Capsizing of Ships Following sea is the most dangerous!
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Transcript of Capsizing of Ships Following sea is the most dangerous!
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Capsizing of Ships
Following sea is the most dangerous!
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Q#5: Perfect Standing WaveQ#5: Perfect Standing Wave(Reflection from vertical wall)(Reflection from vertical wall)
cos( ) cos( )A kx t A kx t
2 cosh ( )cos sin
cosh
gA k z hkx t
kh
( )kze deep
Total Pressure
,u wx z
p gzt
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Partial Standing Wave
cos( ) cos( )2 2( )cos ( )sin
( ) cos cos( )2 2where
( ) sin sin( )2 2
i r
i r
i r
H Hkx t kx t
I x t F x t
H HI x kx kx
H HF x kx kx
2 2
( )Max/Min when 0 tan
( )
cos(2 )2 2 2i i rr
F xt
t I x
H H HHkx
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max
min
max min
max min
max min
1At quasi-antinode : ( )
21
At quasi-node : ( )2
distance between and 4
Reflection coefficient
i r
i r
i
r
r
i
H H
H H
L
H
H
H
H
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Typical Size of LNG Tank
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Seiching
Long-period oscillation of harbors due to resonance sloshing
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[1] (24%) Select proper answer When celerity depends on wave length, the wave is
called (dispersive wave, non-dispersive wave). With (dispersive wave, non-dispersive wave),
communication is possible. Acoustic waves are (dispersive waves, non-dispersive
waves). Wave induced dynamic pressure is (linearly,
quadratically) proportional to wave height. When the distance between semi-antinode and semi
node of a partial standing wave is 30m, the wavelength of the incident wave is (120m, 60m)
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(Longer, Shorter) water waves travel faster in deep water. The front of water waves in deep water moves with (celerity,
group velocity). The primary restoring force for water waves of wavelength=20-
200m is (gravity, Coriolis, surface tension) force. The wave energy is (linearly, quadratically) proportional to wave
height. Long waves generated by large-scale atmospheric pressure
variation are called (tidal waves, tsunamis, storm surge) The maximum vertical acceleration of water-wave particles occurs
at (crest, crossing point) Water depth=200m is considered to be (deep, transitional) for a
sinusoidal water wave of wavelength=470m.
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[2] (6%) When a hypothetical sinusoidal wave satisfies the dispersion relation ω²=2k² between circular frequency ω and wave number k, find its celerity and group velocity.
[3] (4%) When the potential energy of a
regular wave for certain area is 20000J, what is the corresponding kinetic energy?
[4] (6%) The group velocity of a shallow
water wave is 3m/s. What is the corresponding water depth?
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[5] Consider a deep-water wave with 8-s period and 4-m height?
(a) (10%) What is the power of this wave along the crest width of 500m?
(b) (10%) If this deepwater wave propagates to the area of 2-m water depth, what is the new wave length and wave height at that location? (Assume 2D wave of normal incidence, shallow-water wave at 2-m depth, and mild bottom slope: use conservation of wave energy flux (power))
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[6] (a) (5%) When wave length is 100m at 10-m water depth, what is the corresponding wave period?
(b) (10%) When wave height=2m, what is the major semi-axis of the elliptical particle trajectory at z=-3m?
(c) (10%) What is the amplitude of the horizontal particle velocity at the same location z=-3m?
(d) (15%) If a vertical wall is present at the 10-m depth, a perfect standing wave will be formed in front of the wall. In that case, what is the dynamic pressure amplitude of the standing wave at z=-3m under the anti-node.
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Wave Refraction
Change of wave heading due to bottom topography
Cf. reflection, diffraction
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Refraction : change of wave direction due to bottom topography
0 10 1
0 0
1 1
0 10 1
0 0
1 1
from geometry
sin , sin. .
sinfind new heading
sin
cos , cos. .
cosfind new B
cos
c t c t
Diag Diag
c a
c a
B B
Diag Diag
B a
B a
< Snell’s law >
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Combined shoaling & Refraction
2 20 0 0
0 0
0
reflectionIf negligible
diffraction
Power(Energyflux) Conservation
1 1
2 2
shoaling coefficientwhere
= refraction coefficient
Normal Incidence no refracti
g g
gs r
g
s
r
gA B C gA B C
C BAK K
A C B
K
K
on
Oblique Incidence refraction occurs!
