Part 01 Ce 769 Oe Mtech Brn Moodle

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CE 769Coastal and Ocean Environment

Part-I

Dr. BALAJI RamakrishnanAssistant Professor

Department of Civil Engineering, IIT Bombay.email: [email protected]

Detailed Syllabus

Dr. BALAJI Ramakrishnan, Assistant Professor, Dept. of Civil Engg., IIT Bombay. email: [email protected]

CE 769: Coastal and Ocean Environment

Module 1

Review of basic Fluid Mechanics - Conservation of mass - Continuityequation - Euler’s equation of motion - Bernoulli’s equation - Velocitypotential.

Tides; description, types, components and characteristics, analysis, levels,prediction – hydrodynamics of tidal inlets, basins and estuaries - tideinduced currents – flushing and circulation processes.

Module 2

Nearshore dynamics- estimation of nearshore wave characteristics, surf zonewaves, wave setup, run-up on beaches and nearshore currents.

Sediment dynamics- characteristics, motion initiation, littoral process, cross-shore transport: equilibrium beach profiles, bar formation, sedimenttransport modelling- beach processes and sedimentation. Inlet sedimentdynamics- estuarine and tidal inlets sediment transport.

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Detailed Syllabus



Module 3

Coastal erosion - Erosion protection measures; seawalls, revetments, groynesand offshore detached breakwaters.

Beach nourishments - methods, borrow area, environmental effects andperformance monitoring.

Module 4

Coastal hazards- meteorological; storms and surges, hurricanes and coastalflooding - geological; tsunamis, sea level rise and implications, landslides andearthquakes – man-made; oil and chemical spill, marine disposals.

Coastal zone management- zones, purpose, principles and CRZ.

Detailed Syllabus



References:

Coastal Engineering Manual (CEM), U.S. Army Corps of Engineers, EngineerManual 1110-2-1100, Washington, D.C. (in 6 volumes), 2002.

Dean, R.G and Dalrymple, R.A., Water wave mechanics for engineers andscientists, Prentice Hall Inc., 1984.

Herbich, J.B., Handbook of coastal and ocean engineering, Gulf publishingco., 1990.

Sorensen, R.M., Basic coastal engineering, Springer, 2006.

Wiegel, R.L., Oceanographical engineering, Prentice Hall Inc., 1964.

Komar, Paul D., Beach processes and sedimentation, Englewood Cliffs:Prentice-Hall, 1976.

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Review of Simple Maths !


For a continuous function f(x, y) of two independent variables x and y, knownat, say, x = x0 then it can be approximated at another location on the x axis,x0 + Δx, as;

-where the derivatives of f(x, y) are all taken at x = x0, the location for whichthe function is known.

-For very small values of Δx, the terms involving (Δx)n, where n>1, are verymuch smaller & can be neglected.

-Through the use of the Taylor series, it is possible to develop relationshipsbetween fluid properties at two closely spaced locations.

Taylor Series



Is an infinite series of trigonometric function.

If a function f(x) is defined in a closed interval x0≤x ≤x0+2 and is periodic witha period of 2, then f(x) can be represented approximately by a trigonometricseries as follows;

-in which the coefficients an and bn are obtained from the integrals;

Due to the periodicity of trigonometric functions & as the ocean waves areperiodic, Fourier series is widely used in ocean engg. applications.

Fourier Series

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A complex number has a form x+iy.

x & y are real numbers and i is the imaginary unit, i2=-1.

As the imaginary number can be assumed to be a ordered pair of realnumbers, it can be represented in a OXY plane.

Complex Numbers



Analogy to circular functions, the hyperbolic functions are related tohyperbola;

And they are related to circular functions as;

As sinkx and coskx are solutions of the 2nd order ODE of X”+k2X=0; the sinhkx and cosh kx are solutions of;

And the solution will appear as;

Hyperbolic function

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When a variable is functionally dependent on more than one variable, itsderivatives are described as partial and the relationships among the variablesare often given in terms of PDEs.

For example; the below is function of x & y. so, it will have two derivatives;variation of z w.r.t x with y constant and ….

