Tides and Currents

Tides and water levels TBA4265 Marine Physical Environment

08 September 2009

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Water level fluctuations, engineering aspec

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TBA4265 Marine Physical Environment – Tides and Water Level

PhD student: Raed Lubbad

Tides and Water Level >>

Engineering aspects

oas a s ruc ure

Large waves!!

Broken waves!!

Overtopping …Flooding!!

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Engineering aspects

an y s ores

small waves!!

Large waves!! Erode the beach!!

Recoverable??!! 4



Water level fluctuations, Classification

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Types of water level fluctuations

-T es -Storm surge -Barometr c surge -Seiche

Seasonal

Lon term 6

- ma c ucu a ons -Eustatic - sos a c -Global climate Change



es

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other large bodies of water. These changes are caused by the gravitational attraction of the moon and, to a lesser extent, of the sun on the earth.

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Tides and Water Level >> Tides >>

…

Datum

usually fixed so that few tides fall below it. All heights are referred to this. 9




… Rise Datum

is the height of high water on the adopted scale (measured from the datum .

Range: st e erence n eve etween t e e g t o g water an the height of the next succeeding or last preceding low water. 10




u

u

…

Rise atum

a currents: the horizontal movement of water due to the tidal effects

Flood current: associated with risin water 11

Ebb current.




the longest oceanic waves. They are characterised by the rhythmic .

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pen ocean : . m coastal areas : 2 - 3 m Maximum: 12 m n ana a

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at causes t es • Tide generating forces: due to the relative motion of the Earth, Sun and Moon. •

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e response o

e oceans o

e


e genera ng orces


e genera ng orces

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Tides and Water Level >> Tides >> Tide generating forces >>

Overview

• The earth rotates around its own axis

• The moon and the earth rotates around their common center of gravity. The moon orbit around the earth is “elliptical” (27.32 day) • The earth and its moon rotate around the sun in “elliptical” orbit . 16




Overview

• The orbit of the moon around the earth is inclined to the orbit of the earth. This means that the moon can be in the same level as the equator only twice every lunar month.

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Overview

Sun

Sun

Solar da 24 h

= Sun overhead X

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Sun overhead X again



Overview

Lunar da 24 h 50 min

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Overview

The gravitational principles elaborated by Newtonin his Principia is the basis for understanding the tide-generating forces.

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Overview

Why don’t, for example, the earth and its moon collide ?! Answer: Thanks to the centrifugal forces

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Overview

m1/ m2 rotates around ccg with an angular velocity ω Common Centre of gravity, ccg.

m1

F

F

F

F m2

r2

r1

d

Fg   22

m1  m2 d2

m1 r1  m2 r2  Fc 1 1 2  2




Assumptions

• Only, the gravitational forces from the moon are considered in the following. (thesam e calculation m ethod can be used for the solar-tide generating forces )

•Let us consider that the system earth/moon rotates around a common centre of ravit with a constant velocit ω.

• In t e centre o t e eart t e grav tat ona orce rom t e moon balance the centrifugal force. Because of the global balance, the acting in the centre of the earth.

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Assumptions

Consider a fixed point P on the earth’s surface

Cancelled by the earth gravity

c0

F

F

F gP

R T rac ve orce:

“Tide generating force”

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Equation a d

The maximum force actin occurs at   45 and  135 



The force acting at the sublunar point (  0 ) = 0 

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Equation

The distribution of tide-generating force is determined in relation to the position of the moon while the earth is rotating on its axis.

The ma nitude and direction of the tide- eneratin force at a given point on the earth’s surface is changing continuously with time.

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The response of the oceans to the tide generating forces

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Equilibrium tide

Basic assumptionsinvolved: • An ocean with a constant depth is covering the whole earth • The water respond instantly to the changing forces (static response) • The surface of the water balances the tide-generating forces by a or zon a p ressure gra en

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Equilibrium tide

In spite of the unrealistic assumptions, the equilibrium tide has proved to be a useful concept which exhibits a number of qualitative features of the actual tides

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Equilibrium tide Surface slope

balance

Pressure gradient

balance tan  

Fs





Tide generating forces

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Equilibrium tide tan  

Fs   g s

Fs  

T s



1 T

s



 s

g   T From the distribution of the tide-generating force, one m calculate the distribution of the equilibrium tide around the ear 31



Equation

Tides and Water Level >> Tides >> Equilibrium tide >>





1 M  a



3

2  (3cos   1)

The elevation has its maximum value at   0 and 180 



The elevation has its minimum value at   90 

.

