For the stability of offshore structures, such as offshore wind foundations, extreme wave conditions need to be taken into account. Waves from extreme events are critical from the design perspective. In a numerical wave tank, extreme waves can be modeled using focused waves. Here, linear waves are generated from a wave spectrum. The wave crests of the generated waves coincide at a preselected location and time. Focused wave generation is implemented in the numerical wave tank module of REEF3D, which has been extensively and successfully tested for various wave hydrodynamics and wave–structure interaction problems in particular and for free surface flows in general. The open-source computational fluid dynamics (CFD) code REEF3D solves the three-dimensional Navier–Stokes equations on a staggered Cartesian grid. Higher order numerical schemes are used for time and spatial discretization. For the interface capturing, the level set method is selected. In order to test the generated waves, the time series of the free surface elevation are compared with experimental benchmark cases. The numerically simulated free surface elevation shows good agreement with experimental data. In further computations, the impact of the focused waves on a vertical circular cylinder is investigated. A breaking focused wave is simulated and the associated kinematics is investigated. Free surface flow features during the interaction of nonbreaking focused waves with a cylinder and during the breaking process of a focused wave are also investigated along with the numerically captured free surface.

References

1.
Stansell
,
P.
,
2004
, “
Distributions of Freak Wave Heights Measured in the North Sea
,”
Appl. Ocean Res.
,
26
(
1–2
), pp.
35
48
.
2.
Soomere
,
T.
,
2010
, “
Rogue Waves in Shallow Water
,”
Eur. J. Spec. Top.
,
185
(
1
), pp.
81
96
.
3.
Baldock
,
T. E.
,
Swan
,
C.
, and
Taylor
,
P. H.
,
1996
, “
A Laboratory Study of Nonlinear Surface Waves on Water
,”
Philos. Trans. R. Soc. A
,
354
(
1707
), pp.
649
676
.
4.
Chaplin
,
J. R.
,
Rainey
,
R. C. T.
, and
Yemm
,
R. W.
,
1997
, “
Ringing of a Vertical Cylinder in Waves
,”
J. Fluid Mech.
,
350
, pp.
119
147
.
5.
Bai, W., Eatock Taylor, R., 2007, “
Numerical Simulation of Fully Nonlinear Regular and Focused Wave Diffraction Around a Vertical Cylinder Using Domain Decomposition
,”
Appl. Ocean Res.
,
29
(1–2), pp. 55–71.
6.
Ning
,
D. Z.
,
Zang
,
J.
,
Liu
,
S. X.
,
Eatock Taylor
,
R.
,
Teng
,
B.
, and
Taylor
,
P. H.
,
2009
, “
Free-Surface Evolution and Wave Kinematics for Nonlinear Uni-Directional Focused Wave Groups
,”
Ocean Eng.
,
36
(15–16), pp.
1226
1243
.
7.
Zang
,
J.
,
Taylor
,
P. H.
, and
Tello
,
M.
,
2010
, “
Steep Wave and Breaking Wave Impact on Offshore Wind Turbine Foundations—Ringing Revisited
,”
25th International Workshop on Water Waves and Floating Bodies
(
IWWWFB
), Harbin, China, May 9–12.
8.
Westphalen
,
J.
,
Greaves
,
D. M.
,
Williams
,
C. J. K.
,
Hunt-Raby
,
A. C.
, and
Zang
,
J.
,
2012
, “
Focused Waves and Wave-Structure Interaction in a Numerical Wave Tank
,”
Ocean Eng.
,
45
, pp.
9
21
.
9.
Paulsen
,
B. T.
,
Bredmose
,
H.
, and
Bingham
,
H. B.
,
2014
, “
An Efficient Domain Decomposition Strategy for Wave Loads on Surface Piercing Circular Cylinders
,”
Coastal Eng.
,
86
, pp.
57
76
.
10.
Chen
,
L. F.
,
Zang
,
J.
,
Hillis
,
A. J.
,
Morgan
,
G. C. J.
, and
Plummer
,
A. R.
,
2014
, “
Numerical Investigation of Wave–Structure Interaction Using OpenFOAM
,”
Ocean Eng.
,
88
, pp.
91
109
.
11.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
,
Aggarwal
,
A.
, and
Arntsen
,
Ø. A.
,
2016
, “
A New Level Set Numerical Wave Tank With Improved Density Interpolation for Complex Wave Hydrodynamics
,”
Comput. Fluids
,
140
, pp.
191
208
.
12.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2015
, “
Breaking Characteristics and Geometric Properties of Spilling Breakers Over Slopes
,”
Coastal Eng.
,
95
, pp.
4
19
.
13.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2016
, “
Hydrodynamic Characteristics and Geometric Properties of Plunging and Spilling Breakers Over Impermeable Slopes
,”
Ocean Model.
,
103
, pp.
53
72
.
14.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2016
, “
Breaking Wave Interaction With Tandem Cylinders Under Different Impact Scenarios
,”
J. Waterw. Port Coastal Ocean Eng.
,
142
(
5
), p.
04016005
.
15.
Alagan Chella
,
M.
,
Bihs
,
H.
,
Myrhaug
,
D.
