topic 3a notes tides

5/20/2018 Topic 3a Notes Tides

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ENM 215; The Oceans, Operability and Humans in the Ocean Topic 3a Tides

PgDip/MSc Energy Program

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In this section the causes of the tides and the factors which affect theirmagnitude are discussed. The three main types of tidal pattern and thelocations in the world where they occur are described. Tidal phenomenaobservable in coastal regions and the generation of power from the tidesare also discussed.

After studying the materials in this section you should be able to:

Describe what causes tides Differentiate between a lunar and solar day Understand why the moon has a greater influence on the tides

than the sun Explain the monthly tidal cycle in terms of Earth-Moon-Sun

positions and the resulting tidal conditions on earth Know how variations in the orbit of the Earth and the Moon cause

changes to the tidal forces Recognize diurnal, semidiurnal and mixed tidal patterns Describe tidal phenomena which can be observed in coastal

regions

Why is a knowledge of tides important? Your answer should consider theeffects on shipping, offshore structures and offshore operations.

1. Explain why the Suns influence on Earths tides is only 46% ofthat of the Moon, even though the Sun is much more massivethan the Moon. (3 marks)

2. What is declination? Discuss the degree of declination of the Moonand Sun relative to Earths equator. What are the effects ofdeclination of the Moon and sun on the tides? (5 marks)

3. How often are the conditions right to produce the maximum tide-generating force and what are these conditions? (3 marks)

Preview

Topic 3a: Tides

Learning Outcomes

Student Activities: Critical Thinking Exercise

Student Activities: Sample Exam Questions


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4. What factors cause the tides which actually occur in the oceans todiffer from the idealized case in which the rise and fall of the tidesis caused by the Earths rotation carrying various locations intoand out of the tidal bulges? (10 marks)

5. Describe, with the aid of diagrams, a diurnal tidal pattern. Where

does this pattern occur? (4 marks)

Important Note: The following pages are summary notes takendirectly from the material in your text book Essentials ofOceanography. They are intended to provide an overview of therelevant aspects that it is important to understand for the purpose ofthis course. For a full and detailed understanding of the topic please

always refer to your text book.

Introduction ................................................................................... 2What Causes the Tides? .................................................................. 2

The Earth-Moon system ................................................................ 3

Gravitational forces in the Earth-Moon System ................................ 3

Centripetal Forces in the Earth-Moon System .................................. 4

Resultant Forces .......................................................................... 4

The Effect of the Sun on Tides ....................................................... 6

How Do Tides Vary During a Monthly Tidal Cycle? ............................... 7Other factors which influence tides................................................. 8

What Do Tides Really Look Like in the Ocean? .................................. 10What Types of Tidal Patterns Exist? .............................................. 11

Tidal Phenomena in Coastal Regions ............................................... 12

Tidal Power .................................................................................. 13

Tides are the periodic raising and lowering of the sea level that occursdaily throughout the ocean. Tides are very long and regular shallowwater waves with wavelengths of thousands of kilometres and heightswhich range to more than 15 m.

Tides are generated by forces imposed on Earth that are caused by acombination of gravity and motion among Earth, the Moon and the Sun.The effect of the moon on the tide is much greater than the effect of the

sun so in the initial explanation of what causes tides, the influence of thesun will be ignored.

Content


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Instead of Moon orbiting the Earth, the Moon and Earth actually rotatearound a common centre of mass. This Centre of mass is called theBarycentre and it is located 1600 km below the Earths surface. TheBarycentre is located there, rather than halfway between the Earth and

the Sun because the mass of the Earth is much greater than that of theMoon.

Newtons law of universal gravitation states that every object that hasmass in the universe is attracted to every other object. The gravitationalforce is directly proportional to the product of the masses of the twobodies and is inversely proportional to the square of the distancebetween the two bodies. If the mass increases, the gravitational force

increases. If the distance increases the gravitational force greatlydecreases. The gravitational force varies with the square of the distancebetween the bodies so even a small increase in the distance betweentwo objects causes a significant decrease in the gravitational force. Thismeans that the gravitational force at different points on Earth vary,depending on their distance from the moon. The greatest gravitationalforce occurs at the zenith which is the point nearest to the moon. Thenadir is the point farthest from the moon and the gravitational attractionis weakest here. Figure 9.3 shows the direction and relative magnitudeof the gravitational forces acting at a particle of mass at various pointson the Earths surface.

