2013 short course on fundamentals of offshore structures...
TRANSCRIPT
To determine wave forces
on an offshore structure
we need to know fluid
velocities & accelerations
under the wave surface
2013 Short Course on Fundamentals of Offshore
Structures and Design of Fixed Offshore Platforms
April 15-26, 2013, UT Austin
Wave Theory and Applications
by
Spyros A. Kinnas
Ocean Engineering Group
UT Austin
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin 1 Copyright 2013 Prof. Spyros A. Kinnas
An offshore structure is
designed to withstand
the 100-year storm
(wave/current/wind). A
mono-chromatic wave of
height Hmax is assumed.
Hmax/L is larger than
required for linear wave
theory to be valid.
Fundamentals of Offshore Structures and Design of Fixed
Platforms, April 9-20, 2012, UT Austin 2 Copyright: Prof. S.A. Kinnas, 2012
Wave velocities and accelerations from linear
wave theory, when used in Morison’s equation,
under-predict wave forces!
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 3
What is the maximum height a wave in deep
water can have (before it breaks)?
L
120o
7breakermax
LHH
Sharp peak!
qcrest
C
Stokes’ Criterion for wave breaking: qcrest=C
Q:How well could linear theory handle waves at breaking?
A: Pretty BAD! (predicts Hmax=L/p in deep water!)
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 4
Stokes’ 2nd order non-linear wave theory (1/2)
)(2cos2
)cos(2
),( 21 tkxH
tkxH
tx
)/4cosh(2)/2(sinh
)/2cosh(
4 and
3
2
21 LdLd
Ld
L
HHHH p
p
pp
1.0/
60/1/
sec 8.3T 60m,L
m1 m, 6d
Ld
LH
H
Case 1
1st order term 2nd order term
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 5
Stokes’ 2nd order non-linear wave theory (2/2)
107/1/
107mL
1) Casein as (same 8.3T
1 water,deep
LH
mH
Case 2
60/1/
sec 6.2T
1) Case as (same m60
1 water,deep
LH
L
mH
Case 3
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 6
Cases 1, 2, & 3
on the graph
by Le Mehaute
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 7
A cleaner version
of the graph
by Le Mehaute
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 8
Different types of waves (1/2):
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 9
Different types of waves (2/2):
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 10
Short-comings of linear wave theory:
Does not produce accurate wave profiles for some
combinations of d/gT 2 and H/gT 2, and cannot handle waves
just before breaking
Does not allow for mass transfer along the wave direction.
Particle trajectories are evolving tight spirals, rather than
closed, as shown here:
Provides inaccurate fluid velocities and accelerations which,
when used in the Morison’s equation (to be described later),
under-predict the forces acting on the elements of an
offshore structure
2013 Short Course on Fundamentals of Offshore Structures and
Design of Fixed Offshore Platforms - April 15-26, 2013, UT Austin Copyright 2013 Prof. Spyros A. Kinnas 11
Detailed formulas for the wave profile and the
corresponding flow-field for a non-linear wave are given
in the provided document:
NOTES ON FIFTH-ORDER GRAVITY WAVE THEORY