Environment: Data for time history waves

A time history wave train defines the wave elevation as a function of time. The data required are as follows

A suitable time history defining the wave elevation as a function of time. The time values must be equally spaced and in seconds. The elevation values must be the elevation at the given wave origin, measured positive upwards from the still water level in the OrcaFlex model, and using the same length units as the OrcaFlex model.
The wave time origin, chosen to position the required subset of wave time history within the simulation period.
The minimum number of components to use in the Fourier representation of the time history wave. It should be set high enough to give desired accuracy, but no higher: a very large number of components may significantly slow the simulation.
The component truncation threshold can be used to remove high frequency components. This can be useful to reduce the number of components used and so reduce the simulation calculation overhead. The truncation threshold specifies the percentage of the total spectral energy to be removed.

How wave time history data are used

A wave elevation time history is, in OrcaFlex, applied in a different way to other time histories. The wave elevation is given at a single point, the wave origin, but OrcaFlex needs to be able to obtain the elevation at any point on the sea surface. To achieve this, OrcaFlex applies a fast Fourier transform (FFT) to transform the wave elevation data into a number of frequency components. Each component is represented by a single Airy wave, and these Airy waves are then combined to give the wave elevation and kinematics at all points. The view wave components button lists these Airy wave components; the view spectrum button displays their power spectral density graph.

Note that the FFT requires the number of samples $N$ it uses to be a power of 2, and it yields $N/2$ components. The time history must therefore contain a sequence of $N$ samples that covers the period of the simulation, where $N$ is a power of 2 and at least twice the specified minimum number of components.

Warning:

If the time history does not contain enough samples to satisfy this, then zero-padding is applied: zero-valued samples are added to extend the time history until it does. This is likely to introduce spurious high frequencies into the waves, so we recommend that, if possible, you avoid it by providing additional genuine sample data.

In more detail then, these are the steps OrcaFlex takes to generate the wavetrain from your elevation time history.

Select the elevation values that cover the time history import range

OrcaFlex will first import elevation values covering the specified import range: $[T_{\rm from} - T_0, T_{\rm to} - T_0]$ where $T_{\rm from}$ and $T_{\rm to}$ are the time history import range from and to times, and $T_0$ is the wave time origin.

Note:

These time origin settings allow you to shift the simulation relative to the time history.

Add more samples, if necessary

Let $n$ be the number of samples selected in the first step. In order to achieve the specified minimum number of components $m$, OrcaFlex needs at least $2m$ samples. So if $n$ is less than $2m$, OrcaFlex selects more samples (taken equally from earlier and later, if possible) until it has $2m$ samples. If there are not enough samples to do this, then an error message is given: zero-padding is not appropriate in this case, so you must either provide more samples or reduce the minimum number of components requested.

Furthermore, the FFT requires that the number of samples $(2m)$ is a power of 2. If this is not the case, then again more samples are selected from the data (taken equally from earlier and later, if possible) until the number of selected samples is $N$, the smallest power of 2 greater than $2m$. If OrcaFlex runs out of samples while doing this then it zero-pads, and issues a warning to that effect.

Apply FFT to obtain Fourier components

The $N$ selected time history samples are transformed into frequency domain form using a fast Fourier transform (FFT), giving $N/2$ sinusoidal Fourier components.

Model the time history wave as the superposition of Airy waves

$N/2$ Airy waves are created, with periods, amplitudes and phases matching the Fourier components. If the component truncation threshold is greater than zero, then high frequency components are removed such that the proportion of spectral energy removed is determined by the component truncation threshold.

Finally, the time history wave train is modelled as the superposition of these remaining Airy waves.

Warning:

This last step effectively uses Airy wave theory to extrapolate from the wave origin, where the wave elevation has been defined, to derive the elevation at other points and to derive fluid kinematics from the surface elevation. This extrapolation introduces errors, which become worse the further you go from the wave origin. We recommend, therefore, that the wave origin (the point to which the time history data apply) is placed close to the main wave-sensitive parts of the model.