Ny kunnskap og prosedyre for prediksjon av ekstreme b

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Laboratory generation of wave-group induced long
waves
Carl Trygve Stansberg MARINTEK/CeSOS , Trondheim,
Norway
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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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 MARINTEK, CeSOS,
ExxonMobil and MIT
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Background Modelling of moored ships / large
floating structures in shallow or finite water -
special physical effects challenges in numerical
modelling
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Background Modelling of moored ships / large
floating structures in shallow or finite water -
special physical effects challenges in numerical
modelling
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Example Surge force QTFs of FPSO in 84m and 25m
depth
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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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
in particular low-frequency group-induced
components.
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The MARINTEK Ocean Basin (50m x 80m x
10m)
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Example from earlier experiment Finite water
depth effects on irregular waves Depth h
0.40m (model scale) Sample elevation
records for two wave heights Hs0.05m
(upper) Hs0.16m (lower) (Tp1.4s in both
cases, kph0.8) Notice significant LF
non-linear contribution under wave groups,
enhanced due to shallow water
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Second-order simulation of random waves in
finite water Infinite, plane horizontal bottom is
assumed (ideal condition)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Wave elevation difference-frequency QTF in deep
and shallow water second-order theory (based on
Sharma Dean 1981 Marthinsen Winterstein 1992)
Deep water d50m d25m
T14s
(Unidirectional waves are assumed)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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• In laboratory Deviations from ideal
  conditions
• Imperfect satisfaction of non-linear boundary
  conditions
• at wavemaker, leads to parasitic free waves.
• Of order second (and higher).
• Difference-frequency sum-frequency
• Similar free waves due to variations in bottom
  depth (e.g. a ramp)
• (this also happens in reality)
• Leads to unwanted second-order waves upon the
  bound components,
• propagating with a different phase speed ?
  modulations in space
• Action Include non-linear compensation signal
  (LF and/or sum-freq.)
• in control signal to wavemaker, in addition to
  the linear input.
• In addition, reflection of LF waves from the
  beach need to be addressed.
• (Not covered in this presentation)

Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Type 1 Finite water depth close to the
wavemaker (Schäffer, 1996)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Type 2) Effects from a ramp
Free (HF) and bound (HB) long wave heights on reef
ref. Karunarathna Tanimoto (1995) See also Mei
Benmoussa (1984) Liu (1989)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Here we focus on difference-frequency (long)
components, which are essential for floating
structures Interference between free and bound
long waves ?L(t,x) ABcos?L(t x/CG) -
AFcos?L(t x/CL) where AB amplitude of
bound long wave AF amplitude of free long
wave ?L frequency of long waves CG group
velocity of primary short waves at actual
depth CL phase velocity of long wave at actual
depth ( v(gh) ) Here x0 at the free wave
generation point, where we assume that the two
components are of opposite sign.
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Present experiment (waves-only) - Purpose To
improve wave generation on shallow water, with
respect to low-frequency components. Target
Stokes irregular waves on an infinite,
horizontal bottom. Verify that free components
are reduced to a minimum - Water depth
0.715m (all data given in model scale) - A set
of 10 different bi-chromatic wave conditions,
without and with correction (irregular wave
tests also run analysis yet in development) -
Corrections made LF free signals added to the
wavemaker input signals, calculated from
second-order Stokes prediction for flat bottom.
Amplitude and phase varied during iteration.
Look for most stable combination in space
(minimum interference effects)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Vertical cross-section of region between
wavemaker and ramp
- With this configuration Type 2 Free
parasitic waves generated at the ramp, mainly.
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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• Expected correction signal needed
• Amplitude approximately 0.5 1.0 of ABound
  (ref. theoretical works by Mei, and others)
• - Phase shift given by the difference in
  propagation time, between free long wave and
  group, in the deep-water region from the
  wavemaker to the ramp

Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Spatial modulation wavelength Lmod 2?/(kbound
kfree) (k wave number)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Example from measurements
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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AF/AB 0.75 Lmod 16m
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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AF/AB 0.84 Lmod 45m
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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AF/AB 0.90 Lmod 34 m
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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AF/AB 0.47 Lmod 13.6m
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Examples from comparison of time series at
different positions
Time (s)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Part 2 of the experiments Diffracted wave
elevation around a large cylindrical GBS (not in
this presentation)
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Summary- Second-order group-bound low-frequency
waves grow significantly in shallow water. They
are important parts of the total second-order
problem.- Laboratory wave generation also
include free long waves. For direct comparison
to numerical wave-structure interaction models it
is preferable to avoid these.- A method to
remove or reduce free waves is described, and
tested in a large wave laboratory. - Results
for tests in bi-chromatic wave tests show good
agreement between corrected LF waves and
second-order theory.
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005
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Further and parallell work - Analysis of
irregular waves - Analysis of tests with
cylindrical model - Comparison to numerical
results - New tests and analysis with more
complex models including force measurements
a ship
Shallow Water Hydrodynamics Seminar, CeSOS,
Trondheim, Norway, 19 December 2005