海岸动力学英文课件CoastalHydrodynamics31

1、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 ch

2、aracteristics,Stating transformations of waves entering shallow water,3/39,Chapter 3,3.1 Ocean Wave Characteristics,Statistical analysis,Spectral analysis,4/39,Statistical characteristics of ocean waves,Chapter 3,3.1 Ocean Wave Characteristics,2. Wave height distribution and wave period distribution

3、,3. Ocean wave energy spectra,4. Deep-water wave propagation,5/39,Chapter 3,The actual sea surface is composed of a large variety of waves moving in different directions and with different frequencies, phases and amplitudes.,1. Statistical characteristics,There is a great amount of randomness in the

4、 sea, and statistical techniques need to be brought to bear.,6/39,Chapter 3,The zero-up crossing method uses the time when the surface wave pro the zero level in the upward direction.,Zero-up crossing method,7/39,Chapter 3,An individual wave height is defined by the vertical difference between the m

5、aximum and 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 maximum wave corresponds to the maximum height in a given wave group.,Statistically representative waves,The one-tenth highest

6、wave corresponds to the average of the heights of the one-tenth highest waves.,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.,The root-mean-square wave height for a

7、 given wave group is defined as,10/39,Chapter 3,Example: What are statistically representative waves?,11/39,Chapter 3,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.,12/39,Chapter 3,The significant wave is the most frequently used in the coastal enginee

8、ring field.,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 can lead to appreciable error if an attempt is made to use it in calculations with the theoretical wave equations.,13/39,C

9、hapter 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 hei

10、ght corresponding to the intersection of the 1st percentile with the cumulative height curve.,14/39,Chapter 3,2. Statistical distribution,The wave height probability density function follows from the Rayleigh probability distribution.,15/39,Chapter 3,Rayleigh distribution curve,16/39,Chapter 3,From

11、statistical theory we can obtain important relationships using the distribution function for the wave height.,17/39,Chapter 3,The distribution of the wave period of a fully developed sea can be expressed as,The above equation means that the probability density function of the square of the wave peri

12、od, follows the Rayleigh probability distribution.,18/39,Chapter 3,For an adequate description of the sea surface, a large number of waves must be superimposed to be realistic.,3. Wave spectrum,19/39,Chapter 3,Broadly speaking, wave energy density spectra are classified into frequency spectra and wa

13、ve number spectra. The former express the wave energy density distribution as a function of wave frequency, while the latter express it as 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 plott

14、ed versus frequency, an amplitude spectrum results. The energy spectrum is a plot of the square of amplitudes versus frequency. If the square of amplitudes over the frequency interval are plotted versus frequency, an energy density spectrum, which is more popular, is obtained.,21/39,Chapter 3,Wave f

15、requency spectrum,For a simple case of waves propagating in one direction, the surface elevation measured at a fixed point is expressed by,and the equation used to define the frequency spectrum is,22/39,Chapter 3,PiersonMoskowitz spectrum,This expresses the spectrum of a fully arisen sea due to a co

16、nstant wind of sufficient duration. The shape of the present spectrum was derived on the basis of the wind wave data obtained by pressure-type wave gages attached to a ships body.,23/39,Chapter 3,Pierson-Moskowitz spectrum,24/39,Chapter 3,Bretschneider spectrum,This spectrum is applicable to wind wa

17、ves under finite fetch, and is valuable for estimating the wave spectrum when the statistically defined wave height and wave period are known.,25/39,Chapter 3,Bretschneider spectrum,26/39,Chapter 3,JONS,Based on extensive wave observations under the auspices of the Joint North Sea Wave Project, JONS

18、 was proposed.,27/39,Chapter 3,JONS,28/39,Chapter 3,The corresponding statistical characteristics of ocean waves can be determined when the wave energy density spectrum is known.,where m0 and m2 are zero and second moment at the origin.,29/39,Chapter 3,Directional wave spectrum,The actual water surf

19、ace pro ocean waves varies widely in time as well as in space.,and the equation used to define the energy spectrum is,30/39,Chapter 3,In general, the directional wave spectrum can be expressed by the product of the frequency spectrum and a directional distribution function. Several approaches have b

20、een taken to establish the directional wave spectra, but definite conclusions have not yet been reached owing to the inaccuracy of wave data.,31/39,Chapter 3,In deep water the wave group velocity, the rate at which the wave energy and the wave group as a whole travels, is given by,4. Wave propagatio

21、n in the ocean,The velocity of propagation depends on the wave period, the longer-period waves traveling faster than the shorter- period waves.,32/39,Chapter 3,It is apparent that, starting together in the generation area, the longer-period waves will outrun and leave behind the shorter-period waves

22、. Dispersion therefore produces a narrowing of energy spectrum with a strong energy peak corresponding to the wave period of the swell, and the greater the distance of the travel from the area of generation the narrower the spectrum becomes.,33/39,Chapter 3,Once waves leave the area of generation an

23、d are no longer under the influence of the wind, they begin to sort themselves out by a process known as wave dispersion and thereby become more regular. The sorting or wave dispersion by the wave period is the main factor in producing the more uniform swell waves from the initially complex sea in the area of generation.,34/39,Chapter 3,Example: a separate wave group moves from the generation area to the coastline.,35/39,Chapter 3,If R is the distance from the leading edge of the s