1、Coastal Hydrodynamics,Chapter 3 WAVE TRANSFORMATIONS,Stating ocean wave characteristics,Stating transformations of waves entering shallow water,2/38,Statistical characteristics of ocean waves,Chapter 3,3.1 Ocean Wave Characteristics,2. Wave height distribution and wave period distribution,3. Ocean w

2、ave energy spectra,4. Deep-water wave propagation,5/39,Chapter 3,What are statistically representative waves?,11/39,Chapter 3,3/38,Rayleigh distribution curve,Chapter 3,3/38,JONS,Chapter 3,Example: a separate wave group moves from the generation area to the coastline.,6/38,Chapter 3,If R is the dist

3、ance from the leading edge of the storm fetch to point A on the coast, then time tob of first observation of arrival of the waves is,For a line source of waves, the final arrival time of waves is,7/38,Wave conservation,Chapter 3,3.2 Wave transformations in shallow water,2. Wave shoaling,3. Wave refr

4、action,4. Wave reflection,5. Wave diffraction,6. Wave breaking,8/38,Chapter 3,Several changes occur as a train of waves propagates into shallow water. One of the most obvious is the change in height as the wave shoals. Other changes such as the decrease in wave length with shallower depths and the c

5、hanges in wave direction are clearly observable from the air.,9/38,Chapter 3,The conservation of wave equation can be expressed as,1. Conservation of wave equations,This equation states that any temporal variation of the wave number vector must be balanced by spatial changes of the wave angular freq

6、uency.,10/38,Chapter 3,If the wave field is constant in time, the wave 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 wave motions but also provides the theoretical basis for the experimenta

7、l simulations of water waves.,11/38,Chapter 3,2. Wave transformation in shoaling water,Assuming that the energy flux is conserved in the process of wave propagation, the wave height at a given water depth can be determined by:,12/38,Chapter 3,ks is named the shoaling coefficient（淺水變 形系數(shù)）,13/38,Chapt

8、er 3,Using the linear theory and recalling the dispersion relationship, we have,It is seen that the wave length at the water depth is determined from the water depth and deep water wave length, the latter easily calculated from the wave period.,14/38,Chapter 3,Wave properties in shallow water,15/38,

9、Chapter 3,It is seen that L and c decrease but n increases with decreasing depth. 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 increase in H as shallower

10、 depths are reached.,16/38,Chapter 3,Upon entering shallow water, waves are subject to refraction（折射）, in which the direction of wave travel changes with decreasing depth of water in such a way that the crest tend to parallel the depth contours.,3. Wave refraction,17/38,Chapter 3,Change of wave ray,

11、The horizontal line along which waves travel is called a wave ray （波向線），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.,18/38,Chapter 3,Wave refr

12、action in shallow water,It can be seen that as the wave celerity decreases as the shore is approached, the angle will also decrease from its deep-water value.,19/38,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

13、in the wave celerity through the same Snells law. For straight coasts with parallel contours,20/38,Chapter 3,21/38,Chapter 3,Change of wave height,In the treatment of wave refraction, it is assumed that no energy flows laterally along the wave crests. Therefore, the transmitted wave energy is conser

14、ved between two rays as waves pass over the changing topography.,22/38,Chapter 3,Conservation 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 across b0 is the same as across b. Finally we have the relationship betwee

15、n deep and intermediate or shallow depth water:,24/38,Chapter 3,In water with straight and parallel offshore contours, it is possible for us to determine the refraction coefficient（折射系數(shù)） kr directly.,25/38,Chapter 3,Wave convergence or divergence,Wave convergence （幅聚） refers to a phenomenon that wav

16、es refract and bend toward headlands so that the wave energy is therefore concentrated. Wave divergence （幅散） refers to a phenomenon that waves refract and diverge over the deep water so that the waves are reduced in height.,26/38,Chapter 3,Wave convergence and/or divergence,27/38,Chapter 3,Wave conv

17、ergence or divergence due to wave refraction is important in deciding where to construct a pier or other structure on coasts.,Case study of wave refraction,28/38,Chapter 3,At the locations of coastal structures or at places where the bottom configuration suddenly changes, a part of wave energy is re

18、flected and the reflected wave is generated. The reflected wave has the same wave period and wave length as the incident wave, but the wave height is different.,4. Wave reflection,29/38,Chapter 3,The reflection coefficient is defined as,which varies with the angle of the slope, the incident wave ste

19、epness and the characteristics of the slope.,30/38,Chapter 3,The reflection coefficient based on the small amplitude wave theory can be determined by measuring the amplitudes at the antinode and node of the composite wave train. However, the determination of the reflection coefficient should be cond

20、ucted experimentally for a concrete engineering.,31/38,Chapter 3,When incoming waves are interrupted by a barrier such as a breakwater or an island, the waves curve around the barrier and penetrate into the sheltered area, meanwhile the wave energy is transferred laterally along a wave crest. This phenomenon is called wave diffraction （波浪繞射）.,5. Wave diffraction,32/38,Chapter 3,Wave diffraction occurs on the sh