海岸动力学英文PPT课件Coastal Hydrodynam(12)
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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.
15/39
Chapter 3
Rayleigh distribution curve
16/39
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_5.1.
2/39
Chapter 5
1. Physical properties
Beach materials mainly consist of the sand and gravel transported by rivers, the sand composing dunes located in the
1/39
§5.1 Characteristics of Coastal Sediment 1. Physical properties of coastal sediment 2. Modes of coastal sediment movement 3. Threshold of coastal sediment motion
influence of waves and nearshore currents in the
onshore or offshore directions, or parallel to the
shoreline. There are two modes of sediment
movement: suspended sediment movement and
and littoral drift, are distribution of grain size,
shape, roundness, mineral composition,
porosity, permeability, etc. Among them, grain
size distribution and mineral composition are
bed load movement.
8/39
Chapter 5
Incoming waves reach a certain water depth (offshore region), then bed material sand particles there begin oscillatory motion due to wave action. In a slightly more shallow area, waves produce a net motion of sand particles in the onshore or offshore direction. The interesting feature in this region is the generation of sand ripples, which seem to have a strong influence on sediment movement.
海岸动力学英文PPT课件Coastal Hydrodynamics_复习
a c gc oko h s k s h z h h sikn x (t)
While the elevation of the water surface is
acoks x(t)
Substituting the velocity potential and the surface elevation into the K.F.S.B.C yields the dispersion relationship.
3/130
§2.1 Description of Wave Motion 1. Classification of waves 2. Methods of describing fluid motion 3. Theories commonly used to describe
wave motion 4. Basic parameters of regular waves
H H0
1 c0 2n c
ks
3. Wave refraction
For straight coasts with parallel contours,
si n1si n2constsain n0 t
c1
c2
c0
HH0
1c0 2nc
b0 b
H0kskr
1
1
1
kr b b02cco o 0ss21 1 ssii2n 2n 04
2 gktankhh
gT2 2
L tanh h
2 L
c2gTtanh2Lh
A deep water wave is a wave whose wavelength is very small compared with the water depth.
While the elevation of the water surface is
acoks x(t)
Substituting the velocity potential and the surface elevation into the K.F.S.B.C yields the dispersion relationship.
3/130
§2.1 Description of Wave Motion 1. Classification of waves 2. Methods of describing fluid motion 3. Theories commonly used to describe
wave motion 4. Basic parameters of regular waves
H H0
1 c0 2n c
ks
3. Wave refraction
For straight coasts with parallel contours,
si n1si n2constsain n0 t
c1
c2
c0
HH0
1c0 2nc
b0 b
H0kskr
1
1
1
kr b b02cco o 0ss21 1 ssii2n 2n 04
2 gktankhh
gT2 2
L tanh h
2 L
c2gTtanh2Lh
A deep water wave is a wave whose wavelength is very small compared with the water depth.
海岸动力学英文PPT课件Coastal Hydrodynamics_6.1
11/32
Chapter 6
Backshore（后滩）: The zone of the beach
profile extending landward from the sloping
foreshore to the point of development of
vegetation or change in the physiography
which is named the equilibrium
Chapter 5
On natural beaches the changing waves give
rise to an ever-varying equilibrium which
respond to the ever-changing waves and
currents imposed from the adjacent body of
the water. However, the only way in which
beach profiles can be understood is in terms
breaking waves. In this region, breaking wave
action predominates to intensify the turbulent
intensity of fluid motion, thus putting a large
amount of sediment in suspension.