For a equation below;

If x & y are functions of time (t) then we use chain rule as;

Partial differential equations

Review of Basic Fluid Mechanics


Methods of studying fluid motion

1. Lagrangian method-to answer, What occurs to a given particle offluid as it moves along its own path ?

2. Eulerian method-to answer, What occurs at a given point in spaceoccupied by a fluid in motion ?

Gives the velocity and pressure at a given point & Most frequentlyused in hydrodynamics.

The primary aim of fluid mechanics, in the field of ocean and coastalengineering, is to estimate the two fundamental quantities;

-Pressure (a scalar quantity)

-Velocity (a vector quantity)

These two parameters to be estimated everywhere in the fluid field and the density is assumed to constant for incompressible fluids.

Basics

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Finite control volume

Applied where the natural boundaries of theproblem may be easily identified.

Differential control volume

Is similar to the arbitrary control volumemethod except that the derivations arerestricted to the coordinate system applied todraw the infinitesimal fluid element (e.g.rectangular Cartesian, circular cylindrical,spherical, etc.).

Arbitrary control volume

Applied for mathematical derivations becausethe resulting integral equations may beapplied to any system.

Methods applied to derive the fundamental laws of fluid mechanics



Conservation of Mass (or) Principle of Continuity

-Expresses the conservation of matter, ie., fluid matter in a given space cannot be created or destroyed.

The continuity relationship is obtained by considering;

Change of fluid mass inside thevolume dx dy dz during thetime dt

difference between the rates of influxinto and efflux out of the volumeduring the same time

Fig. Control volume

The fluid mass at the time t = dx dy dz

After a time dt, the mass(due to change of density)=

Hence the change of fluid mass in a time dt is;

Eq.1

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The quantity of fluid mass entering through sideACEG is;

Where, u is mass flux.

Fig. Control volume

Now the quantity of fluid mass coming outduring same interval of time through the sideBDFH is;

The difference in the rates of influx & efflux is;

Similarly, the difference in the rates of influx & efflux can be estimated for y& z directions. The total change of mass within the control volume during thetime dt is;

Eq.2




Equating both the equations and dividing by dx dy dz dt yields;

Expanding the terms, as;

Nil for incompress

ible fluid

Leads to continuity eqn for 3-dimensional motion of an incompressible fluid

Negligible

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Momentum Equations-Euler equations

Momentum equation is obtained by equating the applied forces to the inertiaforces for a unit volume of the fluid. For x-direction;

Local inertia Convective inertia pressure

Similarly one can get for y & z directions.

As velocity is function of time and space, u(x,y,z,t); the total differential of u is;

Applying this, the momentum equation takes the form as;

gravity

Inertia forces Applied forces

Euler equation



Momentum Equations-Navier-Stokes equations

N-S equations are obtained by introducing friction forces in Euler equations.

Localinertia

Convectiveinertia Pressure gravity friction

Inertia forces Applied forces

Bernoulli equations

-Bernoulli equations are integrated form of Euler equations of motions.

-Provides relationship between pressure field and kinematics.

-Replacing the velocity terms in Euler equations (u, v & w) by velocitypotential form (u=c/cx, v=c/cy, w=c/cz), we get;

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Bernoulli equations

Since, and

Applying this, the equation simplifies to;

And by integrating the above equation;

Similar equations can be obtained for Y and Z directions, so that the functionF is a function of time only.

Where, p*=p+gz

The Physical Setting


-There is only one ocean !!!.

-It is divided into three named parts by international agreement: the Atlantic,Pacific, and Indian ocean (International Hydrographic Bureau, 1953).

-Seas are part of the ocean.

Oceans & Seas

The Atlantic

The Atlantic Ocean extends northwardfrom Antarctica;

and includes all of the Arctic Sea, theEuropean Mediterranean, and theAmerican Mediterranean morecommonly known as the Caribbeansea.

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Oceans & Seas

The Pacific

extends northward from Antarctica tothe Bering Strait.

The Indian

extends from Antarctica to thecontinent of Asia including the RedSea and Persian Gulf.



-Mediterranean Seas are mostly surrounded by land. By this definition, theArctic and Caribbean Seas are both Mediterranean Seas, the ArcticMediterranean and the Caribbean Mediterranean.

