EM 1110-2-1100 (Part II)
30 Apr 02
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.
Wave train (wave-by-wave) analysis.
(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
zero up-crossing period for the period deduced from successive up-crossings.
(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