Part 02 Ce 769 Oe Mtech Brn Moodle

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CE 769Coastal and Ocean Environment

Part-II

Dr. BALAJI RamakrishnanAssistant Professor

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

Estimation of nearshore waves

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

Nearshore environment-Most coastal engineering problems are near the shoreline normally in waterdepths of less than 20m.

-Generally, project designs usually require knowledge of the wavecharacteristics over an area of 1-10sq.km in which the depth may varysignificantly.

-Specifically, projects involve understanding of shoreline change and beachprotection frequently requires analysis of coastal processes over entire littoralcells, which may span 10-100 km in length.

-Wave data are generally not available at the site or depths required.

-Often a coastal engineer will find that data have been collected or hindcastat sites offshore in deeper water or nearby in similar water depths.

-Conservative wave characteristics can greatly increase the cost of a projectand may make it uneconomical, where as underestimating results incatastrophic failures/ significant maintenance costs.

-The various nearshore processes and the dynamics of waves will bediscussed in this section.

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Nearshore environment



Nearshore environment-Waves in the nearshore are influenced by seabed contours & currents.

-Any change in bathymetry (sloping/undulating/shoals/underwater canyons)leaves large changes in wave height and direction of travel.

-For example; shoals can focus waves & sometimes leading more thandoubling wave height behind the shoal. Where as; other seabed features canreduce wave heights.

-The magnitude of these changes is particularly sensitive to wave period anddirection and how the wave energy is spread in frequency and direction (asshown below figure).

Amplification of wave height behind ashoal for waves with differentspreads of energy in frequency anddirection

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Processes affect the wave characteristics(a) Refraction

(b) Shoaling

(c) Diffraction

(d) Dissipation due to friction

(e) Dissipation due to percolation

(f) Breaking

(g) Additional growth due to the wind Source mechanism

(h) Wave-current interaction

(i) Wave-wave interactions

Propagation effects

Sink mechanism



Processes affect the wave characteristics

-1m

-2m

-3m

-4m

-5m

A

B

C

5m/s

6.5m/s

9m/s

Shoreline/beach

Shoaling Diffraction

Refraction Breaking

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Brief overview of linear waves theory


Summary of linear wave characteristics



Energy, energy flux & group celerityThe total mechanical energy in a surface gravity wave is the sum of the

kinetic and potential energies.

applying u & w

Energy flux: The rate at which the energy is transferred by the waves.

For the linear wave theory it is the rate at which work is being done by thefluid on one side of a vertical section on the fluid on the other side.

d

d

For the vertical section AA (in Fig.), theinstantaneous rate at which work is beingdone by the dynamic pressure per unit widthin the direction of wave propagation is;

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The avg. energy flux is obtained by averaging over a wave period andapplying the equation of p and u;

Integrating the above equation will lead to;

d

dd

dd

dd

Energy, E Celerity, C n

(or)

where Cn is the speed at which the energy is transmitted; this velocity iscalled the group velocity (or group celerity) Cg,

In which, dd

Energy, energy flux & group celerity



Energy, energy flux & group celerityExample problem: A wave, of height, H=1m and period T=15sec, ispropagating on a sea. Calculate the energy flux at d1=500m and d2=3m.

Solution:

-Calculate the deepwater wavelength; L0=1.56T2.

-Calculate the wavelengths for d1 & d2-Estimate celerity (C=L/T)

-Calculate

-and finally, energy flux;

-Compare the results.

In which, dd

Wave direction

Shoreline

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Surf zone hydrodynamics


Incipient wave breaking-Breaker types; (spilling, plunging, collapsing and surging).

-Surf similarity parameter;

-Breaker index (breaker depth index & height index);

And for the regular waves;

The semi-empirical relationship for the breaker height index;

Hb is on both sides!, iteration..



Incipient wave breakingExample problem: Over a beach with a 1 on 100 slope, a deepwater wave ofheight Ho = 2m, and period T=10sec is propagating. Estimate the wave heightand water depth at incipient breaking occurs. Assume, a unrefracted waveheight of 2.1m.

Solution:

-Calculate the deepwater wavelength; L0=1.56T2.

-Use and get Hb from;

-Estimate a & b, for beta=1/100; &

-Calculate

-and finally, db=Hb/b.

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Wave transformation in surf zoneAfter the incipient wave breaking, the waveshape resemble like a bore.

At this stage, the leading edge of the wavecrest becoming nearly vertical and takes asawtooth profile.

Along the surf zone, the wave either continueto dissipate energy or, re-forms and breakagain on the shore.

This transformation of wave height throughthe surf zone impacts wave setup, runup,nearshore currents, and sediment transport.

outside surf zone

inside surf zone

Changes in wave profile


Similarity method

Using the breaker index and assume a constant height-to depth ratio fromthe break point to shore;

This method is good for constant decrease of water depth through the surfzone & suggested to be fine for a beach slope of approximately 1/30.

Underestimate on steeper slopes & overestimate on milder slopes.

Smith and Kraus (1988) developed expression that includes beach slope;

Surf zone hydrodynamicsWave transformation in surf zone

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Energy flux method

Solving the steady-state energy balance equation;

where is an empirical decay coefficient (=0.15), and ECg,s is the energy fluxassociated with a stable wave height;

The quantity is an empirical coefficient (=0.4).

The stable wave height is defined as the height at which a wave stopsbreaking and re-forms.

Surf zone hydrodynamicsWave transformation in surf zone


Surf zone hydrodynamicsRadiation stressThe average value of the sum with respect to time, integrated alonga vertical plane of unit width.

Vn is velocity component perpendicular to the considered plane & pw ispressure fluctuation due to water waves around the hydrostatic pressurefrom the still water level.

i.e. where p is the total pressure, and Vn2 is the momentumflux.

When the plane is vertical and parallel to the wave crest (V=u), the radiationstress is;

Applying the values of pw and u from linear wave theory and integrating;

Wave thrust(or)

Radiation stress

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Surf zone hydrodynamicsRadiation stress

The wave thrust reduces to;

A wave traveling over a gently sloping bed from deep water into shallowwater, the wave thrust increase by a factor of 3.

Therefore, the momentum balance requires an external force. This externalforce is obtained by differences in the hydrostatic pressure.

Shallow water Deep water


Surf zone hydrodynamicsWave set-up & set-downLet us consider the momentum balance in a slice of water bounded by thefree surface, z=, a gently sloping bottom, z=-d(x) and two vertical planesparallel to the wave crest at x=x0, x=x0+dx.

The variation of midwater level is defined as;

The total forces exerted on the planes are the sum of hydrostatic pressureand wave thrust.

@ x0

@ x0+dx

As the bottom is not horizontal,another external force is due tobottom pressure exist and thehorizontal component of the same is,

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Surf zone hydrodynamicsWave set-up & set-downBy balancing the momentums;

Since,

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Sediment dynamics


Characteristics of sedimentImportance in Coastal engineeringDredging -Entrainment: fluid, loose, firm, or hard

Pumping: cohesive, noncohesive, or mitigated

Near-vertical banks: degree of cohesiveness.

Environmental concerns: Size (turbidity, current-interactions)

Beach fill: borrow & native material

median size of borrow sand should not be < native.shore protection & recreation conflict sediment sizes.

Scour protection: revetment/riprap or scour blanketheavy enough to resist movements under currentsadequate porosity & thickness - dissipate wave energy

Sediment transport studies

Sediment properties: grain size, density, fall velocity, angle of repose,volume concentration

Sediment size distribution and grain shape.

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Characteristics of sedimentClassification by sizeSize

-Particle diameter

-Size classifications (Wentworth / ASTM)

-Median (D50) and mean grain sizes.

Compositional Properties

-Density

-Sp. Weight & Sp. Gravity


Characteristics of sedimentFall/settling velocityWhen a particle falls through water, it accelerates until it reaches its fall/settling velocity.

This is the terminal velocity that a particle reaches when the (retarding) dragforce on the particle just equals the (downward) gravitational force.

A particle's fall velocity is a function of its size, shape, and density; as well asthe fluid density, and viscosity, and several other parameters.

For a single sphere falling in an infinite still fluid, after balancing the drag &gravitational forces, the fall velocity is;

CD = dimensionless drag coefficient, D = grain diameter, = density of water,s = density of the sediment.

Unit of Wf is same as the unit of (gD). CD is fun Re (Re = Wf D/, where isthe kinematic viscosity)

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Characteristics of sedimentFall/settling velocity

Fall velocity as a function of Reynolds number


Characteristics of sedimentFall/settling velocity

Fall velocity of quartz in water & air

The fall velocity equation is re-arranged to get;

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Characteristics of sedimentFall/settling velocity - ProblemCalculate the Wf, Re & Cd for 0.2mm quartz sediment falling in 400C of fresh& salt water. water = 0.011 cm2/sec, fresh water = 1000 kg/m3, salt water = 1030kg/m3, quartz = 2648 kg/m3.

Solution:

-Using 0.2mm size & 40deg, get the fall velocity from graph.

-Get the Re; Re = Wf D/,

-Get Cd, using;

For salt water

-fall velocity depends on;

-For fresh water the ratio is 1.28 (for quartz) and for salt water the ratio is1.25 and hence, the fall velocity decreases with increase in density of water.

