OCEN 201Introduction to Ocean &

Coastal Engineering

Ocean Environment &WavesJun Zhang

Jun-zhang@tamu.edu

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