The tides or tides ( Low German Tid, Tied [tiːt] "time"; Pl. Tiden, Tieden [tiːdən] "times") are the water movements of the oceans that are caused by the associated tidal forces as a result of the gravitation of the moon and the sun . The tides mainly affect the coasts. Since the moon has a stronger influence, there are two high tides and two low tides in almost 25 hours rather than in 24 hours, because the moon is only in roughly the same position in the sky after an average of 24 hours and 49 minutes .
The tidal forces act in the sense of a symmetrical stretching of the earth along the line to the moon or the sun. Since no stable deformation can occur due to the earth's rotation , the tidal forces in the oceans periodically stimulate currents, especially in mid-latitudes. These cause the periodic rise and fall of the water level. With full and new moon, the sun and moon are on the same line from Earth, which is why their effects add up to a particularly large tide, the spring tide . With a half moon, on the other hand, the sun and moon are at right angles to each other and this results in a particularly small tide, the nipp tide . The tidal forces of the sun are about 46% of those of the moon.
Particularly large tidal forces and spring tides occur about every 15 months when the moon is again as close as possible to the earth due to the slow rotation of the elliptical lunar orbit . In addition, the inclination of the lunar orbit, which is variable relative to the earth's axis, results in an approximately annual variation in the tides.
Terms and designations
Flood is the period and the process of rising, "rising" water. Ebb is the period and the process of sinking, "running" water. The time of the highest water level is called high water (HW), that of the lowest water level is called low water (NW). The water level at these times is called high water height (HWH) or low water height (NWH). Successive high and low water levels in the same location are generally different because the positions of the moon and sun change relative to that location. The point in time when the water changes from running water to running water or vice versa is called capsizing. When the tide capsizes, the tidal current, the backwater, comes to a standstill for a short time .
The difference in height between the low water level and the next high water level (during high tide) is called the tide rise. The difference in height between high water level and the following low water level is called the tide fall. The mean of the rise and fall of the tide is called the tide range . The time course of the water level between low water, high water and the subsequent low water results in the tide curve. The tide-related height of the water level in relation to the local chart zero (mostly LAT ) is called the height of the tide.
Tide water levels:
|Highest possible tidal water level||Highest Astronomical Tide||HAS||Cover for headroom under bridges|
|Medium spring flood||MSpHW||Mean High Water Spring||MHWS|
Medium flood ,
medium tidal flood
|MThw||Mean high water||MHW||Definition of the coastline|
|Mean tidal water||MTmw||Mean Sea Level||MSL|
|Mean water (tidal waters)||MW||Nautical chart zero in tide-free waters, where the water depths in nautical and maps correspond|
|Mean low tidal water||MTnw||Mean low water||MLW|
|Medium spring low water||MSpNW||Mean Low Water Spring||MLWS||formerly zero level for water depths (according to IHO outdated)|
|lowest possible tidal water level||NGzW||Lowest Astronomical Tide||LAT||Nautical chart zero in tidal waters, zero level for water depths in nautical charts|
The German abbreviations are no longer used in official IHO works . In addition to “MThw” and “MTnw”, the level portal of the Federal Waterways and Shipping Administration uses the empirical values “HThw” (highest tidal high water) and “NTnw” (lowest tidal low water).
|Height of the tide||Height of Tide||Difference between the current water level and chart zero|
|Medium spring tidal range||Spring Range of Tide||Difference between low and high tide during springtime (greatest tidal range)|
|Mean nipptide range||Neap Range of Tide||Difference between low and high tide at sipping time (stroke smallest)|
Nautical chart zero:
|Nautical chart zero||SKN||Chart date||CD||Basis for:
• Official definition of the baseline
• Zero level for the measurement of water depths
is related to:
• LAT Lowest Astronomical Tide (or MLLW)
• or to MSL in tide-free waters
Explanatory history of the tides
The fact that ebb and flow are predominantly correlated with the moon is probably one of the earliest astrophysical discoveries made by humans. Because it can be observed directly on the ocean coasts that the moon visible at high tide is regularly in almost the same place at the next but one high tide, i.e. two tides occur during one of its apparent orbits. More detailed knowledge of the relationship between the moon and the tides, including the long-term periodicity depending on the phases of the moon and the seasons , has already been proven in ancient India , with the Phoenicians and Carians , and was also known to the navigator and explorer Pytheas .
