精编海岸动力学英文PPT课件Coastal Hydrodynamics_3.1
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Coastal Hydrodynamics_3.1 WAVE TRANSFORMATIONS 海岸动力学课件
Statistically representative waves
➢ The maximum wave corresponds to the maximum height in a given wave group.
➢ The one-tenth highest wave corresponds to the average of the heights of the one-tenth highest waves.
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Chapter 3
Rayleigh distribution curve
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Chapter 3
From statistical theory H110 2.03H
we can obtain important H13 1.60H
relationships using the
distribution function Hrm s1.13H
a function of wave number. In fact, it has
been shown that the wave number and the
frequency are uniquely correlated.
20/39
Chapter 3
If the amplitudes are plotted versus frequency,
There is a great amount of randomness in
the sea, and statistical techniques need to
be brought to bear.
6/39
Chapter 3
Zero-up crossing method
海岸动力学英文PPT课件Coastal Hydrodynamics_2.2
A field of propagating waves consisting of many frequencies would separate due to the different celerities of the various frequency components.
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Chapter 2
Take the pressure on the free surface to be zero.
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Chapter 2
What is the Taylor series ?
If a continuous function f(x,y) of two independent variables x and y is known at the position where x is equal to x0, then it can be approximated at another location on the x axis, by using the Taylor series.
2 gktankhh
LgT2 tanh2h 2 L
cgTtanh2h 2 L
17/21
Chapter 2
Dispersion relationship
This relationship shows that the wave length continually decreases with decreasing depth for a constant wave period. That is to say, waves of constant period slow down as they enter shallow water.
海岸动力学英文PPT课件Coastal Hydrodynamics_2.2
13/21
Chapter 2
2. Solution
Coordinates System
14/21
Chapter 2
How to obtain the solution ? L.B.C G.D.E B.B.C
D.F.S.B.C
Velocity Potential
15/21
Chapter 2
Assuming that the wave slope is small (H/L<<1) and that the water depth is much greater than the wave height (h/H>>1), the solution of velocity potential is:
A field of propagating waves consisting of many frequencies would separate due to the different celerities of the various frequency components.
18/21
Chapter 2
1/21
Assumptions Water is treated as a uniform and incompressible fluid.
The fluid viscosity is normally ignored.
The surface tension and Coriolis force are ignored.
7/21
Chapter 2
What is a small amplitude wave ?
A small amplitude wave is also called a linear wave. It is a wave which travels very slowly, the wave height is far smaller than the wave length and the water depth is much greater than its wave height.
海岸动力学英文PPT课件Coastal Hydrodynamics_2.2
Case study of “wave dispersion”
19/21
Chapter 2
MINI-EXAMINATION (1)
Had we used the surface elevation
asikn x(t) instead of
acoks x(t), how would
f x 0 x , y f x 0 , y f x x 0 , y x 2 f x x 2 0 , y 2 x ! 2 n f x x n 0 , y n x ! n
13/21
Chapter 2
2. Solution
Coordinates System
14/21
Chapter 2
How to obtain the solution ? L.B.C G.D.E B.B.C
D.F.S.B.C
Velocity Potential
15/21
Chapter 2
Assuming that the wave slope is small (H/L<<1) and that the water depth is much greater than the wave height (h/H>>1), the solution of velocity potential is:
11/21
Chapter 2
What is the linear KFSBC ?
Retaining only the terms that are linear in our small parameters,η ,u, v, and w, and recalling thatη is not a function of z, the linear KFSBC can be written as follows.
海岸动力学英文PPT课件Coastal Hydrodynamics_2.2
on z=η
x ,z ,t x c,zt
3/21
Chapter 2
§2.3 Small Amplitude Wave Theory
1. Linearization of basic equations 2. Solution of the linearized equations 3. Dynamic & kinetic characteristics
Coastal Hydrodynamics 海岸动力学
Chapter 2 WAVE THEORY
Stating description of wave motion Stating basic equations of wave motion Stating the small amplitude wave theory Stating the finite amplitude wave theory Stating wave theory limits of applicability
G.D.E. B.B.C. D.F.S.B.C. K.F.S.B.C. L.B.C.
2 0
hz, x
0
z
on z= -h
on t1 2[ x2 z2]p 0g z0 z=η
0
t xx z
1/21
Assumptions Water is treated as a uniform and incompressible fluid.
The fluid viscosity is normally ignored.
The surface tension and Coriolis force are ignored.
海岸动力学英文PPT课件Coastal Hydrodynamics_2.2
t
z
z0
12/21
Chapter 2
Summary
G.D.E. B.B.C. D.F.S.B.C. K.F.S.B.C. L.B.C.
2 0
h z, x
z
zh
0
1
g t
z0
t z
z0
x ,z ,t x c,zt
7/21
Chapter 2
What is a small amplitude wave ?
A small amplitude wave is also called a linear wave. It is a wave which travels very slowly, the wave height is far smaller than the wave length and the water depth is much greater than its wave height.
f x 0 x , y f x 0 , y f x x 0 , y x 2 f x x 2 0 , y 2 x ! 2 n f x x n 0 , y n x ! n
1/21
Assumptions Water is treated as a uniform and incompressible fluid.
The fluid viscosity is normally ignored.
The surface tension and Coriolis force are ignored.
the velocity potential be changed?
2019年-海岸动力学英文PPT课件Coastal Hydrodynamics_2.2-PPT文档资料-PPT精选文档
the velocity potential be changed?
Chapter 2
Homework
A wave with the period of 5s travels in water of 5m, what is its celerity and what is its length?
