the sea surface at a point is used, the undulations are identified as waves, and statistics of the record are

developed. This is a very natural introduction to irregular waves and will be presented first before the more

complicated spectral approach is presented. The primary drawback to the wave-by-wave analysis is that it

cannot tell anything about the direction of the waves. Indeed, what appears to be a single wave at a point

may actually be the local superposition of two smaller waves from different directions that happen to be

intersecting at that time. Disadvantages of the spectral approach are the fact that it is linear and can distort

the representation of nonlinear waves.

(1) Introduction.

(a) Wave train analysis requires direct measurements of irregular seas. A typical irregular wave record

obtained from a wave-measuring device is shown in Figure II-1-25. The recorded wave traces have to be of

finite length with the sea surface sampled at a set interval (typically every second). The time-history of sea

surface elevation at a point is a random-appearing signal exhibiting many maxima and minima (Figures II-1-

26 and II-1-27). It is necessary to develop a criterion for identifying individual waves in the record.

(b) In a wave-by-wave analysis, undulation in the time-history of the surface must be divided into a

series of segments, which will then be considered as individual waves. The height and period of each wave

will be measured. Once this is done for every segment of the record, statistical characteristics of the record

can be estimated, and the statistics of the record are compiled.

(c) Knowing the statistics of one record can be useful in itself, particularly if the record is important

(such as the observation of waves at a site when a structure failed). However, it would be helpful to know

whether the statistical characteristics of individual wave records followed any consistent pattern. Statistics

of the sea state could be predicted knowing only a little about the wave conditions. It would be very useful

if the distribution of wave characteristics in a wave record followed a known statistical distribution. After

defining characteristics of individual records, the larger statistical question will be addressed.

(d) In the time-domain analysis of irregular or random seas, wave height and period, wavelength, wave

crest, and trough have to be carefully defined for the analysis to be performed. The definitions provided

earlier in the regular wave section of this chapter assumed that the crest of a wave is any maximum in the

wave record, while the trough can be any minimum. However, these definitions may fail when two crests

occur within an intervening trough lying below the mean water line. Also, there is not a unique definition

for wave period, since it can be taken as the time interval between either two neighboring wave troughs or

two crests. Other more common definitions of wave period are the time interval between successive crossings

of the mean water level by the water surface in a downward direction called *zero down-crossing period *or

(2) Zero-crossing method.

(a) The adopted engineering procedure is the zero-crossing technique, where a wave is defined when

the surface elevation crosses the zero-line or the mean water level (MWL) upward and continues until the

next crossing point. This is the *zero-upcrossing *method. When a wave is defined by the downward crossing

of the zero-line by the surface elevation, the method is the *zero-downcrossing*.

(b) The *zero-crossing wave height *is the difference in water surface elevation of the highest crest and

lowest trough between successive zero-crossings. The definition of wave height depends on the choice of

trough occurring before or after the crest. Here, a wave will be identified as an event between two successive

zero-upcrossings and wave periods and heights are defined accordingly. Note that there can be differences

Water Wave Mechanics

II-1-65

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