The Greek astronomer Seleukos of Seleukia took over the heliocentric worldview of Aristarchus in the second century BC and based his theory of the tides on it. An extensive work by Poseidonios from the 1st century BC. BC is lost, but from ancient quotations it can be concluded that it contained the lunisolar theory, i.e. the explanation of the daily and monthly effects due to the mutual action of the three heavenly bodies.
In the 16th century Andrea Cesalpino gave an explanation of the tides through the movement of the earth in his work Quaestiones Peripatetica (1571) - similar to the sloshing of water in a moving bucket. In 1590, Simon Stevin declared the attraction of the moon to be the cause of the tides.
In 1609, Johannes Kepler sketched a theory of gravity in the foreword of his Astronomia Nova , according to which all matter has a mutually attractive effect, so that the moon causes the tides through the attraction of the oceans. Kepler interpreted qualitatively correctly why the ebb and flow on different coasts are differently strong and differently out of phase with the moon, but could only explain one tide per day. Galileo Galilei denied any influence of the moon and in 1616 interpreted in his Discorso sopra il Flusso e Reflusso del Mare (unpublished) and in Dialogo (published 1632) the tides as a result of the earth's rotation combined with the earth's orbit around the sun: Moved as seen from the sun The day side of the earth is slower than the night side, which means that the tides, but only once a day, should arise due to the different accelerations. In the 17th century, René Descartes gave an explanation based on the friction of the " ether " between the earth and the moon, but this was quickly refuted.
Isaac Newton started in 1687 in his work Mathematical Principles of Natural Science from the model of a two-body system of earth and moon that rotates around the common center of gravity , the barycentre . He was the first to be able to calculate the different gravitational forces of the moon and the sun at different places on earth and the resulting deformation of the sea surface, which correctly leads to two - albeit far too weak - tides per day. Daniel Bernoulli , Leonhard Euler , Pierre-Simon Laplace and Thomas Young extended Newton's observation and found that the uplift and downward movement of the water surface is caused less by the vertical components of the tidal forces than by the currents that are driven by the horizontal components. With this they confirmed the approach of Cesalpino ("sloshing in a water bed") and Kepler. In 1739 Euler discovered the mathematical derivation of the phenomena of forced vibrations and resonance , and Young gave their full mathematical description for the first time in 1823. However, the predictions obtained by calculation were very imprecise. Only with increasing knowledge of the mechanics of the forced vibrations in flowing liquids and the masses of the celestial bodies involved did the results gradually become more accurate from the middle of the 19th century.
|1st century BC Chr.||Poseidonios||The moon has more influence on the tides than the sun|
|1590||Simon Stevin||Attraction of the moon|
|1609||Johannes Kepler||Attraction by gravity of the moon|
|1616/1632||Galileo Galilei||kinematic tidal theory|
|17th century||René Descartes||Friction of the "ether" between earth and moon|
|1687||Isaac Newton||Calculation of the forces of attraction of the moon and sun|
|1740||Daniel Bernoulli||Equilibrium theory|
|1740||Leonhard Euler||forced vibration|
|1799||Pierre-Simon Laplace||dynamic tide|
|1824||Thomas Young||Theory based on the complete formulas of the forced oscillation|
|1831||William Whewell||Tidal waves|
|1842||George Biddell Airy||Theory based on simply shaped basins with uniform depth|
|1867||William Thomson||harmonic analysis|
|20th century||Sydney Hough||dynamic theory including the Coriolis force|
Explanation of the tides
Tides arise from the interaction of the daily rotation of the earth in the (almost fixed) gravitational field of the moon and sun and the fact that this gravitational field is not equally strong everywhere, but rather elongates the earth. The forces that cause this are called tidal forces . A place on the earth's surface reaches two points with maximum and minimum tidal force with each revolution. The tidal force accounts for less than a ten-millionth of the earth's gravity, but it represents a periodic disturbance of an otherwise stable state of equilibrium. The oceans react to this disturbance with oscillating currents, which are noticeable on the coasts by periodic rise and fall of the sea level. In many places, height differences of well over 1 meter are achieved.
Explanation of the tidal forces
A gravitational field calls an otherwise force-free ground point (ground ) at the location by the gravitational force an acceleration produced. If one looks at an extended cloud of mass points that do not feel any other than these gravitational forces, then the center of mass of the cloud will show a certain acceleration at its location , as if the sum of the gravitational forces of all mass points here acted on a body with the sum of their masses (see Focal point ).
