Proceedings of the Shallow Water Hydrodynamics, With special attention to effects on floaters, NTNU, 19 December 2005, Trondheim, Norway

with special attention to effects on floaters

Monday, 19 December 2005

at Marine Technology Centre, Otto Nielsens Vei 10, Auditorium T7

Organized by CeSOS/ MARINTEK/ NTNU

Trondheim, Norway

Programme:

09:30 - Opening

Prof. Odd M. Faltinsen, CeSOS : "Hydrodynamic activities at CeSOS"

Prof. Chiang C. Mei, MIT, "Nonlinear resonance of long waves in a harbour by

short random waves"

Prof. Bjorn Gjevik, Ui0, "Modelling of tidal currents, shelf edge eddies and

tsunamis with shallow water equations"

Prof. Jo Pinkster, TU Delft, "Computations of forces and motion

_{response to}

arbitrary fluid motions around stationary vessels"

12:00 - Lunch

Carl T. Stansberg, MARINTEK/CeSOS, "Laboratory generation of

wave-group-induced long waves"

Rong Zhao, MARINTEK/CeSOS, "Shallow water waves and interaction with large

structures - activities at MIT/ExxonMobil"

Per Teigen, Statoil, "Diffraction analysis of shallow water barge response"

Bas Buchner and Radboud van Dijk, MARIN, "Overview of Shallow

_Water

Initiative (Hawai) JIP"

XiaoBo Chen, Bureau Ventas, "New aspects of second-order

_{wave loads"}

Discussion

15:30 - Meeting ends

16:00 - Lab tour

P2005-10

Participants

Organization

Marintek /CeSOS.

1.-

Carl Trygve Stansberg

2.-

Prof. Chiang C. Mei

MIT

3.-

Rong Zhao

Marintek /CeSOS.

4.-

Per Teigen

Statoil

5.-

Prof. Odd Faltinsen

CeSOS.

6.-

Prof. Bjorn Gjevik

Ui0

7.-

Fldvard Austefjord

DNV

8.-

Arne Nestegdrd

DNV

9.-

Prof. Jo Pinkster

TU Delft

10.- Bas Buchner

MARIN, NL

11.-

Radboud van Dijk

MARIN, NL

12.-

Geir Loland

Statoil

13.- XiaoBo Chen

Bureau Ventas

14.-

Kjell Larsen

Statoil

(0

15.-

Trygve Kristiansen

CeSOS

16.-

Prof. John Grue

Ui0

17.-

Tor Vinje

Aker Marine Contractors

Hydrodynamic activities at

CeS0S

0.M .Faltinsen, CeSOS.NTNU

Breaking

Fragmentation

Air entrainms

Viscosity

Pholo of tho Bluo Planal from Apollo 17 in Decembor 1972

tttittaAppeoaches for Vilave-liedy

_interaclion

,r

,itk,t

IBEMI

VVetdeck slamming on offshore

plafforms

Problem Modelling and SoltitioiL

air entrapm,

nvadelirrTgl

4 . . .

Water exit of a neutrally buoyant

cylinder

& hod, 1744.49 1544.75 1345 114525 945.505 745.758 546.011 346164 146.518 -53/293 -252.976 -452.723 -652.47 -852.215 -1051.96

Accidental drop of pipe from

platform

Water entry of a neutrally buoyant

cylinder

Hammer-Fist Type WOD

Plunging type water on deck

(WOD)

Hammer-Fist Type WOE

Hammer-Fist Type WOD

Hammer fist and karate

I' esi. &made : S-L

. Main grid Dar ship with

A

Constant spe Uu

11..

-,

incident wave as BC -

\

,

,

,

SPH

SLOSHING

Multi-modal approach

Potential flow, no overturning waves

Vertical wall and no tank

_roof

Free surface elevation for 2-D flow

Oi(t) cos

('(x73.51))

L

Ordering of

_Pi-terms

Nonlinear ordinary differential equations

for

pi

3D extension of multimodai method

to square based tank

Possible steady-state wave motions are

- planar waves (2D)

- sguare-like (diagonal) waves

- swirling

No stable steady wave motions may exist

Comparison between theory and

experiments

Theory predicts more than one stable

steady-state wave type for certain

frequencies

Wave type with smallest amplitude is then

most likely

Longitudinal excitation. Amplitude :0.078_

0.6 0.55 0.5 0.45

T 0.4

0.35 0.3 0.25 0.2 chaotic 1.1

-a

al

ID chaotic 0.6 0.55 0.5 0.45

T 0.4

0.35 0.3 0.25

Flow types in square basad tank with longitudinal excitation.

Effect of fluid depth

chaotic 0.6 0.55 0.5 0.45

T 0.4

0.35 0.3 0.25

02

I '

09

095

1I0

105

'

a

D planar

DI 'squares'-like D swirling

CI chaotic

0.2

-planar

.

swirling

Swirling

chaotic

a-ct,

swirling ID chaotic

1.05 1.1 0.9 0.95 1.0 1.05

planar

'squaresHike D swirling

0.9 0.95 1.0

0.6 0.55 0.5

0.45

li

0.4 0.35 0.3

-planar

chaotic

1+-4- swirling

S planar

0.25 -

... ---..._-0.2 ' I o-0:9 0:95 1'.0 1.05 11

(n

0 planar

_{ID 'sguares'-like 0 swirling CI chaotic}

0.6 0.55 0.5 0.45

T 0.4

0.35 0.3 0.25

-planar

0.2 0.9 o planar chaot c

- swirling

planar

-800

Amplitude 10mm, frequency 0.96Hz, filling level 633mm

Strain (AS) 150 100 50 -100

3.

2.

Impact starts 800 Time (s) Tank motion

rI70

0.6 0.55 0.5 0.45

T 0.4

0.35 0.3 0.25 0.2 chaotic

planar D 'sguares'-like

nnpacts with air

ir pocket. is

te

tafnrkgibcti5ofrfilet(16:71r6T1 ':11:1661,'

Impressibility of

air results in

oscillating

pressure

1.05 1.1

-2:

0'i.

swirling D chaotic

01 02 025 03 035 0 50 00 1 (51 ienoOlICY 0-1O "ge,

ertmnal in shallow water.

5111

7

0.9 0.95 1.0 0.95

10

105

1. 1 CT o

squares'-like D swirling

1:1 chaotic

Wash in finite water depth

Boussinesq-type equations by Nwogu

incorporation of the ship by either

slender ship theory or

hybrid method

Generalization to the incident wave

problem

Replenishment.

Seakeeping and

maneuverir-Hydroelastic behavior of seismic

cables

Vvave

rappir4.4

Dynamic

stability-Strong nonlinearities may occur

Heel may cause sign change in yaw

moment at relatively small heel angle

Major achievements

Sloshing

Development of the multimodal method.

Discovery of new flow phenomena.

Slamming

Understanding of the effect of cavities and

hydroelasticity

Green water on deck

Development of numerical rnethods.

Understanding of flow phenomena.

Planing craft

Large-scafie intercon net= te6

structures

-s--Potential use:

Sea farming in weather

exposed areas are

considered.

- Mobile installations.

- Flexible/rigid structures

Planned hydrodynamic activities

Shallow water terminals

Ship-ship interactions. Moonpools

Damaged ship

Nonlinear hydroeiastic behavior of VLFS

Nonlinear wave loads on floaters of fish farms

Dynamic stability and maneuvering of semi-displacem en!

vessels

Springing of ships

Sloshing and slamming

Nonlinear ship motions with green water and slamming

Long-period Harbor Oscillations

due to Short Random Waves

Meng-Yi Chen & Chiang C. Mei

Massachusetts Institute of Technology

12/19/2005

_{Shallow Water Hydrodynamics,}

1

Typhon Tim 1994:

Hualien HarborlTaiwan

3.0

0.0

I...

Spectral in Ha

140E-LIE0 Ma.-boo-

.00

2994/07/10. /500 129 tried

TIPh-TYPrION

outside

61S 100 JO

Pr2oc115.01

I SO

ok

-3ide

0.0-1--20 013

ic

ea 100

do

H60 163 I00 203

Per lod 1561

MM., lEm Him-ber"

22

1999/07/10. 16: 00 130 MI. TIP1,1,110N

jklik

inside

0o 2201 120I /40 10 180I

'

209

Period 1Sec 1

994-1 I EN Harlow- .06 1999/07/10. i 61 00 160 1,In1 11P4-TYPHON

03 100 120 10

Potelod ISes1

T (sec)

200

plAw-LIENHa,tm, .99 3990/07/10.M00 130 P2In1 TIM-7,1,10N

3.0

,

inside

401, 010

do

PriodlSo<1

Mar-Imm-

.10

1994/07/10. 16: 00 130 MIN TIM-TTPKOM

H22

inside

10071010. 01.16

IInstitute of Harbor

Marine Techno/ogy

12/19/2005

Shallow Water Hydrodynamics,

2

H t. 3

0.3

0 0

#00

#05

#22

#8

#10

Port of Hualien

lz

4

I

a

12/19/2005

Shallow Water Hydrodynamics,

₃

Trondheim, Norway

'7

10

106

7-_-E

1O2

101

100

1994.07.10 12;00 TIM TYPHON

I

ILIHIH

I

111M111

2

Legend Tstle

e

408

#10

A-- *22

ST. 2 1

1111111

1 1

1111111

10-3

10.2

10-1

FREQUENCY (HZ)

OUTER

BASIN

INNER

BASIN

Typhoon Longwang, Oct. 2nd

2005

12/19/2005

_{Shallow Water Hydrodynamics,}

₅

Past Works

Harbor Oscillations

-

Linear theory

Miles & Munk (1961), Miles( 1971), Lee(1971),

Unluata & Mei (1973), (1978)5 Carrier,Shaw &

Miyata(1971)

Nonlinear approximation

--

narrow-banded

Bowers(1977), Agnon & Mei (1989), Wu & Liu (1990)

Standing

waves near a

cliff-Random

sea

Sclavounos (1992)

Stochastic theory

Simple progressive and standing wave in

deep water

Incident

_{waves: stationary, Gaussian}

Higher order spectrum depends

on

first, second, and third-order

Shallow Water Hydrodynamics,

₇

Correlation

H()

( (t) (* (t +

T)

S (w)

1 f

oc

dT ei

w T

H

(T)

27r

-Do

(

(1 + (-2 + (3 +

Stationary and Gaussian Incident wave

(nx,

y,

t)

-

r

A(,),ik.xwtdu;

oc

f

Do

j

A (w)

eik(w)r co

6s(19

V)iwt

dw

,

Gaussianity

A (w

1

)

A

(w2 )

A

(c.03 )

0

.. .

H(T)

H2(7) +

H4(T) +

H3

=O

H2

(1 (t)(*(t + T),

H4

_{H22 + H13 + H31}

H22

(2G, H13

-1_

0

,

H31

Spectrum

S(w)

_{s2(w) +}

_{s4 (w) +}

82

i=

f

271 J

112

(T)eiwTdT

12/19/2005

_{Shallow Water Hydrodynamics,}

₉

Trondheim, Norway

A(w)

Stationary & random

A

(c.44) A*

_(w2)

_S

_A

(wl) 6 (ui

-

_W2)

.

First order solution

00

(i_ (x, y, t)

f

A (w) r1 (x, y,

w)eiwtdw,

00

Wiener-Khintchine relation

S2

_{(x, y,w)}

_{sA (w) Iri (x7}

_Y,(-4))12

-Example of Jonswap spectrum

Higher orders

ff-00

A (w1) A (w2) F2 (x,

y, wi, w2)

e-i(w1±w2)tdwidw2,

(3 (x,

y, t)

_froo

A (w1) A (w2) A (w3)

-i

3

(x,

y, wi, w2, w3) e-i(w1+w2±w3)tdwidw2dw3

Frequency responses -2,

3

are to be found.

12/19/2005

Shallow Water Hydrodynamics,

11

After solving I-2 at second order,

S22 (w)

(o)

[(2]2

(w)

roc

GO

_{SA (w1)}

_SA(w

w1) r2(w1,w wi)

[1-2(wi,w

wl)

wi,

wi)] dwi,

For long-period response in a harbor, w

small.

1-2(w1,w2),

w2

w

is small

12/19/2005

Pairs of frequencies

F2(copco2)

_w

_{col +(02}

CO2

wa I \

wa

Shallow Water Hydrodynamics,

13

In principle one needs to solve F3 at

third order

to get

Do

S31 (w)

S (w) 1-1 (w)

S

A

(w2) [1-3 (w,w2, w2)

Do

±F3 (w2, Lo, w2) + [3 (W2,

c.t))] dw2.

For small

w,

SA(w)

0,

Hence Si3, S31

O.

No need to ge, F3.

10

Example of Jonswap spectrum

12/19/2005

Shallow Water Hydrodynamics,

14

Frequency

responses

By Mild slope Approximation

First-order

oi

=

f

A(04)

ig Fi(N)

coshk(h+ z)i

e

(0,-

t

do

coshkh

V (C1CgVF1)+[k2CCg

+U(N)

Chamberlain & Porter (1995)

V(N) Vh

00

4-1

JA(a)

11(N)e-iw

t

doA

-00

Far field

:

analytical solution +radiation condition

12Nigar field: FEM

_{Shallow Water Hydrodynamics,}

₁₅

Frequency response

r1

Linear Mild-slope approximation.

ig AGO

cosh k(z

+ h)

e_iwt

w

cosh

kh

w2

gk

tanh

kh

Chamaberlain & Porter

(1985):

V(CCg\71-1)-F

[k2ccg + uv2h± v(vh)2]1-1

o

col

A 2-D elliptic equation.

12/19/2005

Hybrid finite element method (Chen

& Mei,1974)

(HFEM)

Y

/

/

/

/

/

,

/ I / / / i 1 ,

>,--%

,

.

,

/

,

,

,

,

,

,

/

,

,

/

---Near Field

QA

Finite element

Far Field'-,,,

,

Q

F

'''

Analyticai'

,,,

, i ,

X

Shallow Water Hydrodynamics,

17

Frequency response I-2

For single frequency, 2nd order mild-slope

ap-proximation, Chen & Mei (2005 in press

JFM).

aa

cl)

2

+F, z = 0,

1

2 cl)

2

Oz

g

at2

where

F

if:

A(w1)

A (,02)

f (x,

y, c..4)1,

w2)

e-i(wi-kw2)tdwidw2

Assume

oo

132

()C7

t)

if

A (wi) A

(w2) 02 (X, W17 W2)

00

.ei(w1-k)2)tdwidw2

Solution:

02 (x,

col,

w2)

where

6-n,

=

(W1

+W2)2

ig1.,, '

6ncos

K

(z

+ h)

wi

-I-

_w2

rn-0

cos

Krnh

(x,

y,

_{wi, W2)}

g

K

tan

Kmh,m

0, 1, 2, 3,

Ko

iRo propagating mode;

Kim, 717,

1, 2, 3,

_...

evanescent modes.

,

12/19/2005

Shallow Water Hydrodynamics,

19

Second-order mild-slope

equa-tions

Applying Green's theorem to cos kn(z

h) and

01,

one gets the simultaneous mild-slope

equa-tionls:

Do

>f,{v.[A¡,,evk

Brn,,eVee Vh

Crn,ge}

f=0

(col + W2) f (x,Y,wi,w2)

= 0,1,

2,3,

Far field: Use 2D Green's functions.

Weak radiation condition for propagating mode

a

Him

_dS

₍₆₀

8G0

_r,

Goo )

o

nOr--'00 Soo

or

ar

After solution by HFEM, the

_seond-order

re-sponse function is

2

(X

Y W1.1 W2)

7w2

wiw2

2

_{1-1 (w1) 1-1}

(.02)+2wiw2V2r1

(W1)*V2r1 (w2)

g

2g

CXD

(u)

w

2)

f=0

12/19/2005

_{Shallow Water Hydrodynamics,}

₂₁

Square harbor, Normal incidence

300m by 300 m, depth h=20m

e

F270

Example of Jonswap spectrum 10 9

300m

cx 8 7 6 E 4 2 3 2

Effect of entrance

60 m opening without protection

30 m opening without protection

30 m opening with protection

0.2 04 0.6 0.8 1.2 1.4 1,6

landom

sea:

TMA Spectrum

70

6{I

_{14ATER DEPTH}

12/19/2005

_{Shallow Water Hydrodynamics,}

₂₃

Trondheim, Norway

(Li

0_3

First-order average response

IF#0)1)

L.-12

6

2

L.

6

4

2

2

o

go.

12/19/2005

60m, no protection

00

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1 8

12

30m, no protection

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

30m with protection

Shallow Water Hydrodynamics,

24

co (rad/sec)

1.1 1.2 1.3 1.4 1.5 1.6 1.7

1 8

1 . 1

1.2 1.3 1.4 1.5 1.6 1.7

1 8

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10

8

-CA

E

CID

Mean Linear

spectrum

100000

75000

50000

25000

O

06

100000

75000

50000

25000

o

100000

75000

50000

25000

o

06

u

66m,

no protection

30m, no protection

30m with

protection-.

