CEPD03 Coastal Sediment Transport 3

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Coastal Sediment Transport

CEPD03

Lecture 3

Prof. Dano Roelvink

Dr. Jan van de Graaff

http://www.tudelft.nl/

http://www.unesco-ihe.org/



Contents

• Overview of problems

• Bed shear stress by waves and current

• Sediment transport by waves and current

• Longshore sediment transport• Cross-shore sediment transport

• Coastline changes

• Dune erosion• Sedimentation in channels and trenches

• Stability of channels and inlets





Exercise about lectures 1 and 2

• V=0.7 m/s

• H=1 m

• h=2 m• T=7 s

• D50=0.2 mm; D90=0.3 mm

• r=0.05 m• Compute

0, , , , , ,c w w cw b su f S S





Longshore transport

• Simple method to estimate longshore

velocity

• Use estimated wave height in surf zone

• Derive radiation stress gradient from this

• Balance radiation stress gradient with

bottom shear stress





Radiation stress









Longshore wave forces

cos sin

yy xy

y

S

F x

n x

S

y

E





















cos sin

sincos

sin

cos

sincos

xy g

y

g

g

g

S C F E x x C

EC x C

EC x C

EC

C x
























sincos

sincos

sin( )

y g

g

w y

F EC x C

EC C x

D F

C

=0

(Snel’s

Law)





































































Assignment

• Hs0=3m, T=8s,

• Angle of incidence:

• 75,60,50,45,40,30,20,10 deg.• Compute conditions at breaker line

• Compute longshore sediment transport

using coefficient B=0.04

0.7





Contents

• Wave energy balance

• Dispersion relation

• Wave celerity and group velocity

• Snel’s Law • Shoaling and refraction

• Wave breaking

• Dissipation

• Solving 1D energy balance

• Radiation stresses and wave forces





Wave energy balance

2 2 2

cos sin

1 1

2 8

g g

rms

E EC EC D

t x y

E g ga gH

Wave energy Group

velocity

Wave angle Wave

dissipation

















Dispersion relation

• Relation between wave period T and wave

length L for given water depth

2

tanh( )2

2

1

2 sinh(2 ) g

gk kh

T

Lk C L T k

d khC nC C

dk kh














Deep water

22

tanh( ) 1 sinh( )

2

2

2

1

2 g

kh kh

gk k g

T

L g gT

k C L T k

d C nC C

dk













Shallow water

2

tanh( ) sinh( )

( ) /

2

2

1

2 sinh(2 ) g

kh kh kh kh

gk kh k gh

T

Lk C g h

L T k d kh

C nC C ghdk kh














Wave refraction

05102030

Depth

contours

Wave rays

Wave crests






Snel’s Law

• Valid for straight contour lines

• Relates local wave angle to deep water

wave angle

0

0

sin sin

c c








Wave breaking

• Complex process

• Various approximations, e.g.

– Battjes and Janssen, 1978

– Thornton and Guza, 1983

– Roelvink, 1993

– Baldock, 1998





Baldock model

2

max

2 2

max

1

4ms

H

H

w p rms D g f e H H

max

0.88tanh( )

0.88

kh H

k

Coefficient

~1

Coefficient

~0.6-0.8















1D Wave energy balance

cos sin g g w

E EC

t y EC D

x

Wave energy Group

velocity

Wave angle Wave

dissipation



















Solving 1D wave energy balance

• Outside surf zone:

– Wave energy flux is constant

– Group velocity follows from dispersion relation

– Wave angle follows from Snel’s Law

0 0 0

cos 0

cos cos

g

g g

E C

x EC E C












Shoaling and refraction

• Shoaling is change in wave height due to

change in group velocity

• Mostly increasing towards shore

• Refraction is bending of wave rays

towards shore, leads to decrease of wave

height because energy is spread over

wider area





Wave refraction

05102030

Depth

contours

Wave rays

Wave crests







• Inside surf zone:

– Group velocity follows from dispersion relation

– Wave angle follows from Snel’s Law

– Dissipation follows from e.g. Baldock, relating wavedissipation to wave energy and water depth

– Solve E numerically, starting from known value

outside breaker zone

cos ( , ) g w EC D E h x






• Very simple numerical scheme:

1 , 1 1 ,

,

1

, 1 1

cos cos( , )

cos ( , )

cos

i g i i i g i i

w i i

i g i i w i i

i

g i i

E C E C

D E h x

E C D E h x

E C

















Radiation stresses

xxS

xxS

yxS yxS

yyS

yyS

xyS

xyS





Wave forces

xy xx x

xy yy

y

S S F x y

S S F x y
















Radiation stresses

2

2

1cos

2

cos sin

1sin

2

xx

xy yx

yy

g

S n n E

S S n E

S n n E

C n

C















Wave forces

• Follow from radiation stress gradients

• Radiation stresses are function of wave

energy, wave direction and ratio wave

celerity to group velocity

• In 1D case we can compute all these

easily



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CEPD03 Coastal Sediment Transport 3

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