FIGURE 9.3 Gravitational Forces on Earth Due to the Moon.Thegravitational forces on object located at different places on Earth dueto the Moon are shown by arrow. The length and orientation of thearrows indicate the strength and direction of the gravitational force.Notice the length and angular differences of the arrows for differentpoints on Earth. The letter Zrepresents the zenith; Nrepresents thenadir. Distance between the Earth and Moon not shown to scale.


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Newtons first law of motion states that a body will remain at rest ormoving at a constant velocity unless it is acted on by an externalunbalanced force. This means that a force needs to act on a body in

order to make it move in a circular path. This force is called thecentripetal force and it acts inwards towards the centre of the circle. Thecentripetal force which holds the moon in its orbit around the Earth iscaused by gravity. Figure 9.4 shows the direction and relative magnitudeof the centripetal forces which act on a particle of mass at various pointson the Earths surface as a result of the Earth-Moon system rotatingabout its barycentre.

FIGURE 9.4 Required centripetal (centre-seeking) forces.Centripetal forces required to keep identical-sized particles inidentical-sized orbits as a result of the rotation of the Earth-Moonsystem about its barycentre. Notice that the arrows are all the samelength and are oriented in the same direction for all points on Earth.Z= zenith; N= nadir.

The gravitational attraction between the a particle of mass on theEarths surface and the moon supplies the centripetal force required tokeep the Earth-Moon system rotating about its barycentre, but the forcesupplied is not equal to the force required. At every point except at thecentre of the Earth there is a difference between the supplied force andthe required force. This force is called the resultant force. The resultantforces are tiny, averaging about one millionth the magnitude of theEarths gravity. Figure 9.5 shows the direction and relative magnitude of

the resultant forces at different points on the Earths surface.


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FIGURE 9.5 Resultant forces. Red arrows indicate centripetalforces (C), which are not equal to the black arrows that indicategravitational attraction (G). The small blue arrows show resultantforces, which are established by constructing n arrow from the tip ofthe centripetal (red) arrow to the tip of the gravity (black) arrow andare located where the red and black arrows begin. Z= zenith; N=nadir. Distance between Earth and Moon not shown to Scale.

If the resultant force is perpendicular to the Earths surface it does nothave a tide generating effect. The resultant force is perpendicular to theEarths surface at the zenith and nadir and along an equator half waybetween the zenith and nadir. The components of the resultant forceswhich act tangential to the Earths surface are known as tide generatingforces. Tide generating forces are maximum at a latitude of 45orelative to the equator between the zenith and Nadir. The tidegenerating forces push the water in the oceans into two bulges: one onthe side of the Earth directed towards the moon and the other on theside directed away from the moon. On the side facing the moon thebulge is created because the provided gravitational force is greater than

the required centripetal force. On the side of the Earth facing away fromthe moon the bulge is created because the required centripetal force isgreater than the supplied gravitational force. The resultant forces on thetwo sides of the Earth are orientated in opposite directions but are equalin magnitude, so the bulges are equal in size. Figure 9.7 shows the tidalbulges for an idealised case in which the ocean has a uniform depth andthere is no friction between the sea water and the sea floor.


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FIGURE 9.7 Idealized tidal bulges. In an idealized case, the Mooncreates two bulges in the ocean surface: one that extends toward theMoon and the other away from the Moon. As the Earth rotates, itcarries various locations into and out of the two tidal bulges so thatall points on its surface (except the poles) experience two high tidesdaily.

The tidal period is the time between high tides. In most places on Earththe tidal period is 12 hours and 25 minutes. This is because tidesdepend on the lunar day and not the solar day. The lunar day ismeasured from the time that the moon is on the meridian of an observer(directly overhead) to the next time the Moon is on that meridian. Alunar day is exactly 24 hours, 50 minutes and 28 seconds long. A solarday is measured from the time the Sun is on the Meridian of an observerto the next time the Sun in on that Meridian and is 24 hours long.

Like the moon, the sun also produces tidal bulges: one oriented towardsthe sun and one on the opposite side of the Earth. Solar bulges aremuch smaller than lunar bulges because, although the sun is 27 milliontimes more massive than moon, it is 390 times further from the Earththan the Moon. The solar bulges are only 46% of the size of the lunarbulges.


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The Moon takes 29 days to complete an orbit around the Earth. This isthe length of the monthly tidal cycle. At new moon and full moon the

Moon is aligned with the Sun. In these positions the tide generatingforces of the moon and sun combine and the tidal range (the verticaldifference between high tide and low tide) is large. The maximum tidalrange is called a spring tide. When the Earth-Moon-Sun system isaligned, the Moon is said to be in syzygy. At first-quarter moon andthird-quarter moon the Moon is at right angles to the Sun relative to theEarth. In these positions the tide generating force of the Sun is workingat right angles to the tide generating force of the Moon so there isdestructive interference between the lunar and solar tidal bulges so thetidal range is small. This is called a neap tide and the Moon is said to bein quadrature. This is shown in Figure 9.10.

FIGURE 9.10 Earth-Moon-Sun positions and the tides. Top:When the Moon is in the new or full position, the tidal bulge createdby the Sun and Moon are aligned, there is a large tidal range onEarth, and spring tides are experienced. Bottom: When the Moon is inthe first- or third-quarter position, the tidal bulges produced by themoon are at right angles to the bulges created by the Sun. Tidalranges are smaller and neap tides are experienced. Note that there isonly one moon in orbit around Earth.

The time between successive spring tides or successive neap tides is onehalf of the monthly lunar cycle (about 2 weeks). The time between a


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spring tide and the next neap tide is a quarter of the monthly lunar cycle(about a week).

There are a number of other factors which influence the tides. Two ofthe most significant are the declination of the Moon and Sun and theelliptical shape of the orbits of the Earth and Moon.

The moon and sun are typically not directly overhead at the equator.The angular distance of the Sun or Moon above or below the equatorialplane is called declination. The declination of the sun and moon meanthat the tidal bulges are rarely aligned with the equator and insteadmostly occur north or south of the equator. This is shown by Figure9.12.

Figure 9.12 Maximum declination of tidal bulges from theequator. The centre of the tidal bulges may lie at any latitude fromthe equator to a maximum of 28.5 degrees on either side of theequator depending on the season of the year (solar angle) and theMoons position.

The declination of the moon determines the position of the tidal bulges.

This means that, for idealised tides, at some locations the height ofsuccessive high tides will differ. This is shown by Figure 9.14.

The Earth revolves around the Sun in an elliptical orbit so the distancebetween the Earth and the Sun varies over the course of a year. Tidalranges are largest when the Earth is near its closest point (perihelion).Tidal range are smallest when the Earth is near its most distant point(aphelion). The moon also revolves around the Earth in an ellipticalorbit. Tidal ranges are largest when the moon is closest to the Earth(perigee) and smallest when the moon is furthest from the Earth(apogee). It takes 27.5 days for the the Moon to cycle between perigee,

apogee and back to perigee. Spring tides coincide with perigee everyone and a half years. This is called proxigean and during this time the


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tidal range is especially large. These effects of elliptical orbit are shownin Figure 9.13.

FIGURE 9.14 Predicted Idealized tides. (a)-(d) Sequenceshowing the tide experienced every 6 lunar hours. at 28 degreesnorth latitude when the declination of the moon is 28 degrees north.(e) Tide curves for 28 degrees north, 0 degrees and 28 degrees southlatitudes during the lunar day shown in the sequence above. The tidalcurves for 28 degrees north and 28 degrees south latitude show thatthe higher high tides occur 12 hours later.