which a constant wave input is maintained,
the beach profile will reach a steady state
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
海岸动力学英文课件CoastalHydrodynam
Nearshore circulation
The horizontal movement of water caused by tides, which can be either towards or away from the shore
Tidal streams
A narrow channel where strong Tidal currents meet, often resulting in turbulence and mixing
The study of coastal dynamics covers a wide range of topics, including wave dynamics, sedimentation transport, coastal erosion and retention, delta formation and evolution, island evolution, and the impact of human activities on coastal environments
The Physical Foundations of Coastal Dynamics
The vertical range of water level changes caused by the gravitational attraction of the moon and sun on the Earth's oceans
Description
01
A simplified model that considers only one spatial dimension, commonly representing the shoreline as a single point
The horizontal movement of water caused by tides, which can be either towards or away from the shore
Tidal streams
A narrow channel where strong Tidal currents meet, often resulting in turbulence and mixing
The study of coastal dynamics covers a wide range of topics, including wave dynamics, sedimentation transport, coastal erosion and retention, delta formation and evolution, island evolution, and the impact of human activities on coastal environments
The Physical Foundations of Coastal Dynamics
The vertical range of water level changes caused by the gravitational attraction of the moon and sun on the Earth's oceans
Description
01
A simplified model that considers only one spatial dimension, commonly representing the shoreline as a single point
海岸动力学英文PPT课件Coastal Hydrodynamics_3.2
tob
R Cg
4 R
gT
For a line source of waves, the final arrival time of waves is
tobRCgDtob4gDT
7/38
Chapter 3
§3.2 Wave transformations in shallow water 1. Wave conservation 2. Wave shoaling
period does not change with space, even as
the water depth changes.
This feature is very important because it is
not only of convenience for the analysis of
It can be found that there should be a small
decrease in the wave height in the intermediate
water depths to a value below the deep water
wave height.
The decrease is then followed by a rapid
Coastal Hydrodynamics
Chapter 3 WAVE TRANSFORMATIONS
Stating ocean wave characteristics Stating transformations of waves entering shallow water
2/38
§3.1 Ocean Wave Characteristics
海岸动力学英文PPT课件Coastal Hydrodynamics_3.2
servation of wave energy flux between two rays
23/38
Chapter 3
Recognizing that there is no energy flux across
the
wave
rays,
the
energy
flux
Chapter 3
The refraction of water wave is analogous to the bending of light rays, and the change in direction is related to the change in the wave celerity through the same Snell’s law. For straight coasts with parallel contours,
H H0
1 c0 2n c
ks
12/38
Chapter 3
ks is named the shoaling coefficient（浅水变 形系数）
ks
1
tanhkh1 2kh
sinh2kh
13/38
Chapter 3
Using the linear theory and recalling the dispersion relationship, we have
17/38
Chapter 3
Change of wave ray
The horizontal line along which waves travel is called a wave ray （波向线），which is defined as a line along which the wave number vector is always tangent. As energy travels in the direction of the wave, the wave energy associated with the wave travels along the wave ray also.
23/38
Chapter 3
Recognizing that there is no energy flux across
the
wave
rays,
the
energy
flux
Chapter 3
The refraction of water wave is analogous to the bending of light rays, and the change in direction is related to the change in the wave celerity through the same Snell’s law. For straight coasts with parallel contours,
H H0
1 c0 2n c
ks
12/38
Chapter 3
ks is named the shoaling coefficient（浅水变 形系数）
ks
1
tanhkh1 2kh
sinh2kh
13/38
Chapter 3
Using the linear theory and recalling the dispersion relationship, we have
17/38
Chapter 3
Change of wave ray
The horizontal line along which waves travel is called a wave ray （波向线），which is defined as a line along which the wave number vector is always tangent. As energy travels in the direction of the wave, the wave energy associated with the wave travels along the wave ray also.
