Wave Kinematics Specification

SIMA allows the user to control the application of wave kinematics at nodes. The nodes for calculation of wave kinematics should be chosen such that important wave loads are captured. Reducing the number of nodes for kinematics calculation improves the simulation efficiency.

The main input is:

  • Default procedure for wave kinematics calculation on/off

  • Node step

  • Z Lower

  • Z Upper

  • Diffracted wave kinematics at nodes

  • Specification of node-step for individual lines

Wave kinematics may be pre-generated using FFT or calculated during the simulation as a sum of cosine terms. Pre-generation is much more efficient than calculating kinematics during the dