Chapter 9 Applications of Hybrid Wave Models to Irregular Waves

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Chapter 9 Applications of Hybrid Wave Models to
Irregular Waves

• 9.1 Computation of Wave Kinematics
• 9.2 Prediction of Wave Elevation
• 9.3 Prediction of Wave Elevation Based on Wave
  Pressures
• 9.4 Prediction of Wave Properties of
  Short-crested Waves.
• 9.5 Accurate determine Wave Energy Loss Due to
  Wave Breaking.
• 9.6 Wave Forces on Slender Bodies

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9.1 Computation of Wave Kinematics

• Problems of computing wave kinematics using
  Linear wave theory
• Revisit of HW 3
• Modifications to LWT (widely used by the
  offshore industry)
• (see Zhang et al. 1991, OTC 6522)
• Wheeler Stretching
• Linear Extrapolation
• Vertical Extrapolation
• 2nd MCM (Stokes) perturbation method (not
  convergent)
• Equivalent Wave High-Order Wave Theory

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Prediction of Horizontal Velocity By HWM MCM
Long wave
HWM
2nd-order
Linear
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Errors in Using Equivalent Regular Wave to
Compute Irregular Wave Kinematics
3rd-order
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Heuristic Interpretations for the horizontal
velocity under the crest -Steep wave crests
are caused by many waves of different
frequencies. -Waves of high frequencies are on
the top of waves of low frequencies.Hybrid
Wave Model (HWM) considers these factors -The
still water level to a SW is the LWs surface -
Considering Waves of high frequencies are on the
top of waves of low frequencies
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PMM Solution for a SW modulated a LW
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Generation of Steep Transient Wave in 2-D Flume
After Wave-breaking
Wave Kinematics
Before Wave -breaking
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Wave Kinematics Prediction
HWM
Wheeler
Linear Extra.
Under crest, Largest Horizontal velocity
Largest Vertical velocity
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Predicted -5.48 m
Input -8.53 m
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FULWACK Data Fulmar Platform at North Sea Time
Nov. 24,1982. Hs 11.2m Input Significant
Wave Breaking During the tests
Zhang et al. 1999b
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Output
Predictions are Compared with Measurements.
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9.2 Prediction of Wave Elevation Comparison with
the corresponding prediction based on LWT (Linear
Wave Theory). See 1996 b Zhang et al.
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9.3 Prediction of Wave Elevation Based on Wave
Pressures (Meza et al. 1999 J. OMAE Vol. 121
pp242-250)
Because of ocean environment and the costs of
deploying and maintaining surface-piercing
instruments, pressure transducers are commonly
used for measuring ocean waves. It does not
directly measure wave elevation. To obtain the
surface elevation, a transfer function relating
wave elevation and wave-induced dynamic pressure
is required. Traditionally, the deterministic
transfer function is based on LWT. Limitation
of pressure measurement When a transducer is
deployed at a depth comparable to the wavelength
of a measured wave train, the pressure induced by
the wave is so weak that the measured pressure is
not reliable (comparable to noises).
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Limitation of Transfer function based on
LWT The relation between the elevation and
pressure of a FW is quite different from that of
a BW. When waves are steep, BWs are significant
or may be dominant at low- and high-frequency
ranges. Predicted elevation based on measured
pressure through a transfer function of LWT may
result in large errors in these frequency
ranges. See the comparison between the
prediction and the corresponding measurements.
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Transfer Function in Deep Water
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• Elevation a steep transient wave train is
  measured .
• Pressure is also measured there (-16 to -50 cm
  below SWL, water depth h 91.0cm) .
• Elevation is predicted based on LWT (Linear
  Spectral Method).
• Elevation is predicted using UHWM.
• Comparison between predictions and measurements.
• - LWT under-predicts the crest height
  greatly
• over-predicts the trough height.
• - LWT over-predicts wave heights.

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Explanation to why LWT under-predicts the crest
heights over-predicts the trough heights.
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9.4 Prediction of Wave Properties of
Short-crested Waves.

• Laboratory Measurements OTRC data see Zhang et
  al. 1999b
• Field Measurements
• Wave Kinematics (FULWACK cases, see Zhang et al.
  1999b)
• Wave Pressure (Harvest Platform Data, see Zhang
  et al. 1999b)
• 3. WACSIS Project (with/without Currents)
  (Zhang et al. 2004, Zhang Zhang 2004)

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• WAve Crest Sensor Inter-comparison Study
  (WACSIS).
• Platform in 18-m water depth (southern North
  Sea, 97-98).
• Various instruments were used.
• Inter-comparison of measurements of various
  instruments.
• Using Directional HWM for the comparison between
  predictions and measurements.
• Consistency May help to correct measurement
  mistakes.