-Multiply calculated Wf by (1.25/1.28=0.977), get revised Re & Cd.


Shore process and changesLittoral zone & processLittoral zone: In beach terminology, an indefinite zone extending seaward

from the shoreline to just beyond the breaker zone.

The coastal zone influenced by wave action, or, more specifically, the shorezone between the high and low water marks.

Littoral processes result from the interaction of winds, waves, currents,tides, sediments, and other phenomena in the littoral zone.

We will discusses those littoral processes which involve sediment motion.Shores erode, accrete, or remain stable, depending on the rates at whichsediment is supplied to and removed from the shore.

Excessive erosion or accretion may endanger the structural integrity orfunctional usefulness of a beach or of other coastal structures.

Therefore, an understanding of littoral processes is needed to predicterosion or accretion effects and rates. A common aim of coastalengineering design is to maintain a stable shoreline.

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Shore process and changes


Environmental factorsWaves: The action of waves is the principal cause of most shoreline

changes. Three important aspects of a study of waves on beaches are;

(1) the theoretical description of wave motion,

(2) the climatological data for waves as they occur on a givensegment of coast, &

(3) the description of how waves interact with the shore to movesand.

Important wave characteristics affecting sediment transport near the beachare height, period, and direction of breaking waves.

Breaker height is significant in determining the quantity of sand placed inmotion; breaker direction is a major factor in determining longshoretransport direction and rate.

Waves affect sediment motion in the littoral zone in two ways: (a) theyinitiate sediment movement and (b) they drive current systems thattransport the sediment once motion is initiated.



Environmental factorsCurrents: The wave induced drift (mass transport) can be important in

carrying sediment onshore or offshore, particularly seaward of thebreaker position.

As waves approach breaking, wave-induced bottom motion in the waterbecomes more intense, and its effect on sediment becomes morepronounced. Breaking waves create intense local currents andturbulence that move sediment.

Since wave crests at breaking are usually at a slight angle to the shoreline,there is usually a longshore component of momentum in the fluidcomposing the breaking waves.

This longshore component of momentum entering the surf zone is theprincipal cause of longshore currents (currents that flow parallel to theshoreline) within the surf zone.

These longshore currents are largely responsible for the longshore sedimenttransport.

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Environmental factorsIn some locations, there may be exchange between the water flowing in the

surf zone and the water seaward of the breaker zone. They are called asrip currents which are concentrated jets of water flowing seawardthrough the breaker zone.



Environmental factorsTides & Surges: In addition to wave-induced currents, there are other

currents affecting the shore that are caused by tides and storm surges.

Tide-induced currents can be impressed upon the prevailing wave inducedcirculations, especially near entrances to bays and lagoons and inregions of large tidal range.

Tidal currents are particularly important in transporting sand at entrancesto harbors, bays, and estuaries.

Currents induced by storm surges are less well known because of thedifficulty in measuring them, but their effects are undoubtedlysignificant.

The change in water level caused by tides and surges is a significant factorin sediment transport since, with a higher water level, waves can thenattack a greater range of elevations on the beach profile.

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Environmental factorsWind: Winds act directly by blowing sand off the beaches and by depositing

sand in dunes. It usually removes the finer material, leaving behindcoarser sediment and shell fragments.

Sand blown seaward from the beach usually falls into the surf zone; thus itis not lost, but is introduced into the littoral transport system.

Sand blown landward from the beach may form dunes, add to existingdunes.

For dunes to form, a significant quantity of sand must be available fortransport by wind, as must features that act to trap the moving sand.

Topographic irregularities, the dunes themselves, and vegetation are theprincipal features that trap sand.

Geological factor: The geology of a coastal region affects the supply ofsediment on the beaches and the total coastal morphology, thus geologydetermines the initial conditions for littoral processes.



Longshore sediment transportThe breaking waves and surf in the nearshore combine with various

horizontal and vertical patterns of nearshore currents to transport beachsediments.

Sometimes this transport results only in a local rearrangement of sand intobars and troughs.

At other times there are extensive longshore displacements of sediments,possibly moving hundreds of thousands of cubic meters of sand alongthe coast each year.

We will see the various techniques that have been developed to evaluate thelongshore sediment transport rate, which is defined to occur primarilywithin the surf zone, directed parallel to the coast.

This transport is among the most important nearshore processes thatcontrol the beach morphology, and determines in large part whethershores erode, accrete, or remain stable.

An understanding of longshore sediment transport is essential to soundcoastal engineering design practice.

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Longshore sediment transportAs waves breaking obliquely to the coast, the longshore currents are

generated, and resulting movement of beach sediment along the coast isreferred to as littoral transport or longshore sediment transport, whereasthe actual volumes of sand involved in the transport are termed thelittoral drift.

