An Irregular Wave can be added to the Hydrodynamic Response system, either individually or as part of an Irregular Wave Group. In addition, it can be added to the Hydrodynamic Diffraction system when Linearized Morison Drag is specified for the analysis (however, only a single Irregular Wave can be used in the Hydrodynamic Diffraction system, and no Cross Swell can be specified).
Note: Although you can add multiple Irregular Wave Groups and individual Irregular Waves to your analysis, you may have only one active wave or wave group; the others must be suppressed.
To add an Irregular Wave:
Select the Hydrodynamic Response object in the tree view.
Right-click the Hydrodynamic Response object and select Insert > Irregular Wave >
Wave Type, or click on the Irregular Wave icon in the Analysis toolbar and select the wave type from the dropdown menu.
For each type of Irregular Wave the Wave Spectrum Definition Data table displays the Directions, Sub-Weights, Frequencies, and Spectral Ordinates that fully define the wave spectrum/sub-spectra. The wave definition in the Wave Spectrum Details section of the Details panel is displayed on the Main Spectrum tab. If you have also defined a secondary spectrum using the Cross Swell Details, the Frequencies and Spectral Ordinates for this are shown separately on the Cross Swell Spectrum tab. Clicking on the Graph tab of the Wave Spectrum Definition Data panel presents a graphical display of the Spectral Ordinates against their corresponding Frequencies (and, for multi-directional wave spectra, Directions). The Main Spectrum and Graph tabs are empty until the Irregular Wave has been fully defined. The Cross Swell Spectrum tab is disabled if no cross swell is defined. Control of the Spectrum and Graph displays is described in greater detail below.
The following parameters are available in the Details panel for all Irregular Wave types.
If the Analysis Type in the associated Analysis Settings is set to Irregular Wave Response, a Ramping Time may be specified. The wave ramp is described in Regular Wave and introduces the same behavior for Irregular Waves. If Ramping Method is set to Program Controlled, tw defaults to the longest period of any wave component in the defined spectrum. Alternatively, change Ramping Method to Manual Definition to allow the Ramping Time to be set to the desired time tw, or set Ramping Method to No Ramping to turn the wave ramp off.
Direction of Spectrum sets the direction of waves within a wave spectrum. This option is not available for an Irregular Wave in a Hydrodynamic Diffraction system, or for a User Defined Spectrum where the Wave Spreading option is set to Manual Definition (Carpet Spectrum).
Wave Spreading allows you to set a multi-directional wave spectrum. The default setting of None (Long-Crested Waves) produces a unidirectional wave spectrum (all the wave energy acts in a single direction). Setting Wave Spreading to Nth-Powered Cosine (Short-Crested Waves) produces a symmetric spread of wave energy over a number of directions. Selecting this option displays the additional parameters Power of Spreading Function, Total Spreading Angle, and Number of Sub-Spectra:
Power of Spreading Function sets the power N to which the cosine of
is raised, where 
is the angle between the main Direction of
Spectrum and a sub-spectrum direction. To find the spectral ordinates in a
sub-spectrum direction, the spectral ordinates in the main spectrum direction are multiplied
by a factor 
. Acceptable values for the Power of Spreading
Function are integer numbers between 2 and 250.Total Spreading Angle defines the spread range of wave energy in the short-crested waves. This angle may take any value in the range 1° to 180° when the Power of Spreading Function is set to 2, but will default to (and cannot be changed from) 180° for any other Power of Spreading Function value.
Number of Sub-Spectra sets the number of directions over which the wave energy is spread. For Nth-Powered Cosine wave spreading this value must be an odd number in the range of 7 to 27.
Note: The Directions and
Sub-Weights for an Nth-Powered Cosine wave spread are always determined
by the program, and correspond to directions and weighting factors that have been
pre-calculated for a Gaussian integration of the 
function over the given Total Spreading
Angle and Number of Sub-Spectra. Note also that the factor
from Equation 2–55 in the
Aqwa Theory Manual is included in the Sub-Weight values.
A third option for Wave Spreading is Manual Definition (Carpet Spectrum). This option is only available when the Wave Type is set to User Defined Spectrum. The definition of, and additional options related to, a Carpet Spectrum are described in User Defined Spectrum.
