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M Ehsan Saeed

Subject-13

Tides

Periods: 6

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diurnal of, relating to, occurring, or performed in a 24-hour period; once daily

semi-diurnal of, relating to, occurring, or performed during half a day; twice daily

Terminology Points

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TGF Tide Generating Force

MHWS Mean High Water Springs

MHWN Mean High Water Neaps

MLWS Mean Low Water Springs

MLWN Mean Low Water Neaps

HAT Highest Astronomical Tide

LAT Lowest Astronomical Tide

CP Critical Point

P Precession

N NutationS Spin

R Rotation

Abbreviations & Acronyms

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Lecture Outline

What are Tides?

Importance of Tides

Why the Tides? Tide Generating Forces

Types of Tides

Tidal Datums

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What are Tides?

Tides are periodic rise and fall and seawater

Tides are caused by gravitational pull of the Moonand the Sun

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Importance of Tides

Dictate navigation of large ships inside harbours

Help fishing

Provide intertidal habitats for some species

Cause sedimentation of harbours from tidalcurrents, necessitating continual dredging ofnavigation channels

Provide a source of renewable energy

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Tides

Rise of Seawater

(High Tide of High Water)

Fall of Seawater

(Low Tide or Low Water)

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Tides

Rise of Seawater

(High Tide of High Water)

Fall of Seawater

(Low Tide or Low Water)

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Newtons Law of Gravitation

Tides are explained in terms of the Newtons Law

of Gravitation, which states:

Every particle of mass (M1) in the universe attractsevery other particle of mass (M2) , with a force (F)

that is proportional to the product of their massesand inversely proportional to the square of thedistance (D) between them, i.e

F = G x M1 x M2D2

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Gravitation attraction (pull) exists between Earth &Moon, and Earth & Sun

Contd

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Newtons Law of Gravitation

Where the Earths surface is fluid (seas & oceans),

gravitational forces due to Moon & Sun causes theseawater to be pulled towards them

Seawater bulges towards Moon & Sun as they

approach the meridian of a location (next diagram)

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EE

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Tide Generating Forces

SE

M

Not to scale

Bulges caused by Sun & Moon

Bulges are not only caused directly towardsMoon & Sun, but also diametrically away fromthem

To be able to understand the phenomenon of2nd bulges, one has to study the variousmovements of Earth

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Earths Movements

Earth undergoes 4 (as opposed to 2) orbital motions:

Rotates around the Sun (3651/4 days cycle)

Spins on its axis (24 hrs cycle)

Spin Axis Precesses (26,000 yrs cycle) Spin Axis Nutates (18.6 yrs cycle)

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Due to gravitational pull of Sun & Moon

Earth also rotates around the Moon !!!

Concept illustrated in the next two slides by analogywith spinning Tops

S i A i

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Precession&

Nutation

Evenly balanced Top

Spin Axis

Tilted Top

Spin

Spin

Precession

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Tilted Topwith

Off-CentredWeight

Spin

Precession

superimposed by

Nutation

Off-Centred Wt

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Earths Various Motions

S

R

Earths Precession (P) & Nutation (N), on closer examination, are in fact Earthsmovements around Moon & Sun, as a direct result of gravitational interplay

This is explained in the next few slides, by drawing analogies with an Athlete spinning a

hammer around her, and with a Sea-Saw

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Two Bodies rotating about each other

+CM

CP Hammer rotating about the Athlete,

about the CP

Athlete rotating about the Hammer,about the CP

Critical Point (CP) is the point about/around

which two bodies rotate about each other

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Two Bodies

rotating abouteach other

CP

Hammer rotating about

the Athlete, about the CP

Athlete rotating about theHammer, about the CP

T B di t ti

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Two Bodies rotating

about each other

CP

CP+ + AthleteHammer

Athlete: 80 kg, Hammer: 4.0 kg (7.3)Athlete:Hammer = 20:1

Earth:Moon = 81:1

hif i f b l

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Shifting of CP to balance Masses

CP

CP 11

31

12

14

15

1

6

To scale

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Shifting of CP towards Body of More Mass

To scale

6

5

4

3

2

1 1

1

1

1

1

1

11

3 1

12

14

15

16

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Bodies Gravitating & Rotating

& Shifting of CP

To scale

1 1

2 1

13

14

15

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i i i

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Precession Precession + Nutation

Distance of Red & Pink Bodies from Blue Not to scale

P i P i N i

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Precession Precession + Nutation

Distance of Red & Pink Bodies from Blue Not to scale

Here, Precession path of the yellow Body (due tored Body) is superimposed by Nutation under thegravitational influence of the pink Body