《海岸动力学》课件
模型材料选择
选择合适的材料和比例，以真实反映海岸地形的 结构和特征，为实验提供可靠的基础。
实验操作与控制
在模拟环境中进行实验，控制各种参数，观察并 记录海岸地貌的变化，分析其演变规律。
现场观测实验
观测点选择
选择具有代表性的观测点，考虑 地形、水深、流速等因素，确保 数据的准确性和可靠性。
长期观测
进行长期现场观测，收集大量实 测数据，分析海岸地貌的演变趋 势和规律。
2
数值模拟与计算可以模拟海岸动力学的各种复杂 现象，如潮汐、波浪、泥沙运动等，为实际工程 和环境保护提供科学依据。
3
数值模拟与计算需要借助高性能计算机和专业软 件，以实现大规模复杂系统的模拟和计算。
04
海岸动力学的实验研究
实验室模拟实验
模拟环境构建
通过模拟海浪、潮汐、风等自然环境因素，研究 海岸地貌在不同环境条件下的演变过程。
流体流动的分类
介绍层流和湍流的概念，以及它们在海岸动力学中的 应用。
波浪理论
波浪的分类
01
根据波高、周期和波长等参数对波浪进行分类。
线性波动理论
02
介绍线性波动理论的基本原理，包括波动方程的推导和求解方
法。
非线性波动理论
03
介绍非线性波动理论的基本原理，以及波浪的破碎和变形等现
象。
潮汐与潮流
潮汐的形成
海岸动力学涉及到海洋学、气象学、 地貌学、工程学等多个学科领域，是 研究海岸带变化和开发利用的重要基 础。
海岸动力学的研究内容
海浪研究
研究海浪的形成、传播、变形 以及与海岸的相互作用，包括 波浪折射、反射、破碎等现象
。Байду номын сангаас
潮汐研究
选择合适的材料和比例，以真实反映海岸地形的 结构和特征，为实验提供可靠的基础。
实验操作与控制
在模拟环境中进行实验，控制各种参数，观察并 记录海岸地貌的变化，分析其演变规律。
现场观测实验
观测点选择
选择具有代表性的观测点，考虑 地形、水深、流速等因素，确保 数据的准确性和可靠性。
长期观测
进行长期现场观测，收集大量实 测数据，分析海岸地貌的演变趋 势和规律。
2
数值模拟与计算可以模拟海岸动力学的各种复杂 现象，如潮汐、波浪、泥沙运动等，为实际工程 和环境保护提供科学依据。
3
数值模拟与计算需要借助高性能计算机和专业软 件，以实现大规模复杂系统的模拟和计算。
04
海岸动力学的实验研究
实验室模拟实验
模拟环境构建
通过模拟海浪、潮汐、风等自然环境因素，研究 海岸地貌在不同环境条件下的演变过程。
流体流动的分类
介绍层流和湍流的概念，以及它们在海岸动力学中的 应用。
波浪理论
波浪的分类
01
根据波高、周期和波长等参数对波浪进行分类。
线性波动理论
02
介绍线性波动理论的基本原理，包括波动方程的推导和求解方
法。
非线性波动理论
03
介绍非线性波动理论的基本原理，以及波浪的破碎和变形等现
象。
潮汐与潮流
潮汐的形成
海岸动力学涉及到海洋学、气象学、 地貌学、工程学等多个学科领域，是 研究海岸带变化和开发利用的重要基 础。
海岸动力学的研究内容
海浪研究
研究海浪的形成、传播、变形 以及与海岸的相互作用，包括 波浪折射、反射、破碎等现象
。Байду номын сангаас
潮汐研究
海岸动力学英文PPT课件Coastal Hydrodynamics_2.5 共40页
32H(H)cos2kh(zh)si2n(kxt)
8 kT L sin4(hkh)
For finite height waves there is an additional term added onto the equation obtained in the linear wave theory.
11/36
Chapter 2
The added term enhances the crest amplitude
and detracts from the trough amplitude, so
that the Stokes wave profile has steeper crests
separated by flatter troughs than does the
13/36
Chapter 2
Second-order solution Velocity components are
wHsinkh(zh)sink(xt)
T sinkhh)(
32H(H)sin2hk(zh)sin2(kxt)
4 T L sin4(hkh)
14/36
Chapter 2
15/36
Chapter 2
Comparison of bottom orbital velocity under Stokes wave with that of linear wave of the same height and length (H=4m, h=12m, T=12sec)
16/36
The relationship for the energy flux is
P T 10 Tdt 0 hp dudzE 1 2 c 1s2 ik2 n khh h Ecn
8 kT L sin4(hkh)
For finite height waves there is an additional term added onto the equation obtained in the linear wave theory.
