Wave Hydrodynamics

.

Beach Terminology

The inner shelf is a friction-dominated realm where

surface and bottom boundary layers overlap.

(From Nitrouer, C.A. and Wright, L.D., Rev. Geophys., 32, 85, 1994. With permission.)

Conceptual diagram illustrating physical transport

processes on the inner shelf.

(From Nitrouer, C.A. and Wright, L.D., Rev. Geophys., 32, 85, 1994. With permission.)

Ocean Waves

Ocean waves may be classified by the generating force

(wind, seismic events, or gravitational pull of the moon),

the restoring force, (surface tension, gravity, the earth’s

rotation), or the frequency of the waves.

Idealized Ocean Wave Spectrum

Wind Waves

A wind wave is

generated by the

friction of the wind

over the water’s

surface.

As the wind blows over the surface of the water, friction and pressure

differences create small ripples in the water surface.

The wind pushes on the back side of the wave and pulls on the front,

transferring energy and momentum to the water.

As the wind continues to transfer momentum to the water, the wave

becomes higher.

Wave Growth

The area where wind waves are form and grow

is called the generation area.

Higher wind speeds mean more momentum to transfer to the water,

resulting in higher waves.

Duration is the length of time the wind is blowing. The longer the

wind blows, the higher the waves and more chaotic the seas.

The heights of the waves in the generation area are determined by three

factors: wind speed, duration, and fetch.

Fetch

Fetch is the horizontal distance that the wind blows across

the water.

Fetch is important in the early stages of wave formation, and will

control how large the wave will be at a given time.

Swell

As deep-water waves depart the generation area,

they disperse with the long waves travel faster. This sorting by wave speed creates long regular wave patterns

called swell.

Shoaling Waves

As a wave shoals (approaches the shoreline) the wave period

remains constant, causing the wavelength to decrease and the

wave height to increase.

Friction slows the bottom of the wave to while the top continues

at the same speed, causing the wave to tip forward.

When H/L, the

ratio of the wave

height to

wavelength,

reaches the

critical value of

1/7, the wave

breaks.

SEAS

Waves under the influence of

winds in a generating area

SWELL

Waves moved away from the

generating area and no longer

influenced by winds

SMALL AMPLITUDE/FIRST

ORDER/AIRY WAVE THEORY

1. Fluid is homogenous and incompressible, therefore, the density is a constant.

2. Surface tension is neglected.

3. Coriolis effect is neglected.

4. Pressure at the free surface is uniform and constant.

5. Fluid is ideal (lacks viscosity).

SMALL AMPLITUDE/FIRST

ORDER/AIRY WAVE THEORY

6. The wave does not interact with any other water motion.

7. The bed is a horizontal, fixed, impermeable boundary which implies that the vertical velocity at the bed is zero.

8. The wave amplitude is small and the wave form is invariant in time and space.

9. Waves are plane or low crested (two dimensional).

Can accept 1, 2, and 3

and relax assumptions 4-9

for most practical solutions.

WAVE CHARACTERISTICS

T = WAVE PERIOD

Time taken for two successive crests to pass a given

point in space

Definition of Terms

ELEMENTARY, SINUSOIDAL,

PROGRESSIVE WAVE

h=eta

WAVE CELERITY, LENGTH,

AND PERIOD

PHASE VELOCITY/WAVE CELERITY:

(C) speed at which

a waveform moves.

Relating wavelength and H2O depth to celerity, then

Since C = L/T, then is

NOTE: L exists on

both sides of the

equation.

DEEP WATER:

Since:

Then:

Here, Since:

Then:

When d/L >0.5 =

DEEP WATER

1. Longer waves travel faster than shorter waves.

2. Small increases in T are associated with large increases in L.

Long waves (swell) move fast and lose little energy.

Short wave moves slower and loses most energy

before reaching a distant coast.

MOTION IN A SURFACE WAVE

Local Fluid Velocities and Accelerations

(VERTICAL)

(HORIZONTAL)

Water particle displacements from mean position for

shallow-water and deepwater waves.

As waves approach a shoreline the water shallows and they change

from deepwater to transitional waves.

As water shallows the waves steepen and finally break to form surf

which surges towards the shoreline.

When surf reaches the beach it rushes up the beach face as swash

and then runs back down the slope as backwash.

Swash and backwash moves sediment up and down the beach face.

SUMMARY OF LINEAR WAVES

C = Celerity = Length/Time

Relating L (Wavelength) and D (Water Depth)

Since C = L/T, then becomes:

Since C = L/T, then becomes:

PROBLEMS

GIVEN: A wave

with a period T =

10 secs. is

propagated

shoreward from a

depth d = 200m to

a depth d = 3 m.