Nutation

If a Body (yellow) is under the gravitationalinfluence of not one but two other bodies (red &

pink), Precession path of the yellow Body issuperimposed by Nutation

CP b E h & M li ll i id E h

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CP between Earth & Moon lies well inside Earth

CP

We x d = Wm x (384,800 km d)

81 x Wm x d = Wm x (384,800 km d)

81d= 384,800 km d

d = 384,800 km/82 = 4,693 km

d

384,800 km

Wm

We

Radius of Earth = 6,340 kmd = 4,693 km

CP6,340-4,693=1,647 km below

Earths surface

6,340 km

1,647

To scale

id G i

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C

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Tide Generating Force

M

Earth precessing as ONE

All points on Earths surface under same CF

GF varies on different points on Earths surfacedue to D2 factor

GF towards M > GF at Earths Centre > GF awayfrom M

Difference in CF & GF results in PG

PG responsible for Tides

Two tidal bulges (HWs): one directly towardsM, other directly away from M

CF: Centrifugal Force

D

GF: Gravitational Force (providing Centripetal Force)

PG: Pressure Gradient

C: Centre of Earth

M: Moon

D: Earth-Moon DistanceNot to scale

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Earth-Moon Gravitation

Earth & Moon exert gravitational pull on each other

(Newtons Law of Gravitation), about the CP The gravitational pull results in:

Moon rotating around the Earth about the CP

The Earth rotating (precessing) around the Moon aboutthe CP

Moons rotation and Earths precession are circular

movements; hence the interplay of Centrifugal &

Centripetal Forces

Earth precessing as ONE

All points on Earths surface under same

Centrifugal Force (CFF)M Ehsan Saeed 26Contd

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Earth-Moon Gravitation

Centripetal Force required to balance Centrifugal

(CFF) Force (to keep Earth in orbit) provided byEarth-Moon Gravitational Force (GF)

GF varies on different points on Earths surface dueto D2 factor

GF towards Moon > GF at Earths Centre > GF awayfrom Moon

Difference in CFF & GF results in Pressure Gradient

(PG) PG responsible for Tides

Two tidal bulges (HWs): one directly towards Moon,

other directly away from MoonM Ehsan Saeed 27

Tid l C l (d t M l )

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Tidal Cycle (due to Moon alone)

Location: A

HW

HW

LW LW

HW

As Earth spins ACW, bulges (HWs) rotate CW

HW at A 50 minlater every day

S i & N Tid

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EE

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Spring & Neap Tides

SE

M

Not to scale

Tide at any point is thecombined effect of TGF ofMoon & Sun

When TGF of Moon & Sunreinforce each other, SpringTides are created i.e. tidalhighs & lows are greater

When TGF of Moon & Sunweaken each other, Neap Tidesare created i.e. tidal highs &

lows are smaller

Spring & Neap Tides dependon position of Moon & Sunrelative to each other

S i & N Tid

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E

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Spring & Neap Tides

S

E

M

Not to scale

SPRING TIDE

SPRING TIDE

SPRINGTIDE

SPRINGTIDE

New Moon

S i & N Tid

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E

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Spring & Neap Tides

S

E

Not to scale

NEAP TIDE

NEAP TIDE

NEAPTIDE

NEAPTIDE Half Moon (after 7 days)

S i & N Tid

F ll M ( ft 14 d )

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E

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Spring & Neap Tides

S

E

Not to scale

SPRING TIDE

SPRING TIDE

SPRINGTIDE

SPRINGTIDE

M Full Moon (after 14 days)

S i & N Tid

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E

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Spring & Neap Tides

S

E

Not to scale

NEAP TIDE

NEAP TIDE

NEAPTIDE

NEAPTIDE

Half Moon (after 21 days)

Spring & Neap Tides

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34

Spring & Neap Tides

S

EEE

M

S & M aligned

TGFs combine

SPRING Tides

New Moon

S

EM

S & M at 900

TGFs work indiff directions

NEAP Tides

Half Moon

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ME

S & M at 900

TGFs work indiff directions

NEAP Tides

Half Moon

S

EE

M

S & M aligned

TGFs combine

SPRING Tides

Full Moon

S

Relative Magnitude of Lunar & Solar TGFs

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Relative Magnitude of Lunar & Solar TGFs

All planets and stars exert tidal forces on Earth; only tidal forces of the Moonand the Sun are significant

TGF due Sun/Moon given by formula: F = Kx Mass of Sun/Moon(Distance from Earth)3

TGF due Moon Fm= Kx Mass of Moon(Moon-Earth Dist)3

TGF due Sun Fs= Kx Mass of Sun = K x (27,000,000 x Mass of Moon)