This longshore movement of beach sediments is of particular importance inthat the transport can either be interrupted by the construction of jettiesand breakwaters (structures which block all or a portion of the longshoresediment transport), or can be captured by inlets and submarinecanyons.

In the case of a jetty, the result is a buildup of the beach along the updriftside of the structure and an erosion of the beach downdrift of thestructure.

The impacts pose problems to the adjacent beach communities, as well asthreaten the usefulness of the adjacent navigable waterways (channels,harbors, etc.)



Longshore sediment transport

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Longshore sediment transportThe direction of longshore transport is directly related to the direction of

wave approach and the angle of the wave crest to the shore.

Thus, due to the variability of wave approach, longshore transport directioncan vary from season to season, day to day, or hour to hour.

The rate of longshore transport is dependent on the angle of wave approach,duration and wave height. Thus, high storm waves will generally movemore material per unit time than that moved by low waves.

Because reversals in transport direction occur and because different typesof waves transport material at different rates, two components of thelongshore transport rate (net & gross) become important.

Most shores consistently have a net annual longshore transport in onedirection.

Determining the direction and average net and gross annual amount oflongshore transport is important in developing shore or highwayprotection plans.



Estimation of Longshore sediment transportCERC formula, adopted by US Army corps of engineers, in SPM (1966).

The potential longshore sediment transport rate, dependent on an availablequantity of littoral material, is most commonly correlated with the so-called longshore component of wave energy flux or power,

where Eb is the wave energy evaluated at the breaker line,

And Cgb is group velocity at breaker line;

where is the breaker index Hb/db.

The term (ECg)b is the wave energy flux evaluated at the breaker zone, andb is the wave breaker angle relative to the shoreline. The immersedweight transport rate Il is given as;

K is an empirical proportionality coefficient.

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Estimation of Longshore sediment transportApplying Pl;

For shallow water breaking;

Or, after simplifying;

In engineering applications, the longshore sediment transport rate isexpressed as the volume transport rate Ql having units such as cubicmeters per year.

Applying Il in the above equation;



Estimation of Longshore sediment transport

Variation of K with sediment grain size

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Estimation of Longshore sediment transport - Problem(1) With Hbrms=2m, =1025kg/m3, s=2650kg/m3 and b=4.5, D50=1mm.

Assume, n=0.4, =0.15 & K=0.65; Calculate the (a) potential immersed-weight and (b) volumetric longshore sand transport rates.

Soln:

(2) The energy density of waves with a peak period of 10sec is measured tobe Eo=2.1x103 N/m, in a deep-water location. The waves make an angleof o=70 with the coast at the this location, but after refraction, the angleat the breaking is found to be b=30. Assume K= 0.6.

Soln: - Calculate group speed of the waves in deep water (Cg)

-The energy flux/unit length in deep water is;

-By conservation of energy flux;

-longshore comp. of the energy flux @ shoreline is;

-Volumetric sand transport rate;



Estimation of Longshore sediment transportGross & Net longshore sediment transport

Cross-shore distribution of longshore sediment transport

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Equilibrium shape of headland-bay beach


Headland-bay equilibrium shoreline shapesarise through wave sheltering bydiffraction at the object serving as theheadland, combined with refraction, whichwill dominate with distance along thebeach away from the headland.

Theoretical shapes

-Log-spiral

-Parabolic bay



Log-spiral

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Parabolic



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Cross-shore transportDuring storm, strong winds generate

high, steep waves. In addition,storm also increase the water leveland exposes the higher parts ofthe beach to wave attack, which isnot ordinarily vulnerable towaves.

The storm surge allows the largerwaves to pass over the offshorebar formation without breaking.

When they finally break, remainingenergy is spent in erosion of thebeach.

The eroded material is carriedoffshore and deposited at bottom,thus forming a berm.

Inlet dynamics


Hydrodynamics of tidal inletsInlets provide access to man & nature between the ocean and a bay/land

enclosed water body.

At the throat of the inlet (min c/s) and bayward, tidal currents are thepredominant forcing agent interacting with sediments.

On the seaward and alongshore away from the inlet, the effect of wavesincreases.

Waves contribute sediment from adjoining beaches & tidal currents movethem in & out of bay.

Sediment may again be moved to adjoining beaches by the combination ofwaves and currents, thus bypassing the inlet.

The interaction of tidal currents, waves, and wave-generated currents is acomplex process.

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Inlet dynamics


Various features of sediment dynamics along the shore

Typical tidal inlet features

Inlet dynamics


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Next.Coastal Erosion & protection


Part 02 Ce 769 Oe Mtech Brn Moodle

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