6
Statistical Descriptions
of Offshore Waves
Bruce J. Muga
Regular waves were treated in Chapter 3 in a classical, deterministic sense in
which the analyses were based on nonviscous hydromechanic flow applied to
either idealized surface wave forms or, in the case of the free-stream function
theory, applied to a prescribed surface wave form of finite length. In this chapter, irregular waves based on experimental measures of surface wave heights are
analyzed in a statistical sense to obtain wave spectra and other statistical parameters which will prove useful in predicting the response of offshore structures
to irregular waves.
6.1
INTRODUCTION TO WAVE SPECTRA
A short time record représentative of measured irregular surface wave forms
offshore is shown in Figure 6.1. For such irregular forms, the wave periods
and wave heights take on new meanings as statistical ways of describing these
waves are now explored. Procedures are now defined to portray the important
fluctuations and to condense these data into manageable forms.
Consider first the time interval at which the wave record is sampled at discrète points to give an adéquate représentation for p(f i For instance, the record
in Figure 6.1 can be marked off in equally spaced time intervals of At = 1sec
such that the sequence of ordinates, when connected by a smooth curve, reproduces the important details of the record. One suspects that there is an
optimum time interval which is neither too fine nor too coarse and which best
approximates the record. It is apparent that a 10-sec interval is too large, but
also the choice of 100 points over the time interval 10 seconds is far too many
The Nj quist sampling theorem aids in the sélection of an optimum interval Ai.
This theorem States:
The continuons time record r)(t) can be adequately represented
by. and reconstituted from, a set of sample values
, Pr0"
\ided that /s, the number of sample values per second, is at least
twice the highest frequency /max présent in
That is, fs ' 2/max144
Statistical Descriptions
of Offshore Waves
Bruce J. Muga
Regular waves were treated in Chapter 3 in a classical, deterministic sense in
which the analyses were based on nonviscous hydromechanic flow applied to
either idealized surface wave forms or, in the case of the free-stream function
theory, applied to a prescribed surface wave form of finite length. In this chapter, irregular waves based on experimental measures of surface wave heights are
analyzed in a statistical sense to obtain wave spectra and other statistical parameters which will prove useful in predicting the response of offshore structures
to irregular waves.
6.1
INTRODUCTION TO WAVE SPECTRA
A short time record représentative of measured irregular surface wave forms
offshore is shown in Figure 6.1. For such irregular forms, the wave periods
and wave heights take on new meanings as statistical ways of describing these
waves are now explored. Procedures are now defined to portray the important
fluctuations and to condense these data into manageable forms.
Consider first the time interval at which the wave record is sampled at discrète points to give an adéquate représentation for p(f i For instance, the record
in Figure 6.1 can be marked off in equally spaced time intervals of At = 1sec
such that the sequence of ordinates, when connected by a smooth curve, reproduces the important details of the record. One suspects that there is an
optimum time interval which is neither too fine nor too coarse and which best
approximates the record. It is apparent that a 10-sec interval is too large, but
also the choice of 100 points over the time interval 10 seconds is far too many
The Nj quist sampling theorem aids in the sélection of an optimum interval Ai.
This theorem States:
The continuons time record r)(t) can be adequately represented
by. and reconstituted from, a set of sample values
, Pr0"
\ided that /s, the number of sample values per second, is at least
twice the highest frequency /max présent in
That is, fs ' 2/max144