The gravitational acceleration of the mass point at the location is related to the acceleration of the center of mass. The difference is the tidal acceleration prevailing at this location of the cloud:
The tidal acceleration shows itself directly in the acceleration of the movement of the (otherwise force-free) mass point relative to the center of mass of the cloud. In the frame of reference in which the center of mass rests, each mass point behaves as if the tidal force was acting on it
works. As an alternative to this derivation, one can explicitly transform the reference system from an inertial system into the rest system of the cloud's center of mass. This reference system is also accelerated, therefore an inertial force that is the same everywhere acts in it , which one has to add to the external force . The result for the tidal force - that is the force effective in this frame of reference - is the same.
The same tidal force is also effective when the mass points that make up the celestial body under consideration feel other forces, e.g. B. mutual gravitation, cohesion, etc., but also another external force field. However, in the accelerated movement of a mass point, the tidal force does not show up immediately, but only as a sum with the other forces acting on the mass point. You can then z. B. cause deformations and / or currents, depending on how tight the mass points are tied to their location.
This derivation of tidal acceleration and tidal force applies regardless of the orbit or the state of motion of the celestial body under consideration (e.g. whether linear or circular, with or without its own rotation). The assumptions made in many textbooks about its circular motions and the associated centrifugal forces (which, by the way, are only exact for a uniform circular motion) only serve to determine the acceleration of the center of mass in order to be able to carry out the transformation in its rest system.
The tidal force caused by a celestial body is strongest at the two opposite points on the earth's surface, which are the smallest or greatest distance from the celestial body. There it points vertically outwards, i.e. at the smallest distance directly towards the celestial body, at the greatest distance directly away from it. At those points on the earth's surface that are the same distance from the celestial body as the center of mass of the earth, the tidal force is smallest and points vertically inwards. In a central area, the tidal force is directed parallel to the earth's surface and can therefore efficiently drive currents in the ocean.
Why is the sun's gravitational field pulling the earth a little longer?
For a simple explanation, consider a fictitious spherical cloud of small particles instead of the solid earth, which together orbit the sun, but do not exert any forces on each other (including no gravity). All particles move (initially) with the same angular velocity around the sun, partly a little closer, partly a little further away from it. Then the entire gravitational force that the sun exerts on the particles delivers exactly the centripetal acceleration at the location of the cloud's center of gravity , which is necessary for the continuation of its circular motion (with radius ) (see center of gravity theorem ). Compared to the center of mass, the particles that are closer to the sun need a smaller centripetal acceleration for their circular orbit at the same angular velocity, but feel a stronger gravitational pull of the sun. Therefore, their path is curved more towards the sun and they move increasingly faster from the center of the cloud. Conversely, the particles at a greater distance feel the sun as less attractive and cannot be kept on a circular path by it. These particles will move away from the center in an accelerated manner. Result: the cloud is pulled apart in both directions along the line to the sun. This “tidal breakup” has already been observed in comets that come too close to a planet (see Shoemaker-Levy 9 ). Now the earth is not a cloud of non-interacting particles, but the tidal forces are the same. As a solid body with a certain elasticity, the earth is deformed (by the sun and moon together) by ± 30 to ± 60 cm (see earth tides ), while currents are generated in the moving air and water masses of the atmosphere and oceans.
Calculation of tidal accelerations
Tidal accelerations are the differences in acceleration between different points in an external field. The outer field is always a superposition of central fields, here mainly the sun and moon. The simplest case is a central field, i.e. the sun or moon. The accelerations are determined using a test mass, which is placed once at the location of the center of mass of the earth and once at the place of interest. The acceleration at the center of mass is equal to the acceleration of a rigid earth. The other location of the test mass can be anywhere in the earth, e.g. B. in the movable hydrosphere.
is the amount of acceleration in the gravitational field of the other celestial body (sun or moon) given by Newton's law of gravitation . This is the distance between the test mass and the causing mass and the gravitational constant . For points on the connecting line from the center of mass of the earth to the celestial body, the accelerations are parallel, so the maximum and minimum tidal acceleration can be calculated simply by the difference between the amounts at the points and ( for the mean earth radius ):
With and the values for the moon, and , results
That is about one-thirtieth the acceleration of the earth towards the moon. The gravitational acceleration on earth, 9.81 m / s 2 , is about 10 7 times greater.
Vertical and horizontal components of tidal acceleration
The following applies to the vertical and horizontal components of the tidal acceleration at any location on the earth's surface that deviates by the angle from the earth → moon when viewed from the center of the earth
- for the vertical component and
- for the horizontal component of the tidal acceleration.
The graphic on the right shows the decomposition of the tidal acceleration into components perpendicular and parallel to the earth's surface.
Sample calculation - acceleration of the earth and tidal acceleration on its surface by the sun
With the constants
for the gravitational acceleration of the earth originating from the sun as well as
for the tidal acceleration.
The tidal acceleration varies with the third power of the distance from the center of gravity and thus drops faster than the quadratic varying acceleration of gravity. Although the sun generates almost 180 times stronger gravitational acceleration than the moon at the location on earth, the tidal acceleration it causes is only 46% of that caused by the moon.
Superposition of the tidal forces caused by the moon and the sun
The tidal forces caused by the moon and sun add up. The strongest total force results when the sun, earth and moon are on one line, which occurs approximately with a full and new moon with a period of about 14¾ days. Then they raise the water level of the ocean about ¾ meter (about ½ meter by the moon and about ¼ meter by the sun) at high tide. At a half moon there is a right angle between the two force fields. Their superposition leads to forces that raise the water level of the ocean less strongly.
The periodic movement of water in the oceans
If the ocean covered the whole earth, the daily rotation of the earth would revolve the mountains and valleys of the water on the earth. Through the continents, the ocean is divided into several more or less closed basins, at the edges of which the incoming water is not only stopped but also reflected. A wave of water runs back and is reflected again on the opposite edge. The water sloshes back and forth in the ocean basins with a period of about 12½ hours, with circular waves being formed by the rotation of the earth. If there is a resonance between the wave propagation and the change in tidal forces caused by the rotation of the earth, the wave amplitude can increase significantly.
Dynamic tidal theory
According to the approach of George Biddell Airy , which was further developed by Henri Poincaré , Joseph Proudman and Arthur Doodson , the tides essentially arise from the horizontal component of the tidal acceleration, especially in the deep ocean. Although the currents cover the entire depth, they are shallow water waves , because the wavelength is much greater than the water depth. Then the speed of propagation of the waves is only determined by the depth of the water. Their period is determined by that of the tidal forces. Propagation speed and period together result in a typical node distance of around 5000 kilometers in standing waves in the oceans, see picture. The level fluctuation amplitude is low in the nodes and the flow velocity is high. As a result of the Coriolis force , circular to elliptical movements arise around the nodes ( amphidromy ). In the shelf seas, the wavelength is shorter because of the shallower water depth. In the North Sea, which is small relative to the oceans, there are three amphidromic points alone.
Ebb and flow on the coasts of the oceans
The amplitudes of the tidal waves are significantly higher than in the otherwise deep oceans due to the shallower water depth of the shelves off the coast. The shallower water depth means that the waves have a slower propagation speed, which leads to a rise in the water level. In bays and estuaries of rivers, the reduction in cross-section causes a further deceleration and increase in the wave amplitude. Particularly large tidal ranges always occur at such locations. Often, purely topographically favored resonance peaks are added, such as in Fundy Bay , which has the world's highest tidal range. It is just long enough that the returning wave outside the bay adds up to a new mountain of water that has just arrived there.
The tidal range is small on steep coasts with great water depths because the wave propagation is not slowed down in contrast to a coast with offshore islands.
"The cause of the tides is astronomical, but the ocean's reaction to it is geographical."
The tides are subject to a large number of individual time dependencies, which have essentially astronomical causes. The location dependency is great because of the diverse shape of the coast and the offshore seabed, but it can be explained with the help of a few topographical parameters that can in principle be described. However, tide forecasts are generally not made for larger stretches of coastline, but usually only for one location, e.g. B. a port.
The apparent orbital period of the moon and the period of the moon phases are around 24 hours and 53 minutes and around 29½ days, respectively, mean values from both short-term and long-term clearly variable values. By means of a harmonic analysis of the actual tides, additional small parts with different periods were made visible separately. The later Lord Kelvin built the first tide calculator as early as 1872/76 , with the help of which ten different oscillation processes were put together to simulate the long-term course of the tides in the Thames ( harmonic synthesis ). Today's tide calculations put together around a hundred partial oscillations, the astronomical background of which is mostly, but not always, known.