Note: The Wave Spreading parameter is not available when a User Time History spectrum is generated from a Wave Height Time History (.WHT) file, as there is no accurate way to combine the Low Frequency Perturbation (LFP) Function (described in User Time History) with an Nth-Powered Cosine spreading function.
Spectrum Presentation Method allows you to change the display mode for the Graph tab of the Wave Spectrum Definition Data panel. For an Irregular Wave with Wave Spreading set to Long-Crested Waves, the graph plots the Spectral Ordinates against the Frequencies calculated or defined for that Irregular Wave (1D Graph option). If you also define a Cross Swell Spectrum in a unidirectional wave, the two spectra are plotted on the same axes.
When Wave Spreading is set to Nth-Power Cosine (Short-Crested Waves) or Manual Definition (Carpet Spectrum), the default Spectrum Presentation Method changes to 2D Spectrogram (Linear) and the Graph tab displays a colored contour plot of Spectral Ordinates against Directions (x-axis) and Frequencies (y-axis). Because a Cross Swell Spectrum is unidirectional (no spreading is applied to the wave energy), it will not be included in a 2D Spectrogram plot.
Alternatively you may display this contour plot on polar axes by selecting 2D Spectrogram (Polar), where Spectral Ordinates are plotted against Frequencies (radius).
While Wave Spreading is set to Nth-Power Cosine (Short-Crested Waves) or Manual Definition (Carpet Spectrum), changing Spectrum Presentation Method to 1D Graph displays all of the sub-spectra (and the Cross Swell Spectrum, if one is included).
For an Imported Time History wave the Spectrum Presentation Method has the additional option Wave Height Time History, which plots the wave elevations against the times from the imported .WHT file. The zoom box in the lower right corner may be used to view a more limited range of the wave elevation trace.
Seed Definition defines the random seed for a wave spectrum. The options available are Program Controlled or Manual Definition. If you select Manual Definition, you can set the seed value.
Number of Spectral Lines Definition defines the number of individual components used to simulate an Irregular Wave. The options available are Program Controlled or Manual Definition. If you select Manual Definition, you can set the Minimum Number of Spectral Lines, up to the maximum of 200. The actual number of spectral lines used will typically be greater than the Minimum Number of Spectral Lines where you have added a Cross Swell Spectrum to an Irregular Wave.
Note: The new user is strongly advised to use the Program Controlled option for Number of Spectral Lines Definition . The program will automatically generate the appropriate number of spectral lines for the particular method of analysis, and it is only in unusual circumstances that user input is required.
In the case of a spectrum imported from a Wave Height Time History (.WHT) file, the analysis will always use 200 spectral lines and the user will not be allowed to modify this value.
Omit Calculation of Drift Forces disables the second order drift force calculations for the current spectrum. Select Yes to disable the calculations and No to have them applied. This option is only available for Irregular Wave Response with Slow Drift calculations.
The user should, in general, specify a spectral sea state whose range of frequencies is less than the range for which the hydrodynamic parameters for the structure are defined (those specified in the Wave Frequencies object). At spectrum frequencies which are outside the range at which the hydrodynamic parameters are defined, the program will automatically extrapolate the values required.
The effects of cross swell are implemented in most of Aqwa. Select the Cross Swell Spectrum type in the Cross Swell Details section of the Details panel. The Cross Swell Spectrum can be different from the current Wave Type. However the parameters used to define the Cross Swell Spectrum are the same as those for the corresponding spectrum Wave Type, except that the start and finish frequencies are calculated by the program.
For all wave types except User Time History and User Defined Spectrum, set Wave Range Defined by to either Period or Frequency. Next, set Start and Finish Frequency/Period Definition. The available options are:
Program Controlled (default)
Manual Start Frequency/Period Auto Finish Frequency/Period
Manual Finish Frequency/Period Auto Start Frequency/Period
Manual Definition
Start Frequency/Period is the lowest frequency or longest period at which the spectrum is defined and Finish Frequency/Period is the highest frequency or shortest period at which the spectrum is defined. Enter values in the fields that are user defined, based on the Start and Finish Frequency/Period Definition setting.
For formulated and User Time History spectra, the Export CSV File option allows you to output (in a comma-separated value (.CSV) file format) the directions, sub-weights, frequencies, and spectral ordinates that define the Irregular Wave.
Other parameters are available in the Details panel based on the wave type defined. The following wave types are available:
The JONSWAP wave spectrum can be used to describe a wave system where there is an imbalance of energy flow (i.e. sea not fully developed). This is nearly always the case when there is a high wind speed. It may be considered as having a higher peak spectral value than the Pierson-Moskowitz spectrum but is narrower away from the peak in order to maintain the energy balance.
If you choose JONSWAP (Hs) as the Wave Type, Significant Wave Height will be used in the calculations rather than the parameter Alpha, (which is used when the Wave Type is set to JONSWAP (Alpha)).
Parameterization of the classic form of the JONSWAP spectrum (with parameters of fetch and
wind speed) was undertaken by Houmb and Overvik (BOSS Trondheim 1976, Vol 1). These empirical
parameters (which you must enter) are termed Gamma (
),
Alpha (
) and Peak Frequency
(
) (the frequency at which the spectral energy is a
maximum). The peak frequency together with empirical parameters termed Gamma and Alpha are used
in this formulation. The spectral ordinate (
) at a frequency (
) is given by
where:
 = the peak frequency in rad/s |
 = the peak enhancement factor |
|
|
 = a constant that relates to the wind speed and peak
frequency of the wave spectrum, which has the following relationship to the significant wave
height  : |
The Pierson-Moskowitz spectrum is formulated in terms of the two parameters of
Significant Wave Height (
) and average (Zero Crossing
Period) wave period (
). This is considered of more direct
use than the classic form, in terms of the single parameter wind speed, or the form involving
the peak frequency, where the spectral energy is a maximum. The spectral ordinate
(
), at a frequency (
, in rad/sec), is given by
The average (i.e. mean zero-crossing) wave period (Zero Crossing Period) and Significant Wave Height are the parameters used to describe the Pierson-Moskowitz wave spectrum, the special case for a fully developed sea.
The Ochi-Hubble spectrum is a bimodal spectrum designed to represent both the low- and high-frequency components associated with storm conditions. Each mode is defined by a Significant Wave Height, a Shape Parameter, and a Modal Frequency or Modal Period. More information on the formulation may be found here.
The Bretschneider spectrum is a special form of the Ochi-Hubble spectrum, with only a single spectral mode and unit shape parameter. The spectrum is therefore defined only by a Significant Wave Height and a Modal Frequency or Modal Period. More information on the formulation may be found here.
The TMA (Texel-MARSEN-ARSLOE) spectrum is a form of the JONSWAP (Alpha) spectrum, modified to account for finite water depth. The spectrum is defined by the parameters Gamma, Alpha, and Peak Frequency or Peak Period, and uses the Water Depth defined in the Geometry details. More information on the formulation may be found here.
The standard Gaussian spectrum is given by
where:
= significant wave height |
 = peak frequency in rad/s |
 = standard deviation |
The Peak Frequency, Significant Wave Height, and
Sigma (
) are the parameters used
to describe the Gaussian wave spectrum. The value of σ must be at least
.
This option may be used to input any user-defined one- or two-dimensional spectrum. It is normally employed for the input of non-deterministic spectra such as tank spectra, recorded full-scale spectra, or simply where the formulated spectrum is not yet available.
In the Wave Spectrum Definition Data table, enter the frequency (or period, depending on the Wave Range Defined by setting) and its corresponding spectral ordinate. The maximum number of frequencies/periods is 200.
The rows of the Wave Spectrum Definition Data table are automatically sorted in ascending order of Frequency. Zero or duplicate Frequency entries are not valid.
If you create an Irregular Wave using one of the formulated spectra available in Aqwa (JONSWAP, Pierson-Moskowitz, or Gaussian) or generate a formulated spectrum from a User Time History, and then change the Wave Type to User Defined Spectrum, the spectral ordinates of the formulated spectrum become editable for you to modify as necessary.
Note: Using a User Time History spectrum as the template for a User Defined Spectrum wave does not retain the Low Frequency Perturbation (LFP) Function of the User Time History wave (described in User Time History). Only the JONSWAP fit of the imported wave elevation spectral density is included.