11/36
Chapter 2
The added term enhances the crest amplitude
and detracts from the trough amplitude, so
that the Stokes wave profile has steeper crests
separated by flatter troughs than does the
13/36
Chapter 2
Second-order solution Velocity components are
wHsinkh(zh)sink(xt)
T sinkhh)(
32H(H)sin2hk(zh)sin2(kxt)
4 T L sin4(hkh)
14/36
Chapter 2
15/36
Chapter 2
Comparison of bottom orbital velocity under Stokes wave with that of linear wave of the same height and length (H=4m, h=12m, T=12sec)
16/36
The relationship for the energy flux is
P T 10 Tdt 0 hp dudzE 1 2 c 1s2 ik2 n khh h Ecn
海岸动力学英文PPT课件Coastal Hydrodynamics_2.3
24/31
Chapter 2
The hydrostatic pressure exists without the presence of waves.
The dynamic pressure is a result of two contributions: the most obvious contributor is the surcharge of pressure due to the presence of the free surface displacement; the other is the vertical acceleration associated with the wave motion.
22/31
Chapter 2
Water particle velocities in a progressive wave
23/31
Chapter 2
Pressure field
The pressure field associated with a progressive wave is determined from the unsteady Bernoulli equation.
6/31
Chapter 2
Dispersion relationship
Substituting the velocity potential and the
surface elevation into the K.F.S.B.C yields
2 gktankhh
LgT2 tanh2h 2 L
cgTtanh2h 2 L
19/31
Chapter 2
In shallow water, the orbital semi-axes reduce
海岸动力学英文PPT课件Coastal Hydrodynam
Bay is an excellent example of the way in which
local beaches orient themselves parallel to the
refracted wave crests and develop the same
curvature.
Chapter 6
Chapter 6
When Qin is equal to Qout, which indicates that there is neither erosion nor deposition within the compartment, therefore the coast is stable. The lack of either beach erosion or deposition indicates that a state of equilibrium exists between the sources and losses.
Chapter 6
A growing spit often
deflects the mouth
of a river or the
entrance to a bay
prolonging it in
the direction of
longshore
sediment
drift.
Chapter 6
1. Shoreline n For a given littoral compartment, suppose the rate of sediment drift into the compartment is denoted as Qin, and Qout is the rate drift out.
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this manner, this theory is also called small
amplitude wave theory.
5/21
Chapter 2
Sir George Biddell Airy(1801-1892) was an English astronomer who worked in a variety of areas of science. His major work with respect to this course is his development of small amplitude water wave theory. His research encompassed magnetism, tides, geography, gravitation, partial differential equations, and sound. In 1826 he was appointed the Chair of Mathematics at Cambridge. He became the Astronomer Royal in 1835.
4/21
Chapter 2
1. Linearization
In 1845, Airy developed a theory for irrotational
waves traveling over a horizontal bottom in any
depth of water. In the derivation of this theory
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 bottom is impermeable. Waves travel in the x-z plane.
2/21
cy potential
gravity only
zero velocity
Chapter 2
Boundary Value Problem of Wave Motion
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
η on z= t1 2[ x2 z2]p 0g z0
0
t xx z
on z=η
x ,z ,t x c,zt
3/21
Chapter 2
§2.3 Small Amplitude Wave Theory
the equation is linearized, and for this reason
the theory is often referred to as the linear wave
theory. In order to develop the linearization,
the waves should be infinitesimally small, in
6/21
Chapter 2
What is linearization ? For infinitesimally small waves, the displacement of the free surface is small, and therefore it is assumed that velocities and pressures are small; thus any products of these variables are small enough to be ignored. This process is called linearization. Linear in the sense that variables are only raised to the first power.
1. Linearization of basic equations 2. Solution of the linearized equations 3. Dynamic & kinetic characteristics
of small amplitude waves 4. Standing waves
8/21
Chapter 2
How to linearize DFSBC & KFSBC ?
➢ Suppose that the wave is a small amplitude wave, namely H<<L or H<<h.
➢ Use the Taylor series expansion to relate the boundary conditions at the unknown elevation to the still water level.
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.