OrcaFlex Manual - Orcina

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System Modelling: Data and Results, Environment
generated for each wave component and added assuming linear superposition. OrcaFlex currently allows you to
specify the number of wave components to use; more components give greater realism but a greater computing
overhead.
The time history generated is just one of an infinite number of possible wave trains which correspond to the chosen
spectrum – in fact there are an infinite number of wave trains which could be generated from 100 components, a
further infinite set from 101 components and so on.
Strictly speaking, we should use a full Fourier series representation of the wave system which would typically have
several thousand components (the number depends on the required duration of the simulation and the integration
time step). This is prohibitively expensive in computing time so we use a much reduced number of components, as
noted above. However, this does involve some loss of randomness in the time history generated. For a discussion of
the consequences of this approach, see Tucker et al (1984).
Finding a Suitable Design Wave
A frequent requirement is to find a section of random sea which includes a wave corresponding in height and period
to a specified design wave. OrcaFlex provides preview facilities for this purpose. If you are looking for a large wave
in a random sea, say Hmax = 1.9Hs, then use the List Events command (on the Waves Preview page of the
environment data form) to ask for a listing of waves with height > H=1.7Hs, say. It is worth looking over a reasonably
long period of time at first – say t = 0s to 50,000s or even 100,000s. OrcaFlex will then search that time period and
list wave rises and falls which meet the criterion you have specified.
Suppose that the list shows a wave fall at t = 647s which is close to your requirement. Then you can use the View
Profile command to inspect this part of the wave train, by asking OrcaFlex to draw the sea surface elevation for the
period from t = 600s to t = 700s, say. You will then see the large wave with the smaller waves which precede and
follow it.
Note that when you use the preview facility you have to specify both the time and the location (X,Y coordinates). A
random wave train varies in both time and space, so for waves going in the positive X direction (wave direction =
0°), the wave train at X = 0 differs from that at X = 300m.
You can use the preview facility to examine the wave at different critical points for your system. For example, you
may be analysing a system in which lines are connected between Ship A at X = 0 and Ship B at X = 300m. It is worth
checking that a wave train which gives a design wave at Ship A does not simultaneously include an even higher wave
at Ship B. If you want to investigate system response to a specified design wave at both Ship A and Ship B, then you
will usually have to do the analysis twice, once with the design wave at Ship A and once at Ship B.
If no wave of the required characteristics can be found, then adjust Hs and Tz slightly and repeat. As we noted above,
the important point is to get the design wave we want embedded in a realistic random train of smaller waves. This is
often conveniently done by small adjustments to Hs and Tz. We need make no apology for this. In the real world,
even in a stationary sea state, the instantaneous wave spectrum varies considerably and Hs and Tz with it. For
further discussion see Tucker et al (1984).
If you are using an ISSC spectrum, or a JONSWAP spectrum with constant γ, then you can make use of some useful
scaling rules at this point. In these 2 cases, provided the number of wave components and the seed are held
constant, then:
� For constant Tz, wave elevation at any time and any location is directly proportional to Hs. For example, if you
have found a wave at time t which has the period you require but is 5% low in height, increasing Hs by 5% will
give you the wave you want, also at time t.
� For constant Hs, the time between successive wave crests at the origin (X = 0, Y = 0) is proportional to Tz. For
example, if you have found a wave at the origin at time t which has the height you require but the period
between crests is 5% less than you want, increasing Tz by 5% will give you the wave you want, but at time 1.05t.
Note: This rule does not apply in general except at the origin of global coordinates.
These scaling rules can be helpful when conducting a study of system behaviour in a range of wave heights. We can
select a suitable wave train for one wave height and scale to each of the other wave heights. This gives a systematic
variation in wave excitation for which we may expect a systematic variation in response. If the wave trains were
independently derived, then there would be additional scatter.
Wave Statistics
The following is based on Tucker (1991).