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Plan View of Sensor Layout
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Fig. 4 Power spectrum density according to
pressure head time series
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Fig. 5 Initial phases of each component of
pressure and velocity
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Table 3 Wave Characteristics of Selected Cases
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Fig. 7 Comparison of free-wave directions based
on DHWM and Waverider (9803011020)
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Comparison between prediction measurement of
Marex before after the orientation of S4 was
corrected
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Comparison between prediction measurement of
SAAB before and after the orientation of S4 was
corrected
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Comparison of free-wave directions based on DHWM
and Waverider (9803051040)
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Comparison between prediction measurement of
SAAB before after the orientation of S4 was
corrected
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Comparison of free-wave directions based on DHWM
and Waverider (9804131100)
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Comparison between prediction measurement of
Marex before after the orientation of S4 was
corrected
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Comparison between prediction measurement of
SAAB before after the orientation of S4 was
corrected
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Governing Eq.s BCs in the Presence of Currents
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Assuming the current is uniform and steady, we
may simplify the computation using a moving
coordinate system.
In the moving coordinates, the governing Eqs. and
BCs reduce to the same form as those in the
absence of current except for the Bernoulli
constant C(t). The solutions in the moving
coordinates in the presence of the current are
the same as those given in the absence of the
currents.
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After transferring the variables back to those in
the fixed coordinates, we obtain the truncated
solutions up to 2nd-order in wave steepness for
the interaction between two free waves using two
different perturbation methods, respectively.
That is, in the presence of currents the freqs.
involved in the phases are the apparent freqs.
instead of intrinsic freqs. as in the absence of
currents.
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Numeric Verification

• Current velo. 1.5 m/s Initial Guess of wave
  direction 20-40 degree
• Test 1 PUV Wave Record and Following Currents
• Test 2 Elevation Records and Opposing Currents

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9.5 Accurately determine Wave Energy Loss Due to
Wave Breaking.
Energy loss due to wave breaking is a dominant
sink in wave energy budget. Field Measurements
to determine wave energy loss is extremely
difficult due severe ocean environment and other
terms such as energy input from wind and
nonlinear wave-wave interaction.
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• Laboratory measurements of wave breaking
• Set-up of Laboratory Measurements
• See Figure 1 from Meza et al. 2000
• Noticing the distance from the wave gages
  (before breaking) to the ones (after breaking) is
  short, approximately of the order of typical
  wavelength. Hence Snl is insignificant.
• No wind in laboratory, and hence Swind 0.
• The energy difference between the measurements at
  the gage before the breaking and the gage after
  the breaking should equal to the energy loss due
  to the breaking.

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• Resultant wave spectrum (based on FFT) may change
  within
• short distance even in the absence of wave
  breaking. This is
• because the superposition of FWs BWs at the
  same frequency.
• FW spectrum (decoupled from BWs) changes very
  little in a short distance and in the absence of
  wave breaking.
• The comparison of FW spectra before after an
  isolated
• wave breaking may accurately reveal the energy
  loss as a
• function of wave frequency.

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• Original wave dissipation model
• Always lose wave energy regardless of wave freq.
• Energy loss is proportional to 2nd power or the
  4th power of wave freq
• Energy loss is proportional to energy density

• Our Measurements indicates
• Free waves at frequency lower than the peak freq.
  may gain small portion of energy loss by high
  freq. Free waves.
• Energy loss of free wave at or near the spectral
  peak freq. Is not proportional their energy
  density.

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9.6 Wave Forces on Slender Bodies
Wave Structure Interactions Floating offshore
structures of a slender body (SPAR) or consisting
of several slender bodies (TLP). Wave loads are
computed using the Morrison Equation or Modified
Morrison Equation.
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Spar Platform
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Tension Leg Platform TLP
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Semi-Submersible
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Time Domain Analyses Used in Motion and Mooring
Analysis of a Moored Floating Structure

• Quasi-static Analysis
• mooring/tendon/risers modeled as nonlinear
  springs.
• mooring line damping estimated or neglected
• Coupled Dynamic Analysis
• structure motion equations and mooring/tendon
  /riser dynamic equations solved simultaneously.
• mooring line damping included.
• Empirical formulation for VIV.

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Numerical Code COUPLE

• Cable dynamics CABLE3D
• Finite element method (Garrett,1982, Ma Webster
  1994).
• Improvement.
• Wave/Current/Wind Loads on the Hull
• Morison Equation Using Nonlinear Wave
• Kinematics (HWM).
• Diffraction Theory WAMIT (Initial force) Morison
  Equation (Drag).
• Interface Between Hull and Its Mooring System
• Hinge Connection

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• Methodology of Coupled Dynamic Analysis
• hinged boundary condition
• Motion equations of a structure

Motions at top of the rod
Forces applied on the structures
Dynamic equations of Cable
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Wave Loads on Structures

• Two Choices of Computation Methods
• Morison equation (Slender Body Structure)
• Wave Kinematics using Hybrid Wave Model
• (HWM). Inertia, drag and lifting (VIV) forces.
• Ship Type Structures, (2nd order Wave Diffraction
  numerical codes, i.e.WAMIT)
• Drag and lifting force based on Morison
  Equation

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Use of the Hybrid Wave Models

• Effects of Nonlinear Wave Interactions.
• Hybrid Wave Model(Uni-directional
• Directional HWMs)
• Output of HWM Tine-dependent irregular wave
  velocity acceleration along the centerline of a
  cylinder from its bottom to the free surface,
  which is the input to the Morrison equation.
• Considering nonlinear wave effects.
• Accurate in predicting slow drift motion of slack
  moored structures.

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Flowchart of COUPLE 6D
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Comparison with Measurements
JIP Spar Cao Zhang (1997) IJOPE Vol. 17
p119-126 Deep Star Spar Ding, Kim, Theckum
and Zhang (2004,2005) Mini Tension Leg Platform
(TLP) Chen et al. (2006)
Ocean Engineering, Vol. 33,
p93-117.
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Main Characteristics of JIP Spar (155)
Diameter 40.54 m Draft 198.12 m
Water depth 318.50 m Mass (with entrapped
water) 2.592E8 kg Center of gravity
-105.98 m Pitch radius of gyration 62.33
m Mooring point -106.62 m  
Tested Predicted Natural periods
(s) Surge 331.86 330.89 Pitch 66.77 62.11
Damping ratio Surge 0.0526 Pitch 0.0086
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Response Of JIP Spar HWM
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Response of JIP Spar Linear Extrapolation Wheele
r Stretching
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Tests of Mini TLP

• Environment Conditions
• Wave 100-year West Africa storm (JONSWAP
  Spectrum, H1/34m TP 16 s). (Wind Current).
• 0 and 45 degree wave heading.
• Set-up (140)
• Fixed model tests (no risers and tendons)
• Compliant model tests (4 tendons 4 (12)
  risers).
• Measurements
• Motions of Hull (TLP) in 6 degrees of freedom.
• Tensions at the bottom of each riser and tendon.

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Mini TLP Complaint Model Test Scale 140
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Mini TLP Properties (Prototype Scale)
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Risers and Tendons Properties (Prototype Scale)
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WAVE (0 deg)
WAVE (45 deg)
T1
T2
R1
R2
Wave Probe 3
R3
R4
T4
T3
Tendon and Riser Locations
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Numerical Code COUPLE

• Cable dynamics CABLE3D
• Finite element method (Garrett,1982, Ma Webster
  1994).
• Improvement.
• Wave/Current Loads on the Hull
• Morison Equation Using Nonlinear Wave
• Kinematics (HWM).
• Diffraction Theory WAMIT Morison Equation
  (Drag).
• Interface Between Hull and Its Mooring System
• Hinge Connection

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Jonswap Hs4m Tp16s ??2.0
Measured Wave Spectrum (Wave Probe 3)
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Measured Natural Periods and Damping Ratios
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Time-Domain Simulations (3 hours)

• Approach A Morsion equationHWM, quasi-static
• Approach B WAMITviscous, quasi-static
• Approach C Morison equationHWM, coupled dynamic
• Approach D WAMITviscous, coupled dynamic

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• Morison Element Model
• Four Column
• diameter 8.64m, length 43.5m
• Cm1.0 (Guichard,2001)
• Cd0.7 ( 0 degree heading) (Teign
  Niedzwechi,1998)
• Cd1.0 (45 degrees heading)
• Four Pontoons
• diameter 7.02m, length 19.935m
• Cm1.5
• Cd1.2 ( 0 degree heading)
• Cd1.4 (45 degrees heading)

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Table Division of Frequency Bands Used in
Statistic Analysis
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Comparison of Surge Spectra (0 deg)
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Comparison of Heave Spectra (0 deg)
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Comparison of Pitch Spectra (0 deg)
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Comparison of Surge Spectra (45 deg)
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Comparison of Heave Spectra (45 deg)
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Comparison of Pitch Spectra (45 deg)
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Accurate Boundary Conditions for Numerical
SimulationT. Liu Prof. Chen

• Accurate Boundary Conditions are crucial to fully
  nonlinear numerical simulation
• B. C. based on linear wave theory results in
  wrong simulation
• Using finite amplitude wave theory (Coklete
  1977), accurate elevation and velocity of a
  periodic very steep wave train can be computed
  numerically.
• B. C. based on FAWT results in accurate
  predictions.

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