2 gktankhh
LgT2 tanh2h 2 L
cgTtanh2h 2 L
17/21
Chapter 2
Dispersion relationship
This relationship shows that the wave length continually decreases with decreasing depth for a constant wave period. That is to say, waves of constant period slow down as they enter shallow water.
The bottom is impermeable. Waves travel in the x-z plane.
2/21
continuity equation
velocity potential
gravity only
zero velocity
Chapter 2
Boundary Value Problem of Wave Motion
13/21
Chapter 2
2. Solution
Coordinates System
14/21
Chapter 2
How to obtain the solution ? L.B.C G.D.E B.B.C
Chapter 2
Homework
A wave with the period of 5s travels in water of 5m, what is its celerity and what is its length?
2 gktankhh
LgT2 tanh2h 2 L
cgTtanh2h 2 L
17/21
Chapter 2
Dispersion relationship
This relationship shows that the wave length continually decreases with decreasing depth for a constant wave period. That is to say, waves of constant period slow down as they enter shallow water.
The bottom is impermeable. Waves travel in the x-z plane.
2/21
continuity equation
velocity potential
gravity only
zero velocity
Chapter 2
Boundary Value Problem of Wave Motion
13/21
Chapter 2
2. Solution
Coordinates System
14/21
Chapter 2
How to obtain the solution ? L.B.C G.D.E B.B.C
海岸动力学英文PPT课件Coastal Hydrodynamics_3.3
3. Wave refraction 4. Wave reflection
5. Wave diffraction 6. Wave breaking
3/34
Chapter 3
1. Conervation of wave equation can be
high steepness values. In spilling breakers the
wave gradually peaks until the crest becomes
unstable and cascades down as “white water”
(bubbles and foam).
12/34
Chapter 3
Limiting wave steepness
For any given water depth and wave period, there is an upper limit to the wave height at which the wave becomes unstable and breaks. The limiting steepness （极限波陡） is
21/34
Chapter 3
Numerical Modeling of Surging Breaker
22/34
Chapter 3
7. Case studies
Damage of Langtongmen Breakwater Caused by No.9119 Typhoon
Three-dimensional Experimental Study on Wave Characteristics in Front of Concave Breakwater
5. Wave diffraction 6. Wave breaking
3/34
Chapter 3
1. Conervation of wave equation can be
high steepness values. In spilling breakers the
wave gradually peaks until the crest becomes
unstable and cascades down as “white water”
(bubbles and foam).
12/34
Chapter 3
Limiting wave steepness
For any given water depth and wave period, there is an upper limit to the wave height at which the wave becomes unstable and breaks. The limiting steepness （极限波陡） is
21/34
Chapter 3
Numerical Modeling of Surging Breaker
22/34
Chapter 3
7. Case studies
Damage of Langtongmen Breakwater Caused by No.9119 Typhoon
Three-dimensional Experimental Study on Wave Characteristics in Front of Concave Breakwater
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3. Ocean wave energy spectra
4. Deep-water wave propagation
5/39
Chapter 3
1. Statistical characteristics
The actual sea surface is composed of a large variety of waves moving in different directions and with different frequencies, phases and amplitudes.
Hmax=4.89m, Tmax=8.0s; H1/10=4.7m, T1/10=7.5s; H1/3=3.6m, T1/3=7.8s;
=2.4m,
=7.0s;
Hrms=2.66m.
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Chapter 3
The significant wave is the most frequently used in the coastal engineering field.
The root-mean-square wave height for a given wave group is defined as
10/39
Chapter 3
Example: What are statistically representative waves?
11/39
Chapter 3
minimum levels with adjacent zero-up
crossing points, and the corresponding wave
period is defined by the interval of the two
crossing points.
8/39
Chapter 3
The significant wave height corresponds
roughly to the wave height that is visually
observed and estimated. The significant
wave period has less physical meaning and
Coastal Hydrodynamics
Chapter 2 WAVE THEORY
Stating description of wave motion Stating basic equations of wave motion Stating the small amplitude wave theory Stating the finite amplitude wave theory Stating wave theory limits of applicability
2/39
Chapter 3 WAVE TRANSFORMATIONS
Stating ocean wave characteristics Stating transformations of waves entering shallow water
3/39
§3.1 Ocean Wave Characteristics
Statistical analysis Spectral analysis
4/39
Chapter 3
§3.1 Ocean Wave Characteristics
1. Statistical characteristics of ocean waves
2. Wave height distribution and wave period distribution
The significant wave corresponds to the
average of the heights of the one-third
highest waves.
9/39
Chapter 3
The mean wave corresponds to the mean wave height in a given wave group.
when the surface wave profile crosses the
zero level in the upward direction.
7/39
Chapter 3
An individual wave height is defined by the
vertical difference between the maximum and
Statistically representative waves
The maximum wave corresponds to the maximum height in a given wave group.
The one-tenth highest wave corresponds to the average of the heights of the one-tenth highest waves.
There is a great amount of randomn Nhomakorabeass in
the sea, and statistical techniques need to
be brought to bear.
6/39
Chapter 3
Zero-up crossing method
The zero-up crossing method uses the time
can lead to appreciable error if an attempt
is made to use it in calculations with the
theoretical wave equations.
13/39
Chapter 3
The probability that the wave height is greater than or equal to an arbitrary wave height can be obtained. Then we can obtain the cumulative height curve. The statistically representative waves defined by the excess cumulative probability can be found. For example, H1% represents a wave height corresponding to the intersection of the 1st percentile with the cumulative height curve.