ocen 201 introduction to ocean & coastal engineering ocean environment &waves jun zhang...
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OCEN 201Introduction to Ocean &
Coastal Engineering
Ocean Environment &WavesJun Zhang
General Information
• 71% of the Earth surface is covered by Oceans• Major Oceans 1. Pacific Ocean (46%) 2. Atlantic Ocean (23%) 3. Indian Ocean (20%) 4. Remaining Oceans (11%)
• Average Ocean Depth is 3800 m• Maximum Depth is 11,524 m
Ocean FloorReading assignment pp17-19
P18
Physical Properties of Ocean WaterReading assignment pp19-20
Primary sea water elements1. Chlorine (55%)2. Sodium (30.6)3. Sulfate (7.7%)4. Sodium (30.6)5. Magnesium (3.7%)6. Potassium (1.1%)Salinity: amount (grams) of dissolved solid
materials (salts) in grams contained in a kilogram seawater (ppt). e.g. Sea Water 35 ppt
Ocean CurrentsReading assignment pp19-25Geostrophic Current (pressure gradients &
Coriolis force)Ekman Current (Surface wind friction force &
Coriolis force)
TidesReading assignment pp23-25
1. Diurnal tide (once in a tidal day)2. Semi-diurnal tide (twice in a tidal day) 3. Mixed tide (tidal day 24.84 hr)
Tidal day: rotation of the Earth with respect to the Moon, ~24.84 hr
Fields Related to Ocean Wave
•Ocean Engineering: Ship, water borne transport, offshore structures (fixed and floating platforms). • Navy: Military activity, amphibious operation,
WW II Allies landing. • Coastal Engineering: Harbor and ports, dredging, coastal
structures, beach erosion, sediment transport.
•Oceanography: Ocean environment, atmosphere, fishing, oil spilling, mixing, pollutant transport. • Environmental Eng.: Capping contaminated dredged material. Diffusion and dispersion of toxic material in ocean and costal water.
Regular and Irregular Waves
Ocean waves are almost always irregular and often directional (short-crested).
Irregular waves can be viewed as the superposition of a number of regular waves.
Regular waves have the same frequency, wavelength and amplitude (height).
0 2 4 6 8 10 12 14 16 18 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
T
Time t
Regular Waves
1; -- frequency (1/s) and -- Wave period
/ 2 a -- amplitude and -- Wave height
f f TT
a H H
Ocean (Irregular) Waves Definitions of Zero-Upcrossing & Downcrossing
Wave Pattern Combining Four Regular Waves
FFT & IFFT – (Inverse) Fast Fourier Transform. Irregular wave Regular Waves (Frequency Domain Analysis)
Pierson-Moskowitz Spectrum
42
4 5
5( ) exp
42
where --- constant depending on wind
PMp
g fE f
ff
JONSWAP Spectrum
2
24 exp2 2
4 5
5( ) exp
42
where --- constant depending on wind
sharp factor =1 - 7 (average 3.3)
p
p
f f
f
PMp
a p
b p
g fE f
ff
f f
f f
Ocean Wave Spectra: P-M & JONSWAP Types
Actual Versus Design Seas
Wave Pressure and Kinematics
•Linear Wave Theory: Simple, good approximation for70-80 % engineering applications.
•Nonlinear Wave Theory: Complicated, necessary for about 20-30 % engineering applications.
•Both results are based on the assumption of non-viscous flow.
•Examples, see animations.
ENVIRONMENT OVERVIEW
• Picture showing wind, wave, current, and seafloor for semisubmersible FPS
Linear Wave Theory ----- Dispersion Relation
2 tanh
where the gravitational acceleration
2 wave (radian) frequency 2
wavenumber 2 /
water depth
wave period
gk kh
g
fT
k k L
h
T
L
2
2 2
wave length
In deep water ( 1, / 1)
In shallow water ( / 1)
hk h L gk
h L gk h
Using the Dispersion Relation to Find T or L
2 tanh
Knowing (or ) and to comput is striaght forward.
However, knowing (or ) to comput (or ) is not.
It is usually done using method. For example,
Given = 0.62832 rad/s
gk kh
k L h
T k L
iteration
2
(1)
1(1) (1) (1)
(1)
2
(2)
( = 10s) and = 20 m,
1st guess, (assuming deep water),
0.04024 m , 2 / 156.131 m
Check 2 , it is not deep water.
2nd guess,
T h
kg
k L k
L h
k
1
(1)
0.06036 m tanh( )g k h
Use of Dispersion Relation
21
(3)(2)
21
(4)(3)
21
(9)(8)
2
(10)(9)
3rd guess 0.04814 mtanh( )
4th guess 0.05397 mtanh( )
.........
9th guess 0.05174 mtanh( )
10th guess 0.05tanh( )
kg k h
kg k h
kg k h
kg k h
1
21
(11)(10)
187 m
11th guess 0.05180 m tanh( )
kg k h
Definition of Deep, Intermediate and Shallow Water Waves
Deep water 1 or / 1
Shallow water 1 or / 1
Deep water / 1/ 2
Shallow water / 1/ 20 or 1/25
Intermediate water 1/ 20 or 1
hk h L
hk h L
h L
h L
Scientific definition
Engineering Definition
/25 / 1/ 2h L
Linear Wave Theory ----- Phase velocity (celerity)
/ /
In intermediate water depth / tanh /
In deep water /
In shallow water
C L T k
C k g kh
C g
C gh
Linear Wave Theory ----- Group (energy) velocity Wave energy propagates at Cg
/
1In intermediate water depth
2 sinh 2
In deep water 2 2
In shallow water
g
g
g
g
C k
khC
k kh
CC
k
C gh C
Linear Regular (Periodic) Wave ----- Elevation & Potential cosh ( )
cos( ) sin( )cosh( )
1where the amplitude ( )
the initial phase ( 0, periodic wave)
the potential (computing wave kinematics
Ag k z hA kx t kx t
kh
Ag t
& pressure)
In deep water = exp( )sin( )
cosh ( ) = cos( )
sinh( )
sinh ( )= sin( )
sinh( )
cosh ( )1cos( )
cosh( )
Agkz kx t
A k z hu kx t
x kh
A k z hw kx t
z kh
A k z hpz z kx t
g g t kh
Linear Regular (Periodic) Wave Energy Density: Average energy per wavelength and per unit width.
2 2
Wave Energy = Potential Energy + Kinetic Energy
Energy Density ( ) =
(Total Wave Energy over one wavelength)/( *1)
1 1
2 8density of water
gravitational acceleration
E
L
E gA gH
g
Nonlinear Wave Theory
•Stokes Expansion
•Hybrid Wave Model
•Boussinesq Equation (shallow water)
•Finite amplitude wave theory
Web-site for animationshttp://cavity.ce.utexas.edu/kinnas/wow/public_html/waveroom/index.html
and Course OCEN 675
http://cavity.ce.utexas.edu/kinnas/wow/public_html/waveroom/index.html