Short-term effects: about ½ day
Because the earth's axis is not perpendicular to the orbit of the earth and the lunar orbit, two consecutive tides in a location away from the equator do not have the same tidal range. During the high tide, the place is in places where the tidal forces are not equally great.
Medium-term effects: around ½ month and ½ year
Because of the change in the position of the moon relative to the sun (moon phases), the resultant of the tidal forces caused by the moon and sun fluctuates, which leads to the roughly half-monthly period of the tidal amplitude: spring and nipptides.
When the tidal range rises from day to day up to the spring tide, the tides follow each other at shorter intervals than when they descend to the nipp tide. The level changes that occur in the oceans advance faster than the less high waves over the shelves.
In the six-month rhythm of the equinoxes , the sun and almost also the moon are perpendicular to the earth's axis. The tidal forces then have the greatest effect over the earth as a whole.
Long-term effects: around 4½ and 9¼ years
The roughly elliptical lunar orbit rotates 360 ° in its plane every 8.65 years. At a certain point of the orbit with the same position of the orbit, a full or new moon is again after about 4½ years and has the same distance from the earth. The effect of the different distance on the tidal range is small, but recognizable as an effect with a period of about 4½ years in long-term comparisons - for example the already extreme spring tides on or near equinoxes.
The orbit of the moon around the earth and the orbit of the earth around the sun intersect at an angle of about 5 °. The cutting line ( knot line ) rotates 360 ° once every 18.6 years. If the moon is in one of the two nodes, is full or new moon at the same time and spring tides take place, the tidal range is slightly higher in this rhythm of about 9¼ years. The cause is the exact same direction of the tidal forces caused by the moon and the sun.
Tide calculations are used to make predictions about the temporal course of the tides and the heights of high and low water . They are primarily of importance for coastal shipping, which is subject to restrictions when the water depth is too shallow . The tidal currents can speed up or slow down navigation. The prediction of the point in time at which it changes direction (capsizing point) is of particular importance . For navigation in estuaries, predictions about the tidal wave that runs upstream at high tide are of particular importance.
Near the coast, the tides are significantly influenced by the geometric shape of the coasts. This applies to both the tidal range and the time when high and low tides occur. The time difference between high tide and the highest point of the moon, which remains approximately constant for each location, is called port time, tidal or high tide interval . In the North Sea z. B. The ebb and flow of the tide run around in a circular wave, so that there are pairs of places on the North Sea coasts where one is currently high tide when the other is low tide. The tidal range not only differs between different regions; it is lower on offshore islands and capes than on the mainland coast, in bays and estuaries sometimes higher than on the front coast.
The tidal range is often greater on the coasts of the world's oceans than on the open sea. This applies in particular to funnel-shaped coastlines. At high tide, the sea sloshes to the coast, so to speak. The tidal range in the western Baltic Sea is only about 30 centimeters, on the German North Sea coast about one to two meters. In estuaries (mouths) of the tidal rivers, for example the Elbe and Weser , the tidal range is up to four meters due to the funnel effect in these sections, also known as tidal flow . The tidal range is even higher at St. Malo in France or in the Severn estuary between Wales and England . He can reach over eight meters there. The Bay of Fundy has the world's highest tides at 14 to 21 meters.
The increase in the height of the tidal wave on the coast follows roughly the same principle as in a tsunami . The speed of the tidal wave decreases in shallow water and the height of the wave increases. In contrast to the tsunami, the tidal wave is not the result of a single impulse , but contains a portion that is constantly re-excited by the tidal force.
The ocean vibrations excited by the tides on the high seas on the coasts can also lead to vibration nodes at which no tidal range occurs at all ( amphidromy ). In a sense, ebb and flow rotate around such nodes. If there is an ebb tide on one side, there is a high tide on the opposite side. This phenomenon is mainly found in secondary seas, such as the North Sea , which has three such nodes (see the related illustration in the article amphidromy ). The tidal response of the Bay of Fundy is particularly outstanding .