ILL

1.1

1.2

1.3

w (rad/sec)

s2(c0)=s,(w) jrl

12)

20000 15000 cn <-4

SA(w)

0

0.2 0.4 0.6 0.8

1 1.2 1.4 1.6 1.8 2

2.2 2.4 2.6 2.8

3 (rad/sec)

12/19/2005

_{Shallow Water Hydrodynamics,}

₂₅

Trondheim, Norway

AA

41frk

...k

0.7

0.8

0.9

0 6

0.7

0.8

0.9

1.1

1.2

1.3

1.4

1.5

1.6

1.7

18

18

0.7

0.8

0.9

.1

1.2

1.3

1.4

1.5

1.6

1.7

30000 25000 5000 O

1.4

1.5

1.6

1.7

18

Second-order Mean: setup/down

12/19/2005

si(co,)F, (x,

y, co, ,-co,

)dco,

0.2

0.15 -0.1 ^

30m, with

o 05

protection

-305 0.05

-....

_{.... ....}

.... ....

_....

....

_{.... ....}

....

.... ....

_....

0.05 -55 150 1°°

30m, no

protection

26

Nonlinear correction: long

wave s22(0))

3000

?.>

2500

2000

1500

a

₁₀₀₀

r,)

500

3000

2500

2000

e

1500

l000

1,-1

500

60m, no protection

o0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

co (rad/sec)

oo

0.05

0.1

0.15

A

0.2

30m with protection

0.25

0.3

0.35

0.4

0.45

0.5

0.55

co (rad/sec)

12/19/2005

_{Shallow Water Hydrodynamics,}

Trondheim, Norway

S, (co)

1 1.2 1.4 1,6 _{1.8 2}

2.2 2.4 2.6 2.8

₃ c(J)(rad/sec)

27

0

3000

o

0.05

0.1

1.9

2500

e

2000

1500

l000

c"

500-

₃₀₀₀₀ 25000 20000 15000 10000 5000 0

06

0 6

0

0.2 0.4 0.6 0.8

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

06

co (rad/sec)

30m, no protection

0.4

0.45

0.5

0.55

12/19/2005

Mean Harbor °Spectrum

f (Hz)

S (f)= S2(f)+S22(f)

0(e2)

0(6.4)

4

10 r

106

10

102

to',

S22 (f

10°

f (Hz)

f (Hz)

2(f)

3011'15

protected

28

10_2

10-1

10"

77:

Qualitative comparison with field data

S

(f)

₌

_S2(f)+S22(f)

0(e2)

_o(e4)

m protected

1994.09.01 05:00 GLADYS TYPHON

I 1

Mir

I

TT 1

I

lirs'

I 1

ITIMI

I i

1111111

I

flil

io7

106

io5

102

101

100

10°

Nater I

o.io_lyl ical

S22 (f)

II

f (Hz)

I.

Numerical Aspects

For 2-nd order problem must be solved for a

manypfirs of fr\equencies by FEM

120)1,0)2)

Large sparse matrix for each pair

--

for variable depth: modes are coupled

--10620 pairs, each pair need around 15 minutes,

at least 100 days for ONE single computer,

20-25 parallel computer (4G ram, 2.8G Hz),

weeks

Summary

Stochastic theory for long-period harbor

resonance

by a broad-banded sea

Long-wave part of

_{response spectrum is dominated}

by second-order correction,

_{not first or third-order}

Mild-slope equation for second

_{order in}

_wave

steepness is sufficient

High-frequency part of

_{response spectrum is}

dominated by first-order

wave

Extendable to Slow drift of floating structures

12/19/2005

_{Shallow Water Hydrodynamics,}

₃₁

e

Modelling tidal

cut rents,

shell'

slope eddies, and tsunamis with

shallow water equations

CeSOS Seminar 19 December 2005

Bjorn Gjevik

Department of Mathematics, University of Oslo

C C

Modelling tidal currents, shell slope eddies, and tsunamis with shallow water equations p.1/?

High resolution models of tidal currents in

coastal waters

Eddy formation in shelf slope currents

Some aspects of tsunami modelling

e o C

Modelling tidal GUe eels, shelf slope eddi., and tsunamis with shallow water equations _p.2/?

Depth integrated eqs. of motion

au

a (u2

a

,uv(971

.\,/u2 + V2 U

(

fV

gH

at

ax' H

0y H

D

H

H+B

OV

0 Uy

0 V2

Di

/(12

+

v2

v

)±(Ty(.17.)-FfU

. yc,o

H

H+13

(U, V)

horizontal volume fluxes

H = Ho + 71

total depth (undisturbed + displacement)

CD

bottom friction coefficient (quadratic)

(Bx, By)

horizontal eddy viscosity (Smagorinski)

acceleration of gravity

Coriolis parameter

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations

Smagorinski turbulence model (LES

Bx

= v

V2 U B=vv2V

with eddy viscosity

aTi

9

1 aTi0-1-)

2

aTi

1

v=ql

Ox)-

+ -2(

-0y

+ --(9x)(9y)2P

where depth mean current

U

V

U,

_{v =}

q = constant

0(0.1)

0 ( 1 )

,

1 = length scale

0(Ax)

v =

0(

1 0 m2/s)

e e e e

Continuity equation

077auOV

at

ar

ay

(U ,V)

horizontal volume fluxes

sea surface displacement

i

e e

i

Modelling tidal current, shell slope eddies, and tsunamis with shallow water equations p.5/?

Classic analytical solutions

Kelvin waves

Topographic Rossby

waves

Quasi-geostrophic flow

o

Finite differencing schemes

Space staggered B and C-grids

Experiments with optimalization (adjoint

models)

o

Modelling tidal currents. shelf slope eddies, and tsunamis with shallow water equations

-Numerics

Iceland

Bathyrnetry Nordic Seas

Norway

Sco tl and

a

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations

-C)

Department of Mathematics

University of Oslo

e

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations - p.91?

Hierarchy of model domains

o

)0

= 500 m

Sea level (cm)

Stasjon

Obs.

Mod.

Bodo

86.9

86.1

Narvik

99.3

99.6

Kabelvag 92.6

91.3

Tangstad 62.3

63.7

Harstad

69.3

67.5

Andenes 64.8

63.0

*

..

half slope eddies, and tsunamis with shallow water equations - p.10/?

,

Lofoten Northern Norway

_(M2)

0

50

3000 2500 2000

p

1500 1000 500 300 250 200 150 100

land MI

00

250

3Oè

350

400

Hinnoya

Harstad

EvenskOr

Nar

Horizontal grid:

Lx = 50-100m

ee a

Modelling tidal cur 'ants, shelf slope eddies, and tsunamis with shallow water equations - p

80

Model domain I

HINNOYA

Ballstad

TJELDOYA

San dtorg

Steinsland

Evenskjm r

Ramsund

=

25-50 m

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations - I

Model domain II

111

U1117--300 200 150 100 75 50 40 30 20 10 land

MUM

SANDTORGSTRAUMEN t

1 hour

RUN65 (11/2)

Mod'curten, shelf slope eddies, and tsunamis with shallow water equations - p.13/?

E

16

151

13'4

I

/ /

. 1 I I

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e e - 7

t

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I

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SANDTORGSTRAUMEN t

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*

helf slope eddies, and tsunamis with shallow water equations- p.14/?

16

15

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13

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shelf slope eddies, and tsunamis with shallow water equations - p.

,e I r

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\ \ "

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kUMEN t

5 hours

RUN65

_(M2)

a

ants. shelf slope eddies. and tsunamis with shallow water equations - p.17,7

1,,, ... .,,,

II', ...

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11.1,11.

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19

20

SANDTORGSTRAUMEN t

6 hours

RUN65

_(M2)

e e e

'shelf slope eddies, and tsunamis with shallow water equations - p.18/7

15,T

14

13

12

-1 I I I

I / ,

,

r 'II

1 .. . t t 1 1 . 1

it

err

r

rt?

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(M2)

lcurrentel, 'les, and tsunamts with shallow water equations p

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r SSS .

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i 5 0

rrents. shelf slope eddies, and tsunamis with shallow water equations - p.

RUN65

(A/2)

0 0 a

ModefIT, currents, shelt slope eddies, and tsunamis wtth shallow water equations - p

:711.Fr7v,

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SANDTORGSTRAUMEN t =13

lou

r4S,i6

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a

shell slope eddies, and tsunamis with shallow water equations - p.251?

lippy...

',/////,'-'s",:.,_-"///.,

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Harmonic analysis (station 19)

0.7

0.6

0.5

E 0.4

t-

0.3

o

0.2

0.1

O

20

Modelling tidal currents. shelf slope eddies, and tsunamis with shallow waterequations - p26/?

30

40

50

60

70

Time (hours)

II

STEINSLANDSTRAUMEN (HW)

RUN65

Mean tide

_(M2)

Max current 2 m/s

Hinnoya

r 1

/

/

,

1

r'r

.

1 1 /

Steinsland

BALLSTADSTRAUMEN (I1W)

Ballstad

12.0

-Tjeldoya

RUN65

Mean tide (.112)

Max current 1.0 m/s

Modelling tidal currents. shell slope eddies. and tsunamis with ,hallow water equations ---a. ---a.

\

"*.

I

/

s

o

I

_ . _

\

\

.

\

.

. N.1, . S,

Sandbogstraumen

Orlogsstasjon

RUN65

Mean tide (112)

Max currentl m/s

a e

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations - p.29r?

RAMSUNDET (HW)

e

On

a rock in Tjeldsundet

Tidal cur -ents in navigation ci

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations p.

4---15102_21332.0I

\

I

I

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1

7

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4--,

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°

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V 77 V V

V V ms/

ft 4-4

7

--7.71ZT

a a e

Modelling tidal cur rif nts stlelt slope eddies, and tsunamis with shallow water equations

NDP measurement programme

.,

4

I

d-t

.,

20

10

nsen

4°

,

A_

o

tl:

0

°

C1 A

0

s

angeD

200

oft

q

,

,-...44

4

,

C

,.

slope eddies, and tsunamis'

o4

-

-.

:uuii

Il k , a

gr

Modelling tidii

.

cun wits. shelf

Curreilt profile Svinoy

section

0

Ei. -600F

o

o

-800

/000,

Y.

SI)

t

a

2 O05.

DI

90

Fig 4. Contour

March-A.ril

Svinoysnitt-Aanderaa Marcn-April 1996

Transpon . 4.6 Sv

---"-

"'-'17-20

r

.)

.

1.., R 1

I 15

----'

.

60

50

40

30

Distancefkm1

----90 *

;--- ;---;---10;---;---;---;---;---6..

80

I. 70

70

________

BO

plot of monthly

1996

mean

60

50

40

30

20

10

0

Distancefkm1

velocity field and vertical integrated transport,

From Orvik and Mork (1996)

.

e

a

*

Modelling_{tidal Gun, 'hrs. shelf slope eddies, and tsunamis with shallow water equations}

Eddies seen from space

4C

ub N

ERS-2 SAR Image 19.07.87, 10:59 UTC

From K. Kloster, NERSC, Bergen

Between Ormen Lange and

Helland Hansen

a e

Modelling tidal CLITI ents, shelf slope eddies, and tsunamis with shallow water equations - p

Barotropic

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations

Eddy formation: Ormen Lange

Inflow 'et

7.5 days

10 days.

Modelling tidal currents, shell slope eddies, and tsunamis with shallow water equations - p ?

mean along shelf current

mean sea surface displacement

wave number

angular velocity

perturbations

Modelling tidal currents, shell slope eddies, and tsunamis with shallow water equations - p.38/?

{

fah.,

hk, hD

Dh} {fi

fl}

gk,

f

fL}

=

C.L1fl

{

gD,

f,

D=

_dy

The eigenvalue problem for Lo is solved by

discretizing on a spaced staggered grid using

NAG-routines.

e

Modelltng tidal currents. shelf slope eddies, and tsunamis with shallow water equations - p.

Linearized eqs. for perturbations

20

40

60

80

Wave length (km)

h shallow watei equations - p

A = 43 km, T=33.7 hours

Mean current added

o e

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations - p.41/?

Eigen-mode: Omen L

Inge profile

,,,,... '

I

I

I

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations - p.421?

e

Run-up along the fjord

S

4.312.0 10.6

9.4 5.7 6.6 .7 Muri\ 10 7 123 12.0 9.6 10.5 Ho Haag buSt Osvik 4.0 24.4 4.6 21.2 12.6 Fiore Oksneset 7 5 KARLSTAD 3l.4 32 -10.8 Alvika 32.7 KORSNES 23 37.3 17.4 10.0

Skred

Seineset 13.6 9.5 15.8 5.0 5.9 1%111..1 13.6 157 4.6

Seda/s-feit-Sklegg vik

As

hammer 25.5 33.8 23.6 MULDAL 17.1 12.9 17.8 19.9 24.8 27.0

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations - p

Three phases of a tunamis event

Generation of waves in the source area

Propagation over open ocean

Amplification and run-up at the coast

For modelling and predictions points 1) and 3)

are the greatest challenges

a

Model equations

-D Boussinesq)

au

a u2

at

ax h

al)

h2 83u

ax+

3 atax2

ail

au

abo

at

ax

at

U

_{Horizontal volume flux}

h = h

+50 + T1

Water depth (mean + changes)

fl

Displacement of sea surface

Sea bed displacement

CD

Bottom friction coefficient

Acceleration of gravity

e e C C C e

Modelling tidal rani, mts. shelf slope eddies, and tsunamis with shallow water equations - p.451?

Pedersen og Johnsgard

₁₉₉₆

e

Modelling hdal k.11 I .1 ts, shelf slope eddies, and tsunamis with shallow water equations - p.48/?

Vertical current profiles from

Ou

077

O

Ou

at

fit)

45-.;

47927

Ov

fu

=

oar/

O

(

Ov

Ot

ay

Ozil

az)

and

U

=

f udz

known from depth integrated

model

e

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations

-e

Extention of shallow water models

Vertical current profile by '2.5-D models'

Non hydrostatic effects

Wave-current interaction

W S

Publications by Oslo group (1)

Gjevik et al.(1994) Model simulations of the tides in the Barents

Sea. J. Geophys. Res., Vol 99, No C2, side 3337-3350.

Moe et al. (2002) A high resolution tidal model for the area around

the Lofoten Islands. Cont. Shelf. Res., Vol 22, 485-504.

Ommundsen (2002) Models of cross shelf transport introduced by

the Lofoten Maelstrom. Cont. Shelf. Res., Vol 22, 93-113.

Moe et al. (2003) A high resolution tidal model for the coast of

More and Trondelag. Norwegian J. Geography, Vol 57, 65-82.

Gjevik et al. (2004) Implementation of high resolution tidal current

fi eld in electronic navigational chart systems. Preprint Series.

Dept of Math., Ui0 ISSN 0809-4403. (J. Marine Geodesy, in

press)

e e

Modelling tidal cut rents. shell slope eddies. and 'tsunamis with shallow water equattons - p.49/?

Publications (II)

Moe et al. (2003) A high resolution tidal model for the coast of

More and Trondelag. Norwegian J. Geography, Vol 57,

65-82.

Gjevik et al. (2004) Implementation of high resolution tidal current

fi eld in electronic navigational chart systems. J. Marine Geodesy

(in press)

Hjelmervik et al (2005) Implementation of Non-Linear Advection

Terms in a High Resolution Tidal Model. Preprint

_{Series, Dept. of}

Math., University of Oslo. No. 1, ISSN: 0809-4403.

Gjevik et al. (2002) Idealized model simulations of barotropic fbw

on the Catalan shelf. Continental Shelf Research, 22, 173-198.

B. Gjevik (2002) Unstable and neutrally stable modes in

barotropic and baroclinic shelf slope currents. Preprint Series,

Dept. of Math., Univ. of Oslo, No 1.

.

.

.

Harbitz, (1992) Model simulations of tsunamis generated by the

Storegga slides. Marine Geology, Vol. 105,1-21.

Harbitz, et al. (1993) Numerical simulations of large water waves

due to landslides. J. Hydraulic Engineering, Vol. 119, No. 12, side

1325-1342.

Johnsgard and Pedersen (1997) A numerical model for

three-dimensional run-up. Int. Num. Meth. Fluids 24,913-931.

Pedersen (2005) Modeling run-up with depth integrated equation

models. In Advances in Coastal and Ocean Engineering. World

Scientifi c Publishing. Eds. Yeh and Synolakis.

Langtangen and Pedersen (2002) Propagation of large

destructive waves. J. Appl. Mech. Engineering. 7,1,187-204.

i i

i

Modelling tidal currents, shelf slope eddies, and tsunamis with shallow water equations p.

Presentation for the Shallow Water Hydrodynamics Seminar, CeSOS, Trondheim, Norway,

19 December 2005.

Computations of forces and motion response to arbitrary fluid motions

around stationary vessels

J.A. Pinkster, TU Delft, The Netherlands

Abstract :

Moored vessels can be influenced by transient fluid motions due to passing

ships at both high or low speeds or other irregular wave patterns due

to complex wave systems developed and modified over large distances and

time by weather and bottom topography.

The presentation discusses a method to couple fluid models which

compute transient or arbitrary stationary irregular fluid motions to

_{a linear}

frequency domain 3-d diffraction code in order to produce corresponding

transient or stationary responses. Examples will be given of results obtained

for the case of wash waves due to a fast passing ship, low-frequency

effects due to a passing

,

slow ship

,

and wave loads on a vessel due to

TU Delft

Computations of Force and Motion

Response to Arbitrary Fluid

Motions around Stationary Vessels

J.A. Pinkster

Developments initially stimulated

by:

Need to predict motions of moored vessels on

inland waters due to passing fast passenger

catamarans (Effect of wash waves)

Need to predict additional passing ship effects

on

large moored tankers and container vessels of

seiches generated by large vessels passing in

restricted waters .This will not be treated further

here.

Supercritical speeds : Diverging

waves only

Basis for computational

procedure:

Forces on moored vessel (first and second order) to be

computed using linear 3-d diffraction code, preferably

using well-tried frequency-domain code.

Duration of passing maneuver is short (a few minutes)

Special problem posed by the fluid motions and pressures

of the incoming wave field ; i.e. generally no analytical

expressions available such as is the case of long-crested

regular waves. Only numerical data for discrete locations

based on other codes

.

For instance the RAPID code

(Raven, MARIN).

Wash Waves computed by RAPID (MARIN). Sub-critical speed

Steps in the computational procedure:

Compute time records of velocity components and pressure

of undisturbed wave at location of all collocation points of

the panel model of the vessel (and harbour)

Using 1-4.1-1: compute complex amplitudes of frequency

components of velocities and pressures for all frequencies

up to maximum frequency

For each frequency solve the diffraction problem using the

data from the I-F1' operation

Transform all frequency domain output back to time domain

using IFFT

Compute second order force terms dependent on products of

first order quantities in the time domain

Propagation of waves outside RAPID domain

Some options:

Use disturbance of ship computed within RAPID

domain as input to a numerical wave-maker

Numerical wave-maker (line of wave-making

sources) generates waves at the location of the

moored ship

Match to time domain wave model such as

TRITON (WL1Delft Hydraulics) based on

Boussinesq equations.

Compute 'wave-cut' inside RAPID domain and

extend wave field by application of linear wave

theory.

.

(This can also be applied to a measured

wave-cut from model tests or full scale)

Real Wavemaker MARIN basin generating oblique waves.

Numerical wave makers

Disturbance

from waves

Numerical wave maker extending

the wave field generated by RAPID

Moored ship

RAPID

Computational scheme

Time domain (real world)

Moored ship

3-D diffraction comp.

Moored ship

Frequency domain (computational world)

'RAPID' wave at wave maker

Example : Wash effect on a ship

moored in a harbour due to a vessel

passing at sub-critical speed

Direction of

Passing ship

100m

Ship moored in a harbour

100m

Moored ship in

Harbour

Analysis of measured or simulated

wave

record (wave-cut)

Decomposition in regular, long-crested

wave components, each with own

amplitude, phase and direction, for

computation of ship responses.

Implemented in DELWASH

Measured (or computed) wave-cut. Extend with

zeros as required in order to obtain sufficient

total duration. Total number of points is a

power of 2 (for efficient FFT)

20

10

-10

-20

o

Measured washwave (model values)

lì

5

10

15

time in s

Fourier analysis of wave-cut

(t) = ao / 2 +

¡Ian

cos(cont) + b

= 21T

SC

(t)cos(cont)dt

b

2/T

SC

(t)sin(cont)dt

con = nAw

&o= 2,r /T

Wave frequency, number and

phase velocity

co2

= kg

tanh(kh)

k =

I

co =

I T.,

w,

kng tanh(knh)

kn = 27r 1 An

cn = con I kn =

17,2

Wave direction

cos(an)

= c,

/U

U

An example: Fast Ferry Wash

Measurements of wash waves of a new Fast

Ferry concept in MARIN' s Shallow Water

Basin, and application to the simulation of the

behaviour of a moored inland barge.

Wave elevation at edge of domain surrounding the moored ves

0.4

0.2

o

-0.2

r7m77711easured

1111E1NEW

V I

-0.4

o

10

20

30

40

50

time in s

Forces on a captive container

vessel ('Scheur')

Simulation of wash waves of a passing ship using the

(real) wave maker.

Model tests carried out in the Vinje Basin of WLI

Delft Hydraulics

Wave propagation computations using TRITON,

a

time-domain, non-linear code based on the Boussinesq

equations

Calculations of waves using

TRITON (Boussinesq eqn.)

after 0.40 seconds

E

3

60000 25000 -25000 -50000 200

Measured and computed forces and moments

on captive model

Roll moment

3

E

3

Sway toroe 500 200 300 330 He

MOM

,

I

_'

Inil

'

-400 300 500

Compare results with results

obtained using undisturbed

wave-cut measured at the location of the

model

1.0

Wave elevation at location of moored vessel

200

300

400

500

time in s

-- Simulated

Measured

0.5

E

_

o

cl)

-0.5

-1.0

4000

2000

o

Predicted forces based on measured wave-cut and DELWASH

Surge force Roll moment

3

30040 200 200 300 Sway force Prtch moment ADO e 600 400 500 e

Now: Long-duration simulations of 3 hours or

more for arbitrary irregular sea conditions

(long-crested or directionally spread)

Of interest for changing coastal topography which

results in complex combinations of directionally

spread short waves with an even more complex

bound, free and reflected sub-harmonic wave field

Codes such as those based on Boussinesq eqn. can

generate the required wave field and fluid

kinematics

Note : Diffracted waves are all free waves (linear

theory)

Computed De!wash --- Measured ..

INIK

ME

200 300 400 500 300 600

Long duration simulations:

Problem:

Number of input frequencies for diffraction computations is extremely

large in the direct application of 1-F1' to the complete record

Solution :

Cut the time-record into shorter, overlapping segments of equal duration

resulting in less frequencies.

Input data from the segments are treated as so many RHS vectors

(Compare with different wave directions in standard diffraction codes)

Two long-duration (3 hours) examples:

Irregular long-crested waves

Two approaches:

Use wave kinematics and pressure as input to

diffraction computations

2. Use computed undisturbed wave elevation at the

location of the vessel combined with DELWASH.

(waves with fixed direction this time)

E

0

The computed wave record at the

location of the vessel

Long-crested waves

W ave elevation in long-crested waves

50000 25000 o -25000 -50000 100

Heave and Sway force time

records

Heave forces

200 300 400

time in s

500 600

30000

20000

10000 -10000

Sway force

-20000 100 200 300

400

time in s

Irregular directional seas

Results based on input from TRITON

only

11,11111,,i,i

Triton

---

Delwash

o -20000 -400000 40000 20000 40000 20000 -20000 -40000 1950

Wave field simulation:

Directional spectrum prescribed

at boundary of TRITON

domain

Some results of forces on the vessel ; 10 time

segments

2500

1980

after 1E15132.00 seconds

ilyyLlOstft Hydraulics

Heave force 'Scheer'

5000 7500

Heave force 'Scheur

overlap 2-3 10000 2010 time in s 2040 2070 40000 20000 o -20000 -40000 40000 -20000 -40000

Heave force 'Scheer' overlap 1-2

Heave force 'Scrteur

overlap 3-4

,Apt\if

3000 3050 tirne In s

.

Je

Same waves, more segments

,

larger overlap

15000 -15000 10000 -10000 Heave force overlap 100 s 2800 time in s 2850

E

10000 -10000 10000 -10000

Last but not Least:

Mean and Low-frequency

,

second order forces

Case 1: 200 kdwt tanker in regular wave group in head

waves in shallow water

Some comparisons between present approach and

'conventional' QTF results

Heave force overlap 1008 ti

_i

/

J

V

J

3725 time in s t.,

(\

o 3000 6000 9000 12000 920 960 1000

Heave force Heave force

-2000 o -3000 -4000 100 -100 -200

Second Order Surge Force

E 6 2

\-"I\V"\jil\fIltir\vi \\v/\\

/-\\

-2 100 150

'\

r

I\

1\

\

On

V

k10111/1011/-\,"\P

Jot v

_v

Bijdrage 1 Bijdrage 3

F=F1+FH±Fm+FIO-F,

F 1=

pgcfCr")2.nrdl

2

wi

2

I I

F 11=- J-1rr --

₂

PI\

7 c131) I

Al.ds

-(1)

F111 =

P(X

.\714:13

10 10

F=

N

di)

.(m-x

3

)

()

F v=-ff-P(0,

2).n1.ds

Second order Surge Force in a regular wave

group

,

components I through IV only.

Dashed red line : QTF-based results

Bijdrage 2 Bijdrage 4

I®

A

r

\k/ sii

v V'i

2 50 100 150 50 100 E 6 E

1

°

8 2

I

L520

Case 2: Sway drift force

on container vessel in

irregular directional seas

.

Sum of components I

through IV

O

-1000

Sway drift forces

100s overlap.

-1000

Conclusions

Coupling of linear 3-d diffraction code to different

codes generating, fluid motions at the location of the

vessel has been realized

First- and second order forces compare well with

results of 'conventional' computations

Long-duration simulations using input from

non-linear time domain wave codes such as TRITON

allow the generation of first- and second order wave

forces for complex wave conditions

Sway drift forces

100s overlap.

o 3000

6000

9000

12000 3650 3700 3750

Laboratory generation of wave-group induced

long waves

JONSIMP SPECtRull 46.1214 TP.145 WATER UPTH 40M

COVP010.

214 OD 511-.10 :011,

2140

COUP

1011, 710 011041 U1117101

Carl Trygve Stansberg

MARINTEK/CeSOS

,

Trondheim, Norway

Shallow Water Hydrodynamics Seminar, CeSOS Trondheim, Norway,

19 December 2005

MARI NTEK

_{rt.) SINTEF}

5620 563C 5640 5650 5660 5620

Contents

Background: Low-frequency wave effects on floating structures

Second-order irregular wave model

bound long waves

"Free" long waves due to finite bottom depth

A method to remove or reduce "free" long waves in laboratory

Laboratory implementation: Results from wave measurements

The work presented is a part of an on-going co-operation

study between MAR1NTEK, CeSOS, ExxonMobil and MIT

Background: Modelling

_{of moored ships / large floating}

structures in shallow or finite water

MARI NTEK

!!

"a111111

Background: Modelling of moored ships / large floating

structures in shallow or finite water

0.12

0.11

0.1

09

0.07

006

0 05

-n

nAL

--004-

0.05

0.06

007

0.08

0.09

01

0.11

0.12

0.13

f [Hz]

Example: Surge force QTF's of

FPSO in 84m and 25m depth

Slow daft surge force OTF on a 200m long monohull Wale( depth 84m 180 deg

_waves

013

Slow daft surge force QTF on a 200m long monohull Water depth 25m 180 deg waves

0,13

0.12

0,11

01

...,009

-'*008

0.07

-0 -06

0.05

0.04

_0.05

_0.06

₀₀₇

_0.08

_0.09

_0.1

_0.11

_0.12

_{0 13}

f, [Hz]

Shallow Water Hydrodynamics Seminar, CeSOS Trondheim, Norway, 19 December 2005

Background: Modelling of moored ships / large

floating

structures in shallow or finite water

-

special physical effects; challenges in numerical modelling

Here: Focus on the laboratory wave generation

The MARINTEK Ocean Basin (50m x 80m x 10m)

r jet t

The Ocean Basin Laboratory

Doubleflap

-wave maker

Multi-flap

-/wave

maker

Cross-section of Ocean Basin

Multi-flap

wave maker

Double-flap

wave maker

50m

Length: 80 m

-

VVidth: 50m

-

Depth: 0-10 m

t xampie trom earlier

experiment:

Finite water depth effects

on irregular waves:

Depth h =0.40m

(model scale)

Sample elevation records for two wave height

Hs=0.05m (upper)

Hs=0.16m (lower)

(Tp=1 As in both cases, kph=0.8)

Notice significant LF non-linear contribution

under wave groups, enhanced due to shallow

water

Shallow Water Hydrodynamics Seminar, C S

II- -ilo-

SO

Second-order simulation of random waves in finite water

Infinite, plane horizontal bottom is assumed ("ideal" condition)

JONSWAP SPECTRUM HS=12M TP=14S WATER DEPTH=40M

12

lo

8

6

5620

r1

- LINEAR COkIPONENT

--- 2ND ORO. SUM-FREQ. COMP.

2ND ORD. DÍFF-FREQ. COMP.

TOTAL 2ND ORDER ELEVATION

5640

5650

5660

5670