, and
Muskulus
,
M.
,
2016
, “
Breaking Solitary Waves and Breaking Wave Forces on a Vertically Mounted Slender Cylinder Over an Impermeable Sloping Seabed
,”
J. Ocean Eng. Mar. Energy
,
3
(
1
), pp.
1
19
.
16.
Kamath
,
A.
,
Bihs
,
H.
,
Alagan Chella
,
M.
, and
Arntsen
,
Ø. A.
,
2016
, “
Breaking Wave Interaction With a Vertical Cylinder and the Effect of Breaker Location
,”
Ocean Eng.
,
128
, pp.
105
115
.
17.
Kamath
,
A.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2015
, “
Numerical Investigations of the Hydrodynamics of an Oscillating Water Column Device
,”
Ocean Eng.
,
102
, pp.
40
50
.
18.
Afzal
,
M. S.
,
Bihs
,
H.
,
Kamath
,
A.
, and
Arntsen
,
Ø. A.
,
2015
, “
Three-Dimensional Numerical Modeling of Pier Scour Under Current and Waves Using Level-Set Method
,”
ASME J. Offshore Mech. Arct. Eng.
,
137
(
3
), pp.
32001
32007
.
19.
Chorin
,
A. J.
,
1968
, “
Numerical Solution of the Navier-Stokes Equations
,”
Math. Comput.
,
22
(
104
), pp.
745
762
.
20.
van der Vorst
,
H. A.
,
1992
, “
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
,”
SIAM J. Sci. Comput.
,
13
(
2
), pp.
631
644
.
21.
Jiang
,
G.-S.
, and
Shu
,
C.-W.
,
1996
, “
Efficient Implementation of Weighted ENO Schemes
,”
J. Comput. Phys.
,
126
(
1
), pp.
202
228
.
22.
Shu
,
C.-W.
,
1997
, “
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
,” Institute for Computer Applications in Science and Engineering (ICASE), Hampton, VA, Technical Report No.
NASA/CR-97-206253
.
23.
Le
,
H.
, and
Moin
,
P.
,
1991
, “
An Improvement of Fractional Step Methods for the Incompressible Navier-Stokes Equations
,”
J. Comput. Phys.
,
92
(
2
), pp.
369
379
.
24.
Shu
,
C. W.
, and
Osher
,
S.
,
1988
, “
Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes
,”
J. Comput. Phys.
,
77
(
2
), pp.
439
471
.
25.
Berthelsen
,
P. A.
, and
Faltinsen
,
O. M.
,
2008
, “
A Local Directional Ghost Cell Approach for Incompressible Viscous Flow Problems With Irregular Boundaries
,”
J. Comput. Phys.
,
227
(
9
), pp.
4354
4397
.
26.
Osher
,
S.
, and
Sethian
,
J. A.
,
1988
, “
Fronts Propagating With Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations
,”
J. Comput. Phys.
,
79
(
1
), pp.
12
49
.
27.
Sussman
,
M.
,
Smereka
,
P.
, and
Osher
,
S.
,
1994
, “
A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
,”
J. Comput. Phys.
,
114
(
1
), pp.
146
159
.
28.
Bihs
,
H.
,
Ong
,
M. C.
,
Kamath
,
A.
, and
Arntsen
,
Ø. A.
,
2013
, “
A Level Set Method-Based Numerical Wave Tank for the Calculation of Wave Forces on Horizontal and Vertical Cylinders
,” Seventh National Conference on Computational Mechanics (MekIT’13), Trondheim, Norway, May 13–14, pp. 59–80.
29.
Kamath
,
A.
,
Alagan Chella
,
M.
,
Bihs
,
H.
, and
Arntsen
,
Ø. A.
,
2015
, “
CFD Investigations of Wave Interaction With a Pair of Large Tandem Cylinders
,”
Ocean Eng.
,
108
, pp.
738
748
.
30.
Mayer
,
S.
,
Garapon
,
A.
, and
Sørensen
,
L. S.
,
1998
, “
A Fractional Step Method for Unsteady Free Surface Flow With Applications to Non-Linear Wave Dynamics
,”
Int. J. Numer. Methods Fluids
,
28
(
2
), pp.
293
315
.
31.
Schäffer
,
H. A.
,
1996
, “
Second-Order Wavemaker Theory for Irregular Waves
,”
Ocean Eng.
,
23
(
1
), pp.
47
88
.
32.
Rapp
,
R. J.
, and
Melville
,
W. K.
,
1990
, “
Laboratory Measurements of Deep-Water Breaking Waves
,”
Philos. Trans. R. Soc. A
,
331
(
1622
), pp.
735
800
.
33.
Ting
,
F. C. K.
, and
Kirby
,
J. T.
,
1994
, “
Observation of Undertow and Turbulence in a Laboratory Surf Zone
,”
Coastal Eng.
,
24
(
1–2
), pp.
51
80
.
34.
Basco
,
D. R.
,
1985
, “
A Qualitative Description of Wave Breaking
,”
J. Waterw. Port Coastal Ocean Eng.
,
111
(
2
), pp.
171
188
.
You do not currently have access to this content.