Selected tidal strokes around the North Sea
|Tidal range [ m ]||Max. Tidal range [m]||place||location|
|2.01-3.76||4.69||Aberdeen||Mouth of the Dee River in Scotland|
|2.38-4.61||5.65||North Shields||Mouth of the Tyne - estuary|
|2.31-6.04||8.20||Kingston upon Hull||North side of the Humber Estuary|
|1.75-4.33||7.14||Grimsby||South side of the Humber Estuary further seaward|
|1.98 - 6.84||6.90||Skegness||Lincolnshire coast north of The Wash estuary|
|1.92-6.47||7.26||King's Lynn||The Great Ouse flows into the Wash estuary|
|2.54 - 7.23||Hunstanton||Eastern corner of The Wash estuary|
|2.34-3.70||4.47||Harwich||East Anglian coast north of the Thames estuary|
|4.05 - 6.62||7.99||London Bridge||up on the Thames - estuary|
|2.38-6.85||6.92||Dunkerque (Dunkirk)||Dune coast east of the Dover Strait|
|2.02-5.53||5.59||Zeebrugge||Dune coast west of the Rhine-Maas-Scheldt Delta|
|3.24-4.96||6.09||Antwerp||up in the southernmost estuary of the Rhine-Maas-Scheldt Delta|
|1.48-1.90||2.35||Rotterdam||Border area of the Aestu delta and the classic delta|
|1.10 - 2.03||2.52||Katwijk||Mouth of the Uitwateringskanaals des Oude Rijn into the North Sea|
|1.15 - 1.72||2.15||The hero .||Northern end of the Dutch dune coast west of the IJsselmeer|
|1.67-2.20||2.65||Harlingen||east of the IJsselmeer , into which the IJssel arm of the Rhine flows|
|1.80-2.69||3.54||Borkum||Island in front of the Ems estuary|
|2.96-3.71||4.38||Emden sea lock||at the mouth of the Ems|
|2.66-4.01||4.74||Bremerhaven||at the mouth of the Weser|
|3.59-4.62||5.26||Bremen- Oslebshausen||Bremen industrial seaports up in the Weser estuary|
|3.3-4.0||Bremen Weser Weir||artificial tidal limit of the Weser|
|2.54-3.48||4.63||Cuxhaven||at the mouth of the Elbe|
|3.4-3.9||4.63||Hamburg St. Pauli||Hamburg Landungsbrücken , up on the Elbe estuary|
|1.39 - 2.03||2.74||Westerland||Sylt island off the North Frisian coast|
|2.8-3.4||Dagebüll||Coast of the Wadden Sea in North Friesland|
|1.1-2.1||2.17||Esbjerg||North end of the wadden coast in Denmark|
|0.5-1.1||Hvide Sands||Danish dune coast, entrance to the Ringkøbing Fjord lagoon|
|0.3-0.5||Thyboron||Danish dune coast, entrance to the lagoon Nissum Bredning|
|0.2-0.4||Hirtshals||Skagerrak , same strokes as Hanstholm and Skagen|
|0.14-0.30||0.26||Tregde||Skagerrak , southern Norway , east of an amphidromic center|
|0.25-0.60||0.65||Stavanger||north of the amphidrome center|
Effect in rivers
With the dredging of fairways for shipping traffic, the high tidal range of the estuary extends far upstream in the estuaries, where it already decreased significantly earlier (see Elbe deepening and Weser correction ). Upstream the tidal range is nowadays limited in many places by weirs , which at the same time act as barrages in the incoming rivers can guarantee a minimum water level for shipping (e.g. Richmond Lock in the Thames ), but are also partially suitable for the use of hydropower (see studies for the Thames and the existing Weser power station in Bremen ).
The mouth of the Thames with its relatively high tidal range is a classic example of how , with very strong tidal currents, the erosion is so strong and the sedimentation so low that an estuary is formed. In the Rhine-Maas-Scheldt Delta , sedimentation and erosion have worked together for thousands of years. The sedimentation caused the flowing rivers to silt up and break out into new beds, creating a multitude of estuaries. Between Antwerp and Rotterdam , where the tidal range is great, the tidal regime pendulums have streams these estuaries widened to estuaries. On the flat coast east of the Dutch dune belt, storm surges penetrated far into the country from the early 12th to the early 16th century and washed out the Zuiderzee from the mouth of the easternmost arm of the Rhine, the IJssel , the Dollart at the mouth of the Ems and even further east Jade Bay . Between this and the estuary of the Weser was from the early 14th to the early 16th century, a Weser Delta from estuaries and flood channels that the delta in Zeeland was similar.
