called syzygy).

The smaller or larger the tide, the smaller or, respectively, the greater the ebb.

The highest tides in the world

It can be observed in the Bay of Fundy (15.6-18 m), which is located on the east coast of Canada between New Brunswick and Nova Scotia.

On the European continent, the highest tides (up to 13.5 m) are observed in Brittany near the city of Saint Malo. Here the tidal wave is focused by the coastline of the Cornwall (England) and Cotentin (France) peninsulas.

Tide physics

Modern wording

In relation to the planet Earth, the cause of tides is the presence of the planet in the gravitational field created by the Sun and the Moon. Since the effects they create are independent, the impact of these celestial bodies on the Earth can be considered separately. In this case, for each pair of bodies, we can assume that each of them revolves around a common center of gravity. For the Earth-Sun pair, this center is located in the depths of the Sun at a distance of 451 km from its center. For the Earth-Moon pair, it is located deep in the Earth at a distance of 2/3 of its radius.

Each of these bodies experiences the action of tidal forces, the source of which is the gravitational force and internal forces that ensure the integrity of the celestial body, in the role of which is the force of its own attraction, hereinafter referred to as self-gravity. The emergence of tidal forces is most clearly seen in the example of the Earth-Sun system.

The tidal force is the result of the competing interaction of the gravitational force directed towards the center of gravity and decreasing inversely with the square of the distance from it, and the fictitious centrifugal force of inertia due to the rotation of a celestial body around this center. These forces, being opposite in direction, coincide in magnitude only at the center of mass of each of the celestial bodies. Due to the action of internal forces, the Earth revolves around the center of the Sun as a whole with a constant angular velocity for each element of its mass. Therefore, as this element of mass moves away from the center of gravity, the centrifugal force acting on it grows in proportion to the square of the distance. A more detailed distribution of tidal forces in their projection onto a plane perpendicular to the plane of the ecliptic is shown in Fig.1.

Fig.2 Deformation of the Earth's water shell as a result of the balance of tidal force, self-gravity force and the force of water reaction to the compressive force

As a result of the addition of these forces, tidal forces arise symmetrically on both sides of the globe, directed in different directions from it. The tidal force directed towards the Sun is of a gravitational nature, while that directed away from the Sun is a consequence of a fictitious inertial force.

These forces are extremely weak and cannot be compared with the forces of self-gravity (the acceleration they create is 10 million times less than the acceleration of free fall). However, they cause a shift in the particles of water in the oceans (resistance to shear in water at low speeds is practically zero, while compression is extremely high), until the tangent to the surface of the water becomes perpendicular to the resulting force.

As a result, a wave arises on the surface of the oceans, occupying a constant position in systems of mutually gravitating bodies, but running along the surface of the ocean together with the daily movement of its bottom and coasts. Thus (neglecting ocean currents) each particle of water makes an oscillatory movement up and down twice during the day.

The horizontal movement of water is observed only near the coast as a result of the rise in its level. The speed of movement is greater, the more gently the seabed is located.

Tidal potential

(the concept of acad. Shuleikin)

Neglecting the size, structure and shape of the Moon, we write down the specific force of attraction of a test body located on the Earth. Let be the radius vector directed from the test body towards the Moon, be the length of this vector. In this case, the force of attraction of this body by the Moon will be equal to

where is the selenometric gravitational constant. We place the test body at the point . The force of attraction of a test body placed at the center of mass of the Earth will be equal to

Here, and are understood as the radius vector connecting the centers of mass of the Earth and the Moon, and their absolute values. We will call the tidal force the difference between these two gravitational forces

In formulas (1) and (2), the Moon is considered to be a ball with a spherically symmetric mass distribution. The force function of the attraction of the test body by the Moon is no different from the force function of the attraction of the ball and is equal to The second force is applied to the center of mass of the Earth and is a strictly constant value. To obtain the force function for this force, we introduce a time coordinate system. We draw the axis from the center of the Earth and direct it towards the Moon. We leave the directions of the other two axes arbitrary. Then the force function of the force will be equal to . Tidal potential will be equal to the difference of these two force functions. Let's designate it , we will receive Constant we will define from a condition of normalization according to which the tidal potential in the center of the Earth is equal to zero. At the center of the Earth , It follows that . Therefore, we obtain the final formula for the tidal potential in the form (4)

Insofar as

For small values of , , the last expression can be represented in the following form

Substituting (5) into (4), we obtain

Deformation of the surface of the planet under the influence of ebbs and flows

The perturbing effect of the tidal potential deforms the level surface of the planet. Let us evaluate this effect, assuming that the Earth is a sphere with a spherically symmetric mass distribution. The unperturbed gravitational potential of the Earth on the surface will be equal to . For a dot. , located at a distance from the center of the sphere, the gravitational potential of the Earth is . Reducing by the gravitational constant, we get . Here the variables are and . Let us denote the ratio of the masses of the gravitating body to the mass of the planet by a Greek letter and solve the resulting expression with respect to:

Since with the same degree of accuracy we get

Given the smallness of the ratio, the last expressions can be written as

Thus, we have obtained the equation of a biaxial ellipsoid, in which the axis of rotation coincides with the axis, i.e. with a straight line connecting the gravitating body with the center of the Earth. The semiaxes of this ellipsoid are obviously equal

At the end we give a small numerical illustration of this effect. Let's calculate the tidal "hump" on the Earth, caused by the attraction of the Moon. The radius of the Earth is km, the distance between the centers of the Earth and the Moon, taking into account the instability of the lunar orbit, is km, the ratio of the mass of the Earth to the mass of the Moon is 81:1. Obviously, when substituting into the formula, we get a value approximately equal to 36 cm.

Notes

Literature

Frish S. A. and Timoreva A. V. Course of General Physics, Textbook for the Physics and Mathematics and Physics and Technology Departments of State Universities, Volume I. M .: GITTL, 1957
Shchuleykin V.V. Physics of the sea. M.: Publishing House "Nauka", Department of Earth Sciences of the Academy of Sciences of the USSR 1967
Voight S.S. What are tides. Editorial Board of Popular Science Literature of the Academy of Sciences of the USSR

Links

WXTide32 is a free tide charting program.

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