Wave Spectrum Definition Data can otherwise be entered manually, can be copied and pasted from an external source (for example, an Excel spreadsheet), or can be imported from a comma-separated values (.CSV) file using the Import CSV File option. For the Import CSV File option, the file must meet the following requirements:
Has the .CSV extension.
Contains values separated by commas, tabs, or single spaces (not multiple spaces).
Contains exactly 2 columns, and no more than 200 rows.
The Direction and Sub-Weight rows are not included.
The unit system of the data in the .CSV file is assumed to match the display unit system of the project. However, the imported data can be modified by setting the Length Unit for Imported Data, Rotation Unit for Imported Data, and Frequency Unit for Imported Data to the required unit system.
When defining a User Defined Spectrum with Nth-Powered Cosine (Short-Crested Waves) wave spreading, only the Frequency and main direction Spectral Ordinate columns are editable. Modifying one of the main direction spectral ordinates causes the other spectral ordinates at that frequency to be updated automatically.
The same rules for importing a .CSV file apply: the first column of the imported file is inserted into the Frequency column, and the second is used for the main direction Spectral Ordinates. The spectral ordinates for all other directions are calculated automatically. The Direction and Sub-Weight should not be included in the .CSV file.
With Wave Type set to User Defined Spectrum and Wave Spreading set to Manual Definition (Carpet Spectrum), any combination of Directions, Sub-Weights, and User-Defined Wave Spectra may be specified.
With Manual Definition (Carpet Spectrum) wave spreading, the Number of Sub-Spectra parameter permits any value in the range of 2 to 41.
Sub-Spectrum Weighting determines the weighting factors for each carpet direction. The available options are:
Manual Definition, which allows the Sub-Weights to be entered manually (default).
Program Controlled (Unit Weighting), which assigns a unit weighting factor to each direction.
Program Controlled (Trapezoidal Weighting), which determines weighting factors
for each direction 
based on a simple trapezoidal integral, where:in which
is the Number of Sub-Spectra and
.
For a User Defined Spectrum with Manual Definition (Carpet Spectrum) wave spreading, the Wave Spectrum Definition Data table maybe populated using the method described in With Wave Spreading: None (Long-Crested Waves): create a User Defined Spectrum with Wave Spreading set to None (Long Crested Waves), turn this into a multidirectional spectrum by changing Wave Spreading to Nth-Powered Cosine (Short Crested Waves), and then make all fields of the Wave Spectrum Definition Data table editable by changing Wave Spreading to Manual Definition (Carpet Spectrum).
Wave Spectrum Definition Data can otherwise be entered manually, can be copied and pasted from an external source (for example, an Excel spreadsheet), or can be imported from a comma-separated value (.CSV) file using the Import CSV File option. For the Import CSV File option, the file must meet the following requirements:
Has the .CSV extension.
Contains values separated by commas, tabs, or single spaces (not multiple spaces).
Contains exactly N+1 columns, where N is the Number of Sub-Spectra, and no more than 200 rows.
The Direction and Sub-Weight rows are included.
The unit system of the data in the .CSV file is assumed to match the display unit system of the project. However, the imported data can be modified by setting the Length Unit for Imported Data, Rotation Unit for Imported Data, and Frequency Unit for Imported Data to the required unit system.
The Direction and Sub-Weight rows must be included in the .CSV file, even if the sub-weights are Program Controlled (where any values in the Sub-Weight row of the .CSV file are ignored). There must also be (arbitrary) entries for the 'Direction' and 'Sub-Weight' header cells.
An example of such a .CSV file, as used to create the table shown above, follows:
dir,-85.42,-66.738,-36.526,0,36.526,66.738,85.42 wt,0,0,0,0,0,0,0 0.050006,0,0,0,0,0,0,0 0.060415,0.0006,0.0156,0.0647,0.1002,0.0647,0.0156,0.0006 ETC.
A time history series of wave elevations may be imported into your Hydrodynamic Response analysis, in order to reproduce model test wave conditions as accurately as possible. Select , or select from the Analysis toolbar, and browse to the file location.
The Imported WHT File field shows the file
location on the disk. If the imported file contains the optional NAME
field, the value is displayed in the Imported WHT Name field.