-Marginal Seas are defined by only an indentation in the coast. The ArabianSea and South China Sea are marginal seas.

-The ocean and seas cover 70.8% of the surface of earth, which amounts to361,254,000 km2.

Oceans & Seas

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Oceans & Seas

Schematic section through the ocean showing principal features of the sea floor.

Note that the slope of the sea floor is greatly exaggerated in the figure.

Tidal hydrodynamics

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Tides and effects


Important of TidesTides have a say in our everyday’s language;

“time and tide wait for none !”

Tides are always important to engineers, because;

Tides produce strong currents in many parts of the ocean. Tidal currentscan have speeds of up to 5 m/s in coastal waters, affecting navigationand mixing coastal waters.

Tidal currents generate internal waves over seamounts, continental slopes,and mid-ocean ridges.

Tidal mixing helps drive the deep circulation, and it influences climate andabrupt climate change.

Tidal currents can suspend bottom sediments, even in the deep ocean.

Greatest scientists worked for the last four centuries to understand,calculate, and predict tides. To name a few; Galileo, Descartes, Kepler,Newton, Euler, Bernoulli, Kant, Laplace, Airy, Lord Kelvin, Jeffreys,Munk and many others.

Tides and effects


Important of TidesIn spite of all these research, the following question remains;

What is the amplitude &

phase of the tides at any place on the ocean or along the coast?

What is the speed &

direction of tidal currents?

What is the shape of the tides on the ocean?

Where is tidal energy dissipated?

Finding answers to these simple questions is difficult.

The first, accurate, global maps of deep-sea tides were only published in1994 (LeProvost et al. 1994).

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Tides and effects


Important of Tides

During high tide During low tide

Tides and effects


Theory of TidesTides are generated by two major systems;

Sun-Earth system &

Moon-Earth system.

Sun-Earth System:

The tide-generating forces may be developed by considering differences inthe gravitational attraction of the sun at various locations on the earth.

At the center of mass of the earth thegravitational attraction must be a valuejust necessary to keep the earth in itsorbit around the sun.

F1>F2, as it is close to sun.

F3<F2, as it is away from sun.

The differences (D) will form a symmetricalegg-shaped distention (referred as tidalbulge of the ocean waters).

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Tides and effects


Theory of TidesMoon-Earth System:

The moon and the earth revolve around their common center of mass in onemonth.

The mean distance between the moon and the earth is about 238,860 miles.The center of mass of the moon-earth system is located within the earthabout 2895 miles (mean) from the center of mass of the earth, alwaystoward the moon.

The F & D are same pattern as sun-earth system, but magnitude varies.

Tides and effects


Theory of TidesThe earth spins counter clockwise in one solar

day. The mean solar day is the period of 24solar hours.

Starting with the point on the equator toward thesun, the point experiences a maximum in thesolar tide-generating force; six hours later, aminimum; then a maximum at twelve hours; aminimum again at eighteen hours; and finallyback to the maximum at the conclusion of thesolar day.

The lunar day is slightly longer than solar day (24.84 solar hours).

Starting with the point on the equator toward the moon, the pointexperiences a maximum in the lunar tide-generating force; 6.21 solarhours later, a minimum; then a maximum at 12.42 solar hours; aminimum again at 18.63 hours; and finally back to the maximum at theconclusion of the lunar day.

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Theory of TidesMoon-Earth System:

Tidal Hydrodynamics

Tides and effects


Theory of Tides

Front view

Top View

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Theory of TidesThe Sun, Earth and Moon system:

Tidal Hydrodynamics

And the Newton’s Law of gravitation:

Tides and effects


Theory of Tides

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Tides and effects


Theory of Tides: Spring & NeapThe range of tide, defined as the vertical difference in height between

consecutive high and low tides, varies from place to place and also variesover time.

The combination of the solar and lunar envelopes during the synodic month(period of moon’s phases) causes spring tides and neap tides.

The lunar tide is 2.16 times more influential than the solar tide, as themoon is closer to earth than sun (although the mass of sun is huge!).

When the moon is new or full, the tide-generating forces of the sun andmoon are aligned.

The high tides of the solar envelope occur at the same time as the high tidesof the lunar. This increases the height of the composite high tides, calledas Spring tides.

Tides and effects


Theory of Tides: Spring & NeapWhen the moon is in its first/third quarter, the tide generating forces of the

sun are at right angles to those of the moon.

The envelope of the tide-generating forces of the sun is shown to conflictwith the force envelope of the moon. The low tides of the solar envelopeoccur at the times of the high tides of the lunar.

This reduces the height of the composite high tides, called as Neap tides.

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Theory of Tides: Spring & Neap

Tidal Hydrodynamics

Tides and effects



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Tides and effects



Tides and effects


Theory of Tides: Other inequalities

Sizes of consecutive tides isinfluenced by theMoon’s orbit.

Another cycle within theMoon’s orbit iscontrolled by the earth-moon distance.

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Theory of Tides: Other inequalities

Tidal Hydrodynamics

Both the Moon and the Earth revolve in elliptical orbits and the distancesfrom their centers of attraction vary.

Increased gravitational influences and tide-raising forces are produced whenthe Moon is at position of perigee.

Though the centrifugal acceleration is the sameeverywhere on the earth, but the gravitational force dueto the moon/sun varies over the surface of the earth.

Tides and effects


Types of TidesIf the Earth were a perfect sphere without large continents, all areas on the

planet would experience two equally proportioned high and low tidesevery lunar day.

The large continents on the planet, however, block the westward passage ofthe tidal bulges as the Earth rotates.

Unable to move freely around the globe, these tides establish complexpatterns.

Within each ocean basin that often differ greatly from tidal patterns ofadjacent ocean basins or other regions of the same ocean basin.

Most coastal areas, with some exceptions, experience two high tides andtwo low tides every lunar day.

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Tides and effects


Types of TidesThe geometric relationship of moon and Sun to locations on the Earth's

surface results in creation of three different types of tides;

Diurnal tides

Semi-diurnal tides &

Mixed tides.

Diurnal tides:

Tides haves one high & one low intidal day.

In parts of the northern Gulf ofMexico and Southeast Asia.

Tides and effects


Types of TidesSemi-diurnal tides:

Tides haves two highs & two lows in tidal day.

They are common on the Atlantic coasts of the US & Europe.

Mixed tides:

Successive high-water and low-water stands differ appreciably

The tides around west coast of Canada and the US.

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Tides and effects


Types of Tides

Global distribution of the three tidal types. Most of the world's coastlines have semidiurnal tides.

Tides and effects


Characteristics of TidesAs the gravitational forces of sun and moon are time varying, the tide is

also a time varying phenomenon.

Similar to waves, tides have;

Height, H, the vertical distance between the level of a crest and the levelof a trough (amplitude, A, is one half the height),

Length, L, the horizontal distance from one crest to the next,

Period, T, the time interval between the occurrence of two successivecrests at a fixed point, and

Speed (celerity), C, the length divided by the period, C = L / T.

Tidal waves are always shallow water waves. That is, the length of a tidalwave is very much longer than the depth.

Therefore, the particulate motion that makes up the wave is just back andforth.

This back and forth particulate motion in a tidal wave is called the tidalcurrent.

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Tides and effects


Characteristics of TidesApart from solar & lunar effects, the tide is influenced by many other

factors.

Each one of the tide-generating motions, represented by a simple harmoniccosine curve, is known as a tidal component, tidal constituent, orharmonic constituent.

S2 - Principal Solar semidiurnal constituent (12 hrs)

M2- Principal Lunar semidiurnal constituent (12.42 hrs)

N2 & L2- Larger Lunar Elliptic semidiurnal constituent and the SmallerLunar Elliptic semidiurnal constituent. These two are assumedconstituents to represent the cycle of perigee to perigee.

K1 & O1- Luni-solar Declinational diurnal constituent & the PrincipalLunar Declinational diurnal constituent. Also assumed constituents torepresent the cycle of maximum declination to maximum declination ofthe moon.


Characteristics of Tides

Tidal Hydrodynamics

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Tides and effects





Typical M2 tidal amplitude around the world

Tidal Hydrodynamics

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Red sea

Arabian Gulf

Tidal Hydrodynamics




Tidal Hydrodynamics

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Tides and effects


Tidal datumTidal datum is vertical reference used as the base elevation from which

measurements of height and depth are made.