FIGURE 9.13 Effects of elliptical orbits. Top: The Moon movesfrom its most distant point (apogee) to its closest point to Earth(perigee), which causes greater tidal ranges every 27 days.Bottom: The Earth also moves from its most distant point (aphelion)to its closest point (perihelion), which causes greater tidal rangesevery year in January. Diagram is not to scale (the elliptical orbits arehighly exaggerated).


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Tides are shallow water waves so their speed is proportional to the waterdepth. Based on the average ocean depth, the average speed with whichtide waves can travel is slower than the speed the idealised tidal bulgesmove across the earth. Thus the idealised bulges cannot exist. Instead

ocean tides break up into distinct large circulation units called cells.

Near the centre of each cell is an amphidromic point and, in the openocean, the crests and troughs of the tide wave rotate around this point.At the amphidromic point there is effectively no tidal range. Radiatingfrom the amphidromic points are cotidal lines which connect all nearbylocations at which the high tide occurs simultaneously. Figure 9.15shows the positions of the amphidromic point and cotidal lines. The tidewave rotates anticlockwise in the northern hemisphere and clockwise inthe southern hemisphere. The size of the cells is limited a the wavemust complete one rotation during the tidal period.

FIGURE 9.15 Cotidal map of the world. Cotidal lines indicatetimes of the main lunar daily high tide in lunar hours after the Moonhas crossed the Greenwich Meridian (0 degrees longitude). Tidal

ranges generally increase with increasing distance along cotidal linesaway from the amphidromic points (centre of cell). Where cotidallines terminate at both ends in ampidromic points, maximum tidalrange will be near the mid-points of the lines.

The continents also affect the tides because they interrupt the freemovement of the tidal bulges across the ocean surface. Two of the mostimportant factors that affect tidal conditions along a coast are theoffshore water depth and the coastline shape. In the deep ocean thetidal range is only about 45cm. As they move into shallow water the tide

waves undergo changes which tend to increase the tidal range.


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The depths, sizes and shapes of the ocean basins modify tides so thatthey exhibit three different patterns. These patterns and the placeswhere they occur are shown in Figure 9.16.

FIGURE 9.16 Tidal patterns.Map showing worldwide tidal patterns.A dirunal tidal pattern (top graph) shows one high and low tide eachlunar day. A semidirunal pattern (middle graph) shows two highs andlows of approximatley equal heights during each lunar day. A mixedtidal pattern (bottom graph) shows two highs and lows of unequalheights during each lunar day.

A diurnal tidal pattern has one low and one high tide each lunar day.Diurnal tidal patterns are common in shallow inland seas such as theGulf of Mexico and along the coast of South East Asia. Diurnal tides havea tidal period of 24 hours 50 minutes.

A semidiurnal pattern has two high and low tides a lunar day and so hasa tidal period of 12 hours 25 minutes. The heights of the successive hightides and successive low tides are approximately the same. Semi diurnaltides are common along the Atlantic Coast of the United States.

A mixed tidal pattern may have characteristics of both diurnal andsemidiurnal tides. Successive high tides and/or low tides havesignificantly different heights. Typically mixed tides have a period of 12


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hours 25 minutes but they may also exhibit diurnal periods. Mixed tidalpatterns are the most common type of tidal pattern and are found inmany places including the pacific coast of North America.

Monthly tidal curves for a number of locations are shown in Figure 9.17.

FIGURE 9.17 Monthly tidal curves. Top:Boston, Massachusetts,showing a semidiurnal tidal pattern. Upper middle: San Francisco,California, showing a mixed tidal pattern. Lower middle: Galveston,Texas, showing a mixed tidal pattern with strong diurnal tendencies.Bottom:Pakhoi, China, showing a diurnal tidal pattern.