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Wave Breaker Type
Spilling: steeper crest : loose stability at cusp: mild beach slope
Plunging: overturning: steeper beach
Surging: bottom part surges over high-sloped beach: very steep beach=high reflection
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Plunging Breaking Waves
Waves break when the crest particle velocity exceeds its celerity.
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Wave Breaking
Deep & transitional depth:General: H/L=(1/7)tanh khDeep: H/L=1/7=0.14
Shallow McCowan’s criterion: flat bottomH=0.78hGoda-Weggel chart: with slope
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Wave Breaker Ex.) SPM 2-135
Given: Ho=2m, T=10s, beach slope=1/20, Kr=1.05
Find: breaker height Hb, depth hb, type by using Goda-Weggel chart
Unrefracted deepwater height: Ho’=Kr*Ho
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Unrefracted deepwater height: Ho’=Kr*Ho =2.1mHo’/GT²=0.00214From fig.2-72(m=0.05): Hb=3.15m; plunging
Hb/Ho’=1.5 & Hb/GT=0.0032From fig.2-73hb/Hb=0.96 therefore hb=3.02m
Surf-zone length=3.02/0.05=60m
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Wave breaking (20pt)
Deepwater T=8s, H=2m (Normal Incidence); beach slope=1/20
Find breaker height, breaker depth, and breaker type using the chart
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Wave-theory Selection Diagram
Water depth=1m, wave period=7s, wave height=0.3 m
Find the best wave theory
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Wave Kinematics
)sin(sinh
)(sinhtkx
kd
zdk
T
Hw
)(2cos)(4sinh
)(2cosh2
16
3)cos(
cosh
)(cosh
2tkx
kd
zdkkHtkx
kd
zdkgkHu
)cos(sinh
)(coshtkx
kd
zdk
T
Hu
)(4sinh
)(2sin)(2sinh2
16
3)sin(
cosh
)(sinh
2 kd
tkxzdkkHtkx
kd
zdkgkHw
Linear Wave KinematicsLinear Wave Kinematics
Stokes 2Stokes 2ndnd-order Wave Kinematics-order Wave Kinematics
t
uax
t
waz
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3/27 SNAME Offshore Sym
Rec. Center (Garden Room)9:00 – 3:00
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2010 OCEN300 MINI-TERM PROJECT
Research on Ocean Hydro-Power
Team (5-member) selects a research topic related to ocean wave energy and tidal/current energy conversion.
Select a particular concept/system and describe how it works.
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Discuss pros and cons compared with other existing concepts.
Discuss its efficiency, survivability, and environmental impacts
Discuss the estimated cost when realized as a proto-type system.
Discuss the ideas how the existing technology and cost-effectiveness can be improved.
Prepare a 5-page report summarizing the study. (Report due on 5/4)
Prepare a team presentation. (Schedule: 4/29 A-E; 5/4)
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A: Allahar Jacquelene, Babbitt Charles, Blackburn Megan, Blackmar Philip, Brotzman Duncan
B: Brzezniak Michael, Cantu Felix, Castro Adrian, Dailey David, Demmer Michael
C: Feldman Kyle, Fields Waylon, Finkelshteyn Michael, Fisher Ian, Fluitt Timothy
D: Ford Bryce, Forester Aaron, Freyman Michael, Galatas Joel, Gibson Allison
E: Goebel Kevin, Gonzales Stephanie, Grant Alexander, Holub Chase, Hulsey Jennifer
F: Keel Ryan, Knoll Alex, Lee Sangwook, Lindanger Christopher, McBee Harvey
G: McClung Evan, McNeil Ryan, Medellin Abel, Messina Michael, Mieras Ryan
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H: Novasad Nicholas, Outten Kyle, Parker Christopher, Ramsey Paul, Ryan Christopher
I: States William, Stevenson Katy, Tallichet Jules, Thi Andy J: Tipton Craig, Vittone Cynthia, Walsh Andrew, Oyenike
Olaniyi
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Wave diffraction: wave deformation by structures
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Stokes’ 2nd-order Wave Theory
η= +
Valid when Ursell #: LH/h< 26.3
cos( )A kx t 21cos(2 2 )
2kA kx t
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Geometric Comparison
Nonlinear waves
higher and sharper crests
Shallower and flatter troughs
large steepness H/L (Linear theory assumes small amplitude)
Opened Orbit: Stokes’ drift
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WAVE-CURRENT INTERACTION
Wave in Coplanar CurrentH smaller, L longer: wave steepness