- SWR Kinderetz: The tides: ebb and flow
- Federal Institute for Hydraulic Engineering: Tide formation and phenomena on YouTube
- How do the tides arise? on YouTube
- How do ebb and flow arise on YouTube
- Kika: Dandelion: Peter is looking for the Wadden Sea, from 10:00 on YouTube
- ARD: Know before eight: Ranga Yogeshwar: How do ebb and flow occur? on YouTube
- Broadcast with the mouse: Ebbe und Flut, 1980 on YouTube
- Wolfgang Glebe: Ebb and flow: the natural phenomenon of the tides simply explained. Delius Klasing, Bielefeld 2010, ISBN 978-3-7688-3193-2 .
- Werner Kumm: tidal science. 2nd Edition. Delius Klasing, Bielefeld 1996, ISBN 3-87412-141-0 .
- Andreas Malcherek: Tides and waves - The hydromechanics of the coastal waters. Vieweg + Teubner, Wiesbaden 2010, ISBN 978-3-8348-0787-8 .
- Günther Sager : Man and tides: interactions in two millennia. Deubner, Cologne 1988, ISBN 3-7614-1071-9 .
- Jean-Claude Stotzer: The representation of the tides on old maps. In: Cartographica Helvetica. Issue 24, 2001, pp. 29-35, (full text) .
- John M. Dow: Ocean tides and tectonic plate motions from Lageos. Beck, Munich 1988, ISBN 3-7696-9392-2 (English).
- Bruce B. Parker: Tidal hydrodynamics. Wiley, New York NY 1991, ISBN 0-471-51498-5 (English).
- Paul Melchior: The tides of the planet earth. Pergamon Press, Oxford 1978, ISBN 0-08-022047-9 (English).
- David E. Cartwright: Tides - a scientific history. Cambridge Univ. Press, Cambridge 1999, ISBN 0-521-62145-3 (English).
- Federal Maritime and Hydrographic Agency: Obtaining tide data and online forecast
- Federal Maritime and Hydrographic Agency: Topic page of the tide service (including definitions of terms)
- Interactive animations to explain the origins of ebb and flow.
- Physical explanation of the tides at WeltDerPhysik.de.
- Tide tables worldwide
- Interactive tide simulation
References and comments
- Günther Sager: Tides and Shipping. Leipzig 1958, p. 59.
- The stimulation of a spring tide is about -fold stronger than that of a nip tide , Andreas Malcherek: Tides and waves - The hydromechanics of coastal waters in the Google book search
- Level selection via map. At: pegelonline.wsv.de.
- Martin Ekman: A concise history of the theories of tides, precession-nutation and polar motion (from antiquity to 1950). In: Surveys in Geophysics. 6/1993, Volume 14, pp. 585-617.
Gudrun Wolfschmidt (Ed.): Navigare necesse est - History of Navigation: Book accompanying the 2008/09 exhibition in Hamburg and Nuremberg. norderstedt 2008, limited preview in the Google book search.
Jack Hardisty: The Analysis of Tidal Stream Power. 2009 limited preview in Google Book search.
- David Edgar Cartwright: Tides: A Scientific History. Cambridge 1999, limited preview in Google Book search.
- Georgia L. Irby-Massie, Paul T. Keyser: Greek Science of the Hellenistic Era: A Sourcebook. limited preview in Google Book search.
- Lucio Russo: The forgotten revolution or the rebirth of ancient knowledge. Translated from the Italian by Bärbel Deninger, Springer 2005, ISBN 978-3-540-20938-6 , limited preview in the Google book search.
- Jacopo Dondi (dall'Orologio): De fluxu et refluxu maris. Edited in 1912 by P. Revelli.
- David T. Pugh: Tides, surges and mean sea-level . John Wiley & Sons, 1996, p. 3 .
- On various theories before Newton see also Carla Rita Palmerino, JMMH Thijssen (ed.): The Reception of the Galilean Science of Motion in Seventeenth-Century Europe. Dordrecht (NL) 2004, p. 200 ( limited preview in Google book search).