(Sun-Earth Dist)3 (390 x Moon-Earth Dist)3

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Kx Mass of Moon(Moon-Earth Dist)3

Kx 27,000,000 x Mass of Moon(390 x Moon-Earth Dist)3

Fm=

Fs

= 2.2

Fm= 2.2 Fs

TGF of the Moon on the Earth is more than twice (2.2 times)

that of the Sun on the Earth

Diurnal Tidal Delay

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Diurnal Tidal Delay

Earth takes 24 hrs to spin once onits axis

Moon takes 29 days to rotateonce (3600) around Earth

In 1 day (24 hrs) Moon

advances 12.40 or 49 min(Calculations on next slide)

At given location, every thinglunar delayed 49 min every 24 hrs:moonrise, moonset, tidal HWs,tidal LWs etc)

24 hrs 49 min is the Lunar Day(also referred to as the Tidal Day)

Not to scale

24 hrs29days

Day 12 pm

C l l ti

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Calculations

Moon takes 29 days to rotate once (3600) around

Earth In 1 day, Moon advances 3600/29 days = 12.40

(12.413793103448280)

To catch up on Moon, Earth has to spin an extra12.40 every 24 hrs

Earth spins 3600 in = 24 hrs

Earth spins 12.40

in = 24 hrs x 12.40

/3600

= 0.83 hrs 49 min

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Tidal Curve

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Tidal Curve

NewMoon HalfMoon HalfMoonFullMoon NewMoon

M

E

sRelativePositionso

f

S,

M&

E

SPRING SPRINGNEAP NEAP SPRING

Tide Tables

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Tide Tables

Diurnal Semi Diurnal or Mixed Semi Diurnal Tides

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Diurnal, Semi-Diurnal or Mixed Semi-Diurnal Tides

Diurnal Tides (daily tides) have one HW and one

LW in each tidal day Semi-Diurnal Tides (half-daily) have two HWs and

two LWs in each tidal day

Mixed Tides Also known as Mixed Semi-Diurnal Tides

Have two HWs and two LWs in each tidal day

But, heights of the HWs (and/or of the two LWs) in eachtidal day are different

Have a Higher HW (HHW) and Lower HW (LHW), as wellas a Higher LW (HLW) and a Lower LW (LLW), each day

Are most commonM Ehsan Saeed 40

Diurnal Semi-Diurnal or Mixed Semi-Diurnal Tides

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41

Diurnal

Semi-Diurnal

Mixed Semi-Diurnal

Tidal Day


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Global Tide Types

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Global Tide Types

Why Diurnal Semi Diurnal or Mixed Tides?

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Why Diurnal, Semi-Diurnal or Mixed Tides?

Whether a place has Diurnal, Semi-Diurnal or

Mixed Semi-Diurnal tides, depends on its locationwith respect to the Moon, measured in terms ofMoons declination

Moons orbit around the Earth continues to shiftNorth & South of the Earths Equator

Angular shift of Moons orbit, North & South oftheEarths Equator, like other heavenly bodies, is

termed Declination

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Declination

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Declination

Angle between a heavenly bodys orbital plane and the Earths Equator,measured North or South of Earths Equator

Declination

Earths

Equatorial Plane

Other BodysOrbital Plane

Declination

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Declination Moons declination varies between 18-290N & 18-290S, during its one

rotation around Earth i.e. one lunar month (29 days)

Suns declination varies between 230

N & 230

S, during its onerotation around the Sun i.e. one solar year (3654 days)

M

250N

250S

Dec 250

N

Dec 25

0

S

Dec 00

M

M


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u a , Se u a o ed Se u a des Declination of Moon & Sun dictates the Diurnal, Semi-Diurnal

or Mixed Semi-Diurnal nature of Tides at a place

For the sake of simplicity, only Moon M being considered here,at declination shown M

N

S

A1

B1B2

C1

D1

E1

D2

A2

E2

C2

HWHW

HWLW

HHWLHW LLW/HLW

48

Consider locations A, B, C, D & Eon Earths surface

Locations B & D too have two HWs each,both towards and away from M. One HW isvery high, the other is very low. LocationsB & D have Mixed Semi-diurnal tides

Location A has HW when facingM directly at A1, and also whenaway from M at A2. Location Ahas Semidiurnal tides, thoughboth HWs are not very high

Locations C & E have only one HW each (Cs HW istowards M & Es is away from M). Locations C & Ehave Diurnal tides

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Tidal Datums

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Tidal Datums

Ordnance Datum

HAT

LAT

Tidal Datums

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Tidal Datums

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13-Tides (2)