decreased, C faster
Wave in Adverse CurrentH larger, L shorter: wave steepness
increased, C slower
If adverse-current velocity > 0.5C: breaking
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Long waves
Tsunami Storm surge Tide
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Tsunami
Long-period (tens of minutes) gravity waves generated by submarine earthquakes, landslides, volcano eruptions, explosion, asteroid impact
Can build up heights in coastal regions as large as 30m
(ex. Hilo, Hawaii: 11m, Wavelength: can be as large as 200km)
Typical speed:Deep: speed of airplane (e.g. 500miles/hr)Coastal: speed of car (e.g.70 miles/hr)
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Tsunami
Magnitude of Earthquake Richter Scale M=log(A/Ao)(A: max. amplitude recorded by a seismograph
at 100km from epi-center, Ao=0.001mm)
Tsunami Magnitude m=2.61M-18.44M=7, m=0(Hmax=1m): small damageM=8, m=2.4(Hmax=10m)M>8.6, m>4(Hmax=30m): considerable damage
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Before 2004 Dec. 26 Tsunami
After December 26 Tsunami
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Storm Surge
Suction effects by large-scale low atmospheric pressure
Wave/water-mass pile up at costal region by strong winds
Max. anomaly=f(max. wind vel., wind direction, lowest atmospheric pressure)
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Storm surge
Although the wind shear stress is usually small, its effect, when integrated over a large body of water, can be catastrophic.
Hurricanes, blowing over the shallow continental shelf of GOM, have caused rises in water levels in excess of 6m at the coast.
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Empirical storm-surge forecasting
Max anomaly (sea-rise in cm)=a P + b V² cos D
a=0.99 cm/mbb=0.048(baylength(km)/ bay
meandepth(m))V=max wind velocity (m/s)P=(spatial mean – lowest) atmospheric
pressureD=wind direction
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Empirical Storm-surge Forecasting EX
Find the maximum sea-rise when
Lowest atm pressure=0.85 barSpatial mean atm pressure=1 barBay length=5kmBay mean depth=5mMax wind velocity=50m/sNormal wind direction
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Tidal Wave: sun-moon-earth gravitation
Semi-diurnal tide: 2 highs & 2 lows/day (ex Cape-Cod)
Diurnal tide: 1 high & 1 low/day (ex New Orleans)
Mixed tide: combination 1 semi-high and 1 major high – (ex Los Angeles)
Tidal Current: Ex. 3.1m/s (San Francisco) max=5.2m/s NOS (National Ocean Survey)
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Tidal Energy (7)
Promising West Coast Sites
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Tidal Energy (3) 21st Century projects
under consideration are based on ‘in stream turbine’ technology at sites with high tidal current velocities
Only a limited number of suitable sites in continental USA with San Francisco the best
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Current Energy Conversion
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Tidal Energy Conversion
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Tidal Energy (2)
La Rance dam and typical turbine/generator configuration
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http://www.youtube.com/watch?v=ZcA3e8_j8XA
http://www.youtube.com/watch?v=rQtMPdLZ2L4&NR=1
http://www.youtube.com/watch?v=94iZa96HpUA
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Tidal Energy
http://www.youtube.com/watch?v=tSBACzRE3Gw&feature=related
http://www.youtube.com/watch?v=4Iq-h4ShZ8s&feature=related
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Have a Good Spring Break!
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WOW (Waves On Web)
Ceprofs.tamu.edu/mhkim/wow
cavity.ce.utexas.edu/kinnas/wow/public_html/waveroom
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Wavemaker: Review
Flap motion: 1.5 cycles/s, h=80cm, H=3cm Find T=?, L=?, C=?, k=?, w=?, Cg=?, Power(tank
width=90cm)=? Breaking? Speed of wave front=? max horizontal particle velocity? max radius of particle orbit? Total max pressure 10cm below MWL?
Mild-slope (m=0.05) is installedH & L at h=4cm? C=? Cg=? Will it break? What
type? Length of surf-zone? Which wave theory?