1  min    max 2

 max   min  53.5cm Closed to the observed values in e oceans 32



Equilibrium tide (moon + sun)

pr ng-t e

Neap-tide 33



Equilibrium tide (moon + sun)

pr ng-t e

Neap-tide 34



Daily inequality

Diurna Ti e- one where high waters occur once daily at intervals averaging 24.8 hours 35



Daily inequality

Semi-Diurnal Tide- one where high waters occur twice daily at intervals averaging 12.4 hours

At the equator:: when alwaysthe moon is in the level of the equator Elsewhere

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Other effects • Theorbitof themoon andsun relative to theearthelliptical is

(The distance etwe b en theearth , sun and o mon changein a periodic fashion) • The earth large land masses will not turn through the tide,

the simple equilibrium model) • The earth geography causes certain tidal constituents to

resonate locally. Thus some constituents are magnif certa n ocat ons w e ot ers may sappear t e at eac location is unique) 37



Other effects

e secon ary e ec s can e v ewe as separa e tide generators where each tide generator ha , theothe rs Tides thus is a complex a addition of effects of the moon, thesun and a mny se condary cause s. Each component is called a tidal constituent

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Tidal analysis and prediction

Tideanalysis consists of separating a measure into as many o its constituents as can e i enti ie from the length of the record available

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Harmonic constituents of the tides The tide-generating potential is a complicated function of time, which may be resolved into the sum of a large number of harmonic constituents Species Semidiurnal

Diurnal

Long period

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Constituent Principal lunar

Symbol

Period

M2

12.42 hrs

r nc pa so ar Large lunar elliptic

N2

. rs 12.66 hrs

Luni-solar

K2

11.97 hrs

Luni-solar

K1

23.93 hrs

Principal lunar

O1

26.87 hrs

Principal solar

P

24.07 hrs

2

1

Lunar fortnightly Lunar monthly

Mf Mm

13.66 days 27.55 days

Solar semiannual

S

182.70 da s



Is the horizontal movement of water due to the tidal effects Tidal wave

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Tidal current



The tidal wave are very long compared to the water depth, therefore the shallow water formulation of the linear wave t eory can e use to ca cu ate t e ve oc y o propaga of the tidal currents

on

The length of the tidal wave then:

T = 24.41 hrs for the lunar semi-diurnal constituent 42



d = 4000m

C = 200m/s

L = 9000km

d = 10m

C = 10m/s

L = 450km

d = 3m

C = 5.5m/s

L = 245km

Shallow water

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Tidal currents Since the length of the tidal waves are substantially large, the (Coriolis). In other words, the tides do not propagate in a straight line, but rotate.

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Tidal currents , (the amplitude is amplified) due to the different land mass to o ra h

Different coastal shapes will yield different tides

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Tidal currents

-

mp

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rom c po nt



Tidal currents Tas : Design a Coastal structure

Required : Tide Data Will This Data Change by the Project?!!

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Tidal currents

tide) with the tidal water level fluctuations (vertical tide)

Deep open ocean

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Tidal inlet and bay


Tidal currents Deep Open Ocean Maximum current velocity at high water Tidal wave

In t e rect on o t e t e propagation

Horizontal and vertical tides are in phase

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Tidal currents Tidal inlet and bay

Small bay and large

Long ay or narrow inlet

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Tidal currents Small bay and a large entrance

There is no phase lag between in the sea

At hi h(High waterwater the flood current is zero slack tide)

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Water level

Flood current

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The Current leads the water level by 90º “Complete wave reflection!!”

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Tidal currents L ong bay or narrow inlet

The maximum water level in the sea

At hi zero h water the flood current is not

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Water level

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The Current leads the water level by less t an 90

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seasonal

Lon term 57




Storm Sur e Is an increase in water level resulting from the shear stress by

Occurs at t e same t me as ma or wave act on an s t e cause o most world’s disastrous flooding and coastal damage

Greatest concern in design 58



Storm Sur e Wind Shear stress

Slope of water surface

1D simple model:

,



The above equation computes maximum surge (good for feasibility study and conservative design 59



Storm Sur e

Negative storm surge may occur in enclosed

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seasonal

Lon term 61




Barometric Surge Strong winds are the result of large pressure fluctuations

Barometric sur e will accom an the storm sur e Wind

h S

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Barometric Surge PAPB  A atmA

  wg

A



atmB

  wg

B

B

Patm  Patm   wghB   wghA

Patm   wg  h P atm

 wg 63

Results in water level rise of about 0.1m/1kPa




seasonal

Lon term 64




When the wind that formed a storm surge stops blowing, the water level will start to oscillate back and forth (seiche) The oscillations will continue for some time because the friction forces are quite small

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Closed Basin

L

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2 Be 1  nh


Seiche

Open ended basin (Open coast)

L

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4 Be 1  2nh


p: www.coas a .u e .e u acu y ra se c e. m

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seasonal

Lon term 69




Tsunami: Tsunami generates due to sudden transfer of a large amount of acoustic or mechanical energy into the ocean. This may be

Tsunami may be generated due to Submarine Earthquakes, Landslides, Volcanic Eruptions, Explosions…

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Eustatic (Sea) L evel Changes: refers to a global change in ocean water levels, resulting from melting or freezing of the polar ice caps and thermal

partly responsible for the fact that most beaches around the World eroding over the long time.

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I sostati

L and Emer enc and Subsidenc :

is a result of the adjustment of the earth’s crust to the release of pressure exerted by the 1 to 2 km thick ice sheet that covered it during the last glaciations

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Global ClimateChange: The most potential and dangerous change in water level results from the recent trends in climate changes globally

sea level rise of 100 to 150 m through melting of the polar ice caps and thermal expansion of the water in the ocean

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Tides and Currents

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