A tidal bore is a wall of water that moves up certain low-lying rivers dueto an incoming tide. The conditions necessary for a tidal bore to developinclude:

a large spring tide range of at least 6m a tidal cycle that has a very abrupt rise of the flood tide phase and

an elongated ebb tide phase a low lying river with a persistent seaward current during the time

when an incoming high tide begins

a progressive shallowing of the sea floor as the basin progressesinland

a progressive narrowing of the basin toward its upper reaches


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Only about 60 places on Earth experience tidal bores. These include theAmazon River, the Qinatng River in China, the Peticodiac River inCanada, the River Seine in France and the Trent ad Severn Rivers in theUK.

The tides produce reversing currents which move into and out of

restricted passages along a coast. A flood current is produced whenwater rushes into a bay or river with an incoming high tide. An Ebbcurrent occurs when water drains out of a bay or river because a lowtide is approaching. At the peak of each high or low tide no currentsoccur for several minutes. This time is called slack water. In some areasthese currents can be very fast, reaching speed of 40km/hour.

Whirlpools are rapidly spinning bodies of water. These can be created bythe reversing currents in restricted coastal passages. They mostcommonly occur in shallow passages connecting large bodies of waterwith different tidal cycles. The difference in surface elevation between

the ends of the passage causes water to move vigorously along thepassage. The shape of the shallow sea floor affects the flow and causesturbulence and this, along with the spin caused by the opposing tidalcurrents, creates whirlpools. The size of the whirlpool increases as thetidal difference between the two bodies of water increases and as thesize of the passage decreases. Examples of whirlpools include theMaelstrom in Norway, The Corryvreckan in Scotland and the whirlpool inthe strait of Messina, Italy.

Concerns about climate change and security of energy supply have ledto a growing interest in the generation of energy from renewablesources. Of the renewable energy sources, tidal power is unique sincethe movement of the tides is predictable decades in advance. This is amajor advantage over wind power which can only be predicted a fewhours in advance and wave power which can only be predicted a fewdays in advance. The energy can be extracted from the tides in twoways: by exploiting the potential energy of the water due to the changein elevation or by exploiting the kinetic energy of the currents generatedby the tides.

A number of tidal barrage schemes which generate power by trappingwater in a bay or estuary at high tide and releasing the water throughturbines have been built worldwide. The scope for building more powerplants of this type is not great because they require sites where the tidalrange is very large. There are also concerns about the environmentalimpact of tidal barrage schemes.

Tidal current power schemes are thought to be more environmentallybenign that tidal barrage schemes. The tidal current energy industry isat an early stage of development. A large number of devices which couldbe used to extract energy from tidal currents have been proposed butonly a few have progressed past laboratory scale model tests to anadvanced demonstration stage.


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Whilst tidal power is predictable a long time in advance, it does notproduce power on demand. The amount of power available varies overthe course of the daily and monthly tidal cycles. At some times in thetidal cycle no energy will be available as there will either not besufficient tidal range or sufficient tidal current speeds to drive thegenerators. The spring-neap cycle also affects the amount of power that

can be generated at a given time.

The tides are caused by an imbalance between the required centripetaland the provided gravitational forces acting on Earth. This differenceproduces residual forces, the horizontal component of which pushesocean water into two equal tidal bulges on opposite sides of Earth. Thetides depend on a lunar day rather than a solar day. A lunar day is 24

hours, 50 minutes and 28 seconds long. The tidal bulges caused by themoon are about twice the size of the those caused by the sun. In anidealized cast h tides are caused by Earths rotation carrying variouslocations into an out of the tidal bulges. Spring tides occur during the fulland new moon, when the lunar and solar tidal bulges constructivelyinterfere, producing a large tidal range. Neap tides occur during thequarter moon phases, when the lunar and solar tidal bulges destructivelyinterfere, producing a small tidal range. The depths, sizes and shapes ofthe ocean basins modify tides so that they exhibit three differentpatterns. These are diurnal, semidiurnal and mixed. Tidal phenomenaoccurring in coastal regions include tidal bores, whirlpools and tidalcurrents. Power can be generated from the tides.

Summary

topic 3a notes tides

Documents

tidal forces

notes tides

earths tides

causes tides

earthmoon system

tidal phenomena

tidal bulges

diurnal tidal pattern