-Highest Astronomical Tide (HAT)

-Mean High Water Spring (MHWS)

-Mean High Water Neap (MHWN)

-Mean Sea Level (MSL)

-Mean Low Water Neap (MLWN)

-Mean Low Water Spring (MLWS)

-Lowest Astronomical Tide (LAT)


Tidal datum

Tidal Hydrodynamics

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Tidal level measurement

Typical tide measuring techniques

Tidal Hydrodynamics




Tidal Hydrodynamics

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Tidal Hydrodynamics



Typical tide measuring station

Tidal Hydrodynamics

Tide stations along Indian coast

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Predictionof TidesFrom the tidal level measurement (at least for 19yrs) at a particular

location, the tidal constituents can be obtained by analyzing the timehistories.

The analysis is called as harmonic analysis, as it involves extracting theperiods of various components.

From a harmonic analysis of the observed water level series, two values areobtained for each tidal constituent.

Amplitude, the vertical distance between mean tide level and the level of thecrest is one of the values.

And the phase lag, the amount of time elapsed from the maximumastronomic event to the first maximum of its corresponding constituenttide, is usually expressed in degrees.

Harmonic constants are unique to the particular station location fromwhich they were derived.

Tidal Hydrodynamics


Predictionof TidesMathematically, the process of prediction involves simple addition of the

cosine curves of the tidal constituents.

This straightforward addition may be developed by;

Tidal Hydrodynamics

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Predictionof Tides

Tidal Hydrodynamics

Tide Predicting Machines !!


Predictionof Tides

Tidal Hydrodynamics

Tide Predicting Machines !!

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Predictionof Tides

Tidal Hydrodynamics

Tide predictionTide table

Softwares


Characteristics of TidesAs the gravitational forces of sun and moon are time varying, the tide is

also a time varying phenomenon.

Similar to waves, tides have;

Height, H, the vertical distance between the level of a crest and the levelof a trough (amplitude, A, is one half the height),

Length, L, the horizontal distance from one crest to the next,

Period, T, the time interval between the occurrence of two successivecrests at a fixed point.

Tidal Hydrodynamics

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Characteristics of TidesThe water waves are classified into three categories, depending upon their

water depth to wave length ratio, (d/L);

Where, the wavelength, L is given as;

The speed of the wave form/celerity of the tidal waves is given as;

C = L/T

And for smaller values of d, (shallow water depth)

Tidal Hydrodynamics

Classification d/LDeep water > 0.5

Intermediate water 0.5 – 0.05Shallow water <0.05


Characteristics of TidesThe horizontal component of water particle velocity under the sine waves

are give as;

The displacement component of the water particle are obtained byintegrating the velocity w.r.t time;

Tidal Hydrodynamics

surface deep water particle speed

particle velocity variation over the verticalwater column at a given location

phasing term dependent onposition in the wave and time

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Tidal Hydrodynamics

dL0

dd

(a) deep water, d/L>0.5

(b) Intermediate water0.5>d/L<0.05

(c) shallow water, d/L<0.05

Water particle displacement under a wave

Tidal waves are always shallow water waves (L >> d).

Therefore, the particulate motion that makes up thewave is just back and forth, causing tidalcurrents.

Tides and effects


Tides in bays, estuaries & harbours

Estuaries/creek are formedwhen rivers meet the sea.

Generally, an estuary is asemi-enclosed river mouthor bay where saltyseawater is diluted byfreshwater from rivers andcreeks.

The components of anestuary includes; tidalmarshes, tidal flats, andopen water channels.

Estuaries are is flooded bythe tides during high tide.

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Tides and effects



Tides and effects



Arabian sea

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Tides and effects


Tides in bays, estuaries & harboursTides can be described in terms of waves. For a tidal wave, the crest is a

high tide and the trough is a low tide. The height of a tidal wave is therange (or tidal range) and the mean of the high and the low tides iscalled mean tide level.

In most gulfs and estuaries of the world, the tidal waves behave as either aprogressive wave or a standing wave.

