NUMERICAL S W PHYSICAL MODELING - uni- · PDF fileNumerical Si mulations ofW ave Pro pagation...

Numerical Si mulations of W ave Pro pagation comp ared to Phys ical Modeling

NUMERICAL SIMULATIONS OF WAVE

PROPAGATION COMPARED TO

PHYSICAL MODELING

Authors:

Stephan Mai

Nino Ohle

Karl-Friedrich Daemrich

Table of Contents

1. Introduction

2. Physical Modeling

3. Numerical Modeling

4. Comparison of the Results

5. Conclusion and Discussion

Dipl.-Phys. S. MaiDipl.-Ing. N. OhleDr.-Ing. K.-F. Daemrich

EXPERIMENTAL RESEARCH AND SYNERGY EFFECTS WITH MATHEMATICAL MODELS

Hydralab 99

Introd uction

1. Introduction

Wave propagation within coastal zones is strongly

influenced by coastal morphology

Predominant processes in the coastal zone are:

Investigations:

• Measurements of the wave propagation along a foreland with and without

a submerged dike (summer dike) in the large wave tank of the FZK

• Numerical simulation of some of the above processes with standard wave

models

• Test of the models by comparing the simulation results with the physical

model - Adjustment of the parameters bottom friction and wave breaking

• Calculation of the transmission coefficients



Introduction

Map and cross -section of a summe r dike

2. Physical Modeling

Location and topographical map of a summer dike:

Cross-section of a summer dike:

drainagesystem

berm

sand

13.00 3.00 13.00 5.00

clay 50cm 50cmclay

5.50

NN+1.7 m 1:7 1:12 1:7NN +1.7 m

NN+3.5m

1:7

seawardside

landwardside

NN+0.0m



Map and cross-section of a summer dike

Summer dike i n natur e and as model

Summer dike in nature Summer dike in model

Due to the grass sods and the flat slope the dike is difficult to be seen. Concrete coverage replaces clay and grass sods



Summer dike in nature and as model

Experi ment set-up an d measuremen ts in the large wave tank

40 m 3 m

B

1:7 1:7

0,5 mNN

2,0 mNN

3,5 mNN

2,0 mNN

waddensea foreland summer dike polder

-Rc

wave generator

mNN= meter above German datum

0

2

4

0 25 50 75 100 125 150 175 200 225

x [m]

d[m

]

x [m]

H[m

]s

0 25 50 75 100 125 150 175 200 2250

1

2

0 25 50 75 100 125 150 175 200 225

0

4

8

T[s

]m

wave gauges:

mean wave period

x [m]

wadden sea foreland submerged dikeforeland /polder

significant wave height



Experiment set-up and measurements in the large wave tank

Calculation of the t ransmiss ion coef ficient

-2.5 -2.0 -1.5 -1.0 -0.50.0

0.2

0.4

0.6

0.8

R /H [-]c S

c[-

]T

,S

0.23 < w < 0.290.29 < w < 0.36

classification:

measurement: by d'Angremond (modified):w = 0.23w = 0.29w = 0.36

ξw=0.58 (B/H ) (1- e )S

-0.48 -2.59

summer dike

c = - 0.41 (R /H ) + wT c s

transmission coefficient:

Calculation of the transmission coefficient:

• cHHT

T= cT: transmission coefficient

HT: transmitted wave heightH: incoming wave height

• d’Angremond (1996): 0,075< cT <0,80 - slopes: tanα > (1:4)

( )cRH

BH

eTC

S S

= − ⋅ +

−

−− ⋅β β

ββ ξ

1 2

3

41RC: freebordHS: significant wave heightB: crest widhtH/L: steepness

• ξ : Iribarren-Number, ( )ξα

=tan( )

,HL

0 5

• β1 = 0,41 β2 = 0,58 β3 = 0,48 β4 = 2,59



Calculation of the transmission coefficient

Transmiss ion coef ficient (measured by dif fe rent autho rs )



Transmission coefficient (measured by different authors)

Theor etical Backgro und of t he Nume rical P rogra ms

3. Numerical Modeling

Standard Wave Models (used):

• HISWA

HIndcast Shallow Water WAves, TU Delft

• SWAN

Simulation WAves Nearshore, TU Delft

• MIKE 21 EMS

Mike 21 Elliptic Mild Slope, Danish Hydraulic Institute

Basic Model Equations:

• HISWA and SWAN

Action Balance Equation

⇒ Wave Breaking by Battjes and Jansen (1978)

⇒ Bottom Friction by Collins (1972) and Madsen (1988)

• MIKE 21 EMS

⇒ Wave Breaking by Battjes and Jansen (1978)

⇒ Bottom Friction by Dingemans (1983)



Theoretical Background of the Numerical Programs



Theoretical Background of the Numerical Programs

Dissipati on o f w av e e ne rgy due to w ave br ea king

Numerical formulation of wave breaking - Formula by Battjes and Jansen:

⋅

γγγ=

−=

−ρα= dktanh

kH,

H

H

Qln

Q1,HgfQ

4D

1

21max

2

max

rms

br

br2maxbrbr

D br : mean dissipation rate per area

Q br : fraction of breaking waves

ρ : water density

H rms : root mean square

H max : maximum wave height

α, γ1, γ 2 : adjustable coefficients

Dissipation of wave energy S ds, br due to wave breaking:

• HISWA: S DE

Eds br x y brx y

tot x y, ( , , )

( , , )

( , )θ

θ= − ⋅ , where E E dtot x y x y( , ) ( , , )= ∫ θ θ

• SWAN: S DE

Eds br x y brx y

tot x y, ( , , , )

( , , , )

( , )σ θ

σ θ= − ⋅ , where E E d dtot x y x y( , ) ( , , , )= ∫∫ σ θ σ θ

• MIKE 21 EMS : ED

ebr

br ∝ .





Dissipation of Wave-Energy due to Wave Breaking



Dissipation of Wave-Energy due to Wave Breaking



Dissipation of wave energy due to wave breaking

Diss ipation of wave ene rgy due to b ottom f riction

Dissipation of wave energy S ds, b due to bottom friction:

• HISWA: S Cg k d

Eds b x y bot x y, ( , , ) ( , , )sinh ( )θ θσ

= −⋅ ⋅

02

2 20

• SWAN: S Cg k d

Eds b x y bot x y, ( , , , ) ( , , , )sinh ( )σ θ σ θσ

= −⋅ ⋅

2

2 2

k0 .σ0 : mean wave number and mean wave frequency

C bot : friction coefficient.

• MIKE 21 EMS - Formula by Dingemans

Df

g

H

k dbe rms=

⋅ ⋅⋅

⋅

16

3

πω

sinh( ) , f

K

a

KKe

N

b

NN

=

<

− + ⋅

≥

−0 24 2

5 977 5 213 20 194

. /

exp . . /.

, a

, a

b

b)

and e D Ef b∝ /

E g H rms= ⋅ ⋅ρ 2 8/ : energy density of the wave field

fe : energy loss factor.

Bottom friction coefficient C bot:

• Collins:C C g ubot fw rms= ⋅ ⋅

and uk d

E d drms x y=⋅∫∫

σσ θσ θ

2

2sinh ( ) ( , , , )

• Madsen: C fg

ubot wr rms= ⋅ ⋅2 ,

1

4

1

4f fm

a

Kwr wrf

b

N

+

= +

lg lg

ak d

E d db x y2

2

1=

⋅∫∫ sinh ( ) ( , , , )σ θ σ θ

u rms : orbital velocity at the bottom

KN : equivalent Nikuradse bottom roughness

a b : representative near-bottom excursion amplitude

C fw, f wr , m f : model parameter



Dissipation of Wave-Energy due to Bottom Friction



Dissipation of wave energy due to bottom friction

Simulation of t he s ignificant wave height by dif fer ent wave mode ls

0 25 50 75 100 125 150 175 200x [m]

0.00

1.00

2.00

3.00

4.00

5.00

wat

erle

velz

[m]

waterlevel

wavedirection

waterdepth: d = 4.0 msig. wave height: Hs= 1.0 mpeak period: Tp= 8.0 s

boundary conditions:

forelandsummer-

dike polder



Simulation of the significant wave height by different wave models

Comparison of the results (tr ansmiss ion coefficients )

4. Comparison of the Results

Comparison of the transmission coefficients :

Boundary conditions of thephysical and numerical models

No. of test cases : 42 (36)

water level : z = 3.5 m up to 4.5 m

incoming significantwave height : H = 0.6 m up to 1.2 mS

P

incomingpeak-period : T = 3.5 s up to 8.0 s






Comparison of the results (transmission coefficients)

Conclus ion and discuss ion - Calibration par ameters

5. Conclusion and Discussion

Adjustment of the parameters bottom friction and wave breaking:

NUMERICAL MODEL DISSIPATION

PROCESS HISWA SWAN MIKE 21 EMS

Wavebreaking

α = 0.95γ1 = 0.85γ2 = 0.95

α = 1.45γ = 0.75

α = 1.0(not adjustable)

γ1 = 1.05γ2 = 0.85

Bottomfriction

C fw = 0.01 KN=0.02 KN = 0.03

Summary:

• All Standard numerical wave models worked well.

• Still it is necessary to calibrate the models.

• This can be done with physical models or field data.

• Advantage of physical models are the well defined boundary conditions.

• Difficulties of field measurements are costs, extreme and unreliable

boundary conditions.






Conclusion and discussion - Calibration parameters



Conclusion and discussion - Calibration parameters

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