FIND: C and L at

d = 200m and

d = 3m.

WAVE ENERGY AND POWER

Kinetic + Potential = Total Energy of Wave System

Kinetic: due to H2O particle velocity

Potential: due to part of fluid mass being above trough.

(i.e. wave crest)

WAVE ENERGY FLUX

(Wave Power)

Rate at which

energy is

transmitted in the

direction of

progradation.

Summary of

LINEAR (AIRY) WAVE THEORY:

WAVE CHARACTERISTICS

Regions of validity for various wave theories.

HIGHER ORDER THEORIES

1. Better agreement between theoretical and

observed wave behavior.

2. Useful in calculating mass transport.

HIGHER ORDER WAVES ARE:

• More peaked at the crest.

• Flatter at the trough.

• Distribution is skewed above SWL.

Comparison of second-order Stokes’ profile with linear

profile.

USEFULNESS OF

HIGHER ORDER THEORIES

MASS TRANSPORT VELOCITY = U(2)

The distance

a particle is

displaced

during one

wave period.

NB: Mass transport in the direction of propagation.

HIGHER ORDER WAVES

Stokes

• Takes wave height to 2nd order (H ) and higher

• Useful in higher energy environments

2

2nd order approximate wave profile is:

If H/L is small, then profile can be represented by linear wave theory

For deep H2O – Eq. reduces to:

THIRD ORDER APPROX. (Wave Velocity)

NB. If (H/L) is small, use linear wave theory equation.

TERM: Peaks crests

Flattens troughs

Conforms to shallow H2O wave profile

VELOCITY OF A WAVE GROUP

WAVE GROUP/WAVE TRAIN

Speed not equal to wave travel for individual waves

GROUP SPEED = GROUP VELOCITY (Cg).

INDIVIDUAL WAVE SPEED = Phase velocity or wave

celerity.

Waves in DEEP or TRANSITIONAL WATER

In SHALLOW WATER

K = .4085376 YT = 1.065959

Keulegan and Patterson (1940) Cnoidal Wave Theory

SI Units (m) Wave Height = .25 Wave Period = 2 WaterDepth = 1.1

Deep Water Length = 6.24 Present Length = 3.757897 Elliptical Modulus = .4085376

Net Onshore Displacement Umass = Mass Transport Velocity

Time U(T) UMassSediment

Transport

Airy Wave Theory LO = 6.24 L = 5.783304

T = 2s

H = 0.25m

D = 1.5m

NB. Umass

Symmetry

Time U(T) UMassSediment

Transport

Airy Wave Theory LO = 6.24 L = 5.363072

T = 2s

H = 0.25m

D = 1.1m

Depth at which C.T.

took place

44

Deformasi Gelombang

• Breaking

• Refraction

• Diffraction

• Reflection

45

Refraction

• Waves travel more slowly in shallow water

(shallower than the wave base).

• This is called refraction

• This causes the wave front to bend so it is more

parallel to shore.

• It focuses wave energy on headlands.

46

Wave Refraction

Eu

rop

ean

Coas

t, 1

99

6

Orthogonal

Surf / Breaker

Zone

Beach

47

Wave Refraction

Seabed contour

Wave Crest

Path of crests diverge

and minimize impact of

waves on shore

Seabed contour

Wave crest

Path of crests converge and maximize

impact of waves on shore

Shallow

Deep

48

Long shore Transport

49

Wave Diffraction

50Orthogonal Wave Crest

Orthogonal

Energy Transfer

Wave Diffraction

Breakwater

Hi

Hd

r

L

b

q

Shadow Zone

Wave Diffraction

Diffraction

Coeficient

( K’ )

K’ = Hd / Hi

K’ = f (r/L, b,

q)

51

Refleksi Gelombang

Eu

rop

ean

Coas

t, 1

99

6

52

Refleksi Gelombang

Untuk dinding vertikal, kedap air, dgn elevasi diatas muka air, hampir seluruh energi akan dipantulkan kembali ke laut.

Hanya sebagian saja energi yang dipantulkan jika gelombang menjalar di pantai yang agak landai

Refleksi tergantung pada kelandaian pantai, kekasaran dasar laut, porositas dinding, dan Angka Irribarren (Ir) :

tanr

i

o

IH

L

Kr = Hr / Hi

Kr = fungsi (a,

n, P, Ir)

53

Perbedaan Gelombang

WAVES – BREAKING

Dean and Dalrymple, 2002

o

o

LH

b

tan5.0

3.35.0

3.3

Suntoyo

Hp. 081230988146

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