- Robert Stewart: Introduction to Physical Oceanography . Orange Grove Texts Plus, 2009, pp. 302 ( online [PDF; accessed October 19, 2019]). Stewart writes: “ Note that many oceanographic books state that the tide is produced by two processes: i) the centripetal acceleration at earth's surface as the earth and moon circle around a common center of mass, and ii) the gravitational attraction of mass on earth and the moon. However, the derivation of the tidal [force] does not involve centripetal acceleration, and the concept is not used by the astronomical or geodetic communities. "
- The center defined in this way would be its geometric center for an exactly spherically symmetrical earth, see Newton's shell theorem .
- Andreas Malcherek: Tides and waves: The hydromechanics of coastal waters. Vieweg + Teubner Verlag, ISBN 978-3-8348-0787-8 , p. 25.
- Günther Sager: Tides and Shipping. Leipzig 1958, p. 61.
- Quote from: Wolfgang Glebe: Ebbe und Flut - The natural phenomenon of the tides simply explained. Delius Klasing Verlag, 2010, ISBN 978-3-7688-3193-2 , p. 81.
- World of Physics: The Forces of the Tides. Section: How the Earth's Slope Distorts Ebb and Flow.
- Wolfgang Glebe: Ebbe and Flood. The natural phenomenon of the tides simply explained. Delius Klasing, Bielefeld 2010, ISBN 978-3-7688-3193-2 , pp. 67-70.
- World of Physics: What Jumps in the Spring Tide? ( Memento of December 27, 2011 in the Internet Archive ).
- Wolfgang Glebe: Ebbe and Flood. The natural phenomenon of the tides simply explained. Pp. 43-47.
- If it is noted that due to the small difference in tidal forces between two spring tides or two nipp tides these are not exactly the same, the period changes to one lunar revolution.
- Wolfgang Glebe: Ebbe and Flood. The natural phenomenon of the tides simply explained. Pp. 61-66.
- This bimonthly repeating distortion in the tide calendar is superimposed by a smaller, monthly repeating distortion that is caused by the varying moon speed on its roughly elliptical orbit. The variation of the moon's distance from the earth also leads to small monthly fluctuations in the tidal range.
- Wolfgang Glebe: Ebbe and Flood. The natural phenomenon of the tides simply explained. Pp. 50-54.
- The half-day fluctuation of successive tides is then canceled.
- Wolfgang Glebe: Ebbe and Flood. The natural phenomenon of the tides simply explained. P. 71 f.
- These are also the positions for a lunar or solar eclipse .
- Wolfgang Glebe: Ebbe and Flood. The natural phenomenon of the tides simply explained. Pp. 73-78.
- Warning! With this information, it is not possible to understand the period in which these data were determined
- tide tables for Lerwick: tide-forecast.com
- Tide table for Aberdeen: tide-forecast.com
- Tide table for North Shields: tide-forecast.com
- Tide tables for Kingston upon Hull: tide-forecast.com
- tide tables for Grimsby: tide-forecast.com
- Tide tables for Skegness: tide-forecast.com
- Jump up Tide tables for King's Lynn: tide-forecast.com
- Tide table for Harwich
- Tide table for London
- Tide tables for Dunkerque: MobileGeographics.com and tide-forecast.com
- Tide tables for Zeebrugge: MobileGeographics.com and tide-forecast.com
- Tide table for Antwerp
- Tide table for Rotterdam
- F. Ahnert: Introduction to Geomorphology. 4th edition. 2009.
- Tide table for Katwijk
- Tide table for Den Helder
- Tide table for Harlingen
- Tide table for Borkum
- Tide table for Emden
- Tide table for Wilhelmshaven
- Tide table for Bremerhaven
- Tide table for Bremen-Oslebshausen
- BSH tide table for Bremen Weserwehr ( memento of the original from February 17, 2014 in the web archive archive.today ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.
- Tide table for Cuxhaven
- Tide table for Hamburg
- Tide table for Westerland (Sylt)
- BSH tide table for Dagebüll ( memento of the original from February 23, 2014 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.
- Danmarks Meteorologiske Institut: Tidal Tables ( Memento of the original from March 16, 2014 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
- Tide table for Esbjerg: tide-forecast.com
- Vannstand - official Norwegian water level information → English language edition. ( Memento from July 20, 2010 in the Internet Archive ).
- From Idea To Reality . Ham Hydro. Retrieved December 19, 2019., English