The horizontal component of the particulate motion under the high tidearea is going in the same direction as the tidal wave form and is known asthe flood tidal current (or flood tide). Its maximum is directly under a hightide.

The particulate motion under the lowtide area is going in the oppositedirection as the tidal wave form and isknown as the ebb tidal current (or ebbtide). Its maximum is directly under alow tide.

Tides and effects



An estuary during flood tide

An estuary during ebb tide

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Tides and effects



Tidal marsh

Tidal flat

Open water channel

Tides and effects


Tides in bays, estuaries & harboursWhen a progressive tidal wave encounters a barrier such as a coast,

embayment, head of an estuary, etc., it reflects upon itself to form astanding wave.

Tide entering an estuary

Tide moving out of the estuary

Resulting tide in the estuary

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Tides and effects


Tides in bays, estuaries & harboursThe tide inside the estuary experiences bottom and internal friction and get

attenuated. Its reflection continues to dampen as it moves seaward.Hence, a perfect standing wave never produced.

Depending upon the estuary’s length and depth, if a node of the estuarywave happens to be near the entrance, the range of the estuarine tidewill be greatly amplified.

Where as if an antinode is near,there will be no significantincrease from this effect.

The tides in Gulf of Khambat isan example of this process. Thetidal range is 9m.

The highest tide is experiencedin Bay of Fundy, North America.The tidal range is 16m !!.

Tides and effects



The average tidal ranges in Bay of Fundy

The average tidal ranges in Gulf of Khambhat

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Typical tidal variation in Bay of Fundy

During high tide

During low tide

Tidal Hydrodynamics



During high tide

During low tide

Typical tidal variation elsewhere

Tidal Hydrodynamics

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Tides in bays, estuaries & harboursTidal inlets provide both man and nature with a means of access between

the ocean and a bay.

Commercial and recreational vessels need a navigable channel for safetransit to interior harbors.

The flow of currents into and out of a bay through an inlet provides naturalflushing to maintain good water quality and reasonable salinity levels.The migration of fish, fish larvae, and other sea life through the inletconduit is also an important function of an inlet.

Successful engineering of inlets requires knowledge of water and sedimentmovement in and adjacent to the inlet.

Tidal Hydrodynamics



Tidal Hydrodynamics

Flood & ebb tidal currents at inlet

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Tides and effects


Tides in bays, estuaries & harboursTidal bores:

The tidal bore is a tidal wave that propagates up a relatively shallow andsloping estuary or river in a solitary wave form.

The leading edge presents an abrupt rise in level, frequently withcontinuous breaking and often immediately followed by severalundulations.

Tidal bore is usually associated with very large ranges in tide as well aswedge shaped and rapidly shoaling entrances.

Tidal bores tend to occur in river estuaries wherefunneling in the entrance topography helps toincrease the range and the river flow tends toretard, and therefore build up, the wave.

Tidal bores occur in several river estuariesthroughout the world. In India, tidal boresoccur at Hooghly River, West Bengal.

Tides and effects



Tidal bores

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Tides and effects


Tide induced currentsThe horizontal movement of water particle under the tide causes “tidal

current”.

Speed/velocity of the tidal current affect navigation of ships and can causepollution.

On the other hand, with large tidal current, one can tap tidal power.

Tidal amplitude around the world

Tides and effects


Tide induced currentsTime series of tidal current & rose diagram

Water level

Current velocity

Current direction

Tide current rose

Direction distribution

Current profile

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Tide induced currents

Tidal Hydrodynamics

Another common way to illustrate how tidalcurrents vary in space, either horizontally orwith depth, is to use tidal ellipses.

The red lines indicate the direction at which thecurrent is pointing at a given time. Blue-counterclockwise; Green-clockwise rotation.

Typical tidal current trajectory (showingdirection and speed @ every hour) over 15days. Note the non-repeating complexnature of current pattern.


Tide induced currents-Measurements

Tidal Hydrodynamics

Acoustic doppler current profiler (ADCP)

Drifter & tidal current trajectory

Tidal current measurement

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NextNear-shore & sediment dynamics….

Part 01 Ce 769 Oe Mtech Brn Moodle

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