DNVGL-RP-N103
Modelling and analysis of marine operations
Edition July 2017
2.2 Description of waves
2.2.1 General
2.2.1.1 Ocean waves are irregular and random in shape, height, length and speed of
propagation. A real seastate is best described by a random wave model.
2.2.1.2 A linear random wave model is a sum of many small linear wave components with
different amplitude, frequency and direction. The phases are random with respect
to each other.
2.2.1.3 A non-linear random wave model allows for sum- and difference frequency
wave component caused by non-linear interaction between the individual wave components.
2.2.1.4 Wave conditions considered for structural design purposes, may be described either
by deterministic design wave methods or by stochastic methods applying wave spectra.
2.2.1.5 For quasi-static response of structures, it is sufficient to use deterministic regular waves
characterized by wave length and corresponding wave period, wave height, crest height and
wave. The deterministic wave parameters may be predicted by statistical methods.
2.2.1.6 Structures with significant dynamic response require stochastic modelling of the sea
surface and its kinematics by time series. A sea state is specified by a wave frequency
spectrum with a given significant wave height, a representative frequency, a mean
propagation direction and a spreading function.
A sea state is also described in terms of its duration of stationarity, usually taken to be 3 hours.
2.2.1.7 The wave conditions in a sea state can be divided into two classes: wind seas and swell.
Wind seas are generated by local wind, while swell have no relationship to the local wind.
Swells are waves that have travelled out of the areas where they were generated.
Moderate and low sea states in open sea areas are often composed of both wind sea and swell.
2.2.2 Regular waves
2.2.2.1 A regular travelling wave is propagating with permanent form.
It has a distinct wave length, wave period, wave height.
2.2.2.2 A regular wave is described by the following main characteristics;
Wave length: The wave length λ is the distance between successive crests.
Wave period: The wave period T is the time interval between successive crests passing a
particular point.
Phase velocity: The propagation velocity of the wave form is called phase velocity,
wave speed or wave celerity and is denoted by c = λ / T = ω/k.
Wave frequency is the inverse of wave period: f = 1/T.
Wave angular frequency: ω = 2π /T
Wave number: k = 2π/λ.
Surface elevation: The surface elevation z = η(x,y,t) is the distance between the still water
level and the wave surface.
Wave crest height AC is the distance from the still water level to the crest
2.2.2 Regular waves
1
(As per Section 2.2.2)
Wave length: The wave length λ is the distance between successive crests.
λ=
1
m
2
Wave period: The wave period T is the time interval between successive crests passing a
particular point.
T=
5
Sec
3
Phase velocity: The propagation velocity of the wave form is called phase velocity,
wave speed or wave celerity and is denoted by c = λ / T = ω/k.
c=
c=
4
λ/T
0.2
m/sec
Wave frequency is the inverse of wave period: f = 1/T.
f=
5
6
7
ω=
1.257
Hz
k=
6.28
Wave number: k = 2π/λ.
Wave crest height AC is the distance from the still water level to the crest
1.2
m
Wave trough depth AT is the distance from the still water level to the trough
At=
9
0.2
Wave angular frequency: ω = 2π /T
Ac=
8
= ω/k
0.2
m/sec
1.2
m
Wave height: The wave height H is the vertical distance from trough to crest.
H=
H=
AC + AT. m
2.4
m