When a time domain analysis is carried out, the wave elevation time-history will be reproduced exactly, within the frequency range of the fitted spectrum and subject to the limitations of roundoff error. This is achieved by multiplying each of the spectral wave components by a different Low Frequency Perturbation (LFP) Function; i.e.:
Wave elevation = 
where:
 = number of spectral lines (set to 200) |
 = wave component number |
 = time |
 = frequency (as normally output by the Aqwa
solver) |
 = phase (as normally output by the Aqwa
solver) |
= amplitude |
= wave number |
= LFP function |
Note that no spurious low frequency waves are generated by the above method. For any wave
component, the minimum frequency present in the wave elevation is 
, where 
is the highest frequency present in the LFP function. Note also that there is
no frequency overlap for each wave component. Each LFP function can be considered as a
frequency spreading function over a limited set of contiguous frequency bands. In this case
each wave component has a different energy (as opposed to the standard Aqwa wave components
which have equal energy).
Import of the time series will also generate a user-defined spectrum, using a Fast Fourier Transform, whose frequency range is based on a JONSWAP fit of the wave elevation spectral density. If Computation Type is Stability Analysis or Frequency Statistical Analysis in a Hydrodynamic Response system, this spectrum will be used in the same way as a normal user-defined spectrum. As the phases of the spectral wave components are allocated randomly, the input wave elevation time history will not be reproduced.
Note: Current is ignored when calculating the phase wave forces on the structure and the wave kinematics for Morison elements.
The *.WHT file is an ASCII file with the wave elevation data in free format with 2 values per line. The first value is the time and the second value is the wave elevation.
The following 2 statements are required in the file:
DEPTH=value G=value
The DEPTH value should match the Water Depth specified in the Geometry Details or else a warning will be generated. The G value is compared to the Gravity specified in the Geometry Details to determine the units used. If no G value is defined, you have the option to set the unit system for the imported data manually, using the Length Unit for Imported Data and Angle Unit for Imported Data controls under Wave Spectrum Details.
The following optional data can also be input. If any are omitted, the relevant value defaults to zero.
DIRECTION=value(degrees) X_REF=value Y_REF=value NAME=Spectrum Name CURRENT_SPEED=value CURRENT_DIRECTION=value(degrees)
Note:
The X_REF and Y_REF values are used in the calculation of the phase of the wave and are the position where the wave elevation was measured. For example (in SI units), if the DIRECTION of the wave is zero degrees (in other words, along the positive X-axis in the global coordinate system) then values of X_REF/Y_REF of 100.0/0.0 will indicate that the wave elevation was measured 100 metres downstream of the 0,0 wave reference point. Omission of these data will default the reference point to 0,0. i.e. the wave elevation will be calculated using the origin of the global coordinate system as the point at which the wave elevation will be reproduced. X_REF, Y_REF and DIRECTION values appear in the Details panel for the Wave object.
The Spectrum Name will be used for graphs and tables where appropriate throughout the program, and is appended to the Wave object name in the tree.
CURRENT SPEED and CURRENT DIRECTION are needed for calculation of the wavelengths of the wave components used to reproduce the wave elevation. If present they must match the corresponding values in the unsuppressed Current object in the tree (if there is no Current object, a warning will be generated.) If omitted, it is assumed that there is no current and a warning will be issued.
The duration of the time history in the file should be at least 7200s. This duration is necessary in order to give sufficient resolution of low frequency resonant responses. If the file contains less data than this, the data will be extended automatically up to 7200s, using a process of mirroring and copying.
The maximum number of timesteps in the .WHT file is 150000.
Comments (starting with * in Column 1) may be added anywhere in the file.
An example of a *.WHT file is shown below.
------------------------------------ * This is an example of a *.wht file * DEPTH=30.0 G=9.81 DIRECTION=0.0 X_REF=100.0 Y_REF=0.0 NAME=EXAMPLE CURRENT_SPEED=0.6 CURRENT_DIRECTION=90 * TIME WAVE HT * s m 0.0000 -1.088 0.2366 -1.188 0.4732 -1.268 0.7098 -1.351 0.9464 -1.427 1.1830 -1.471 1.4196 -1.494 1.6562 -1.476 1.8928 -1.406 2.1294 -1.293 2.3660 -1.149 2.6026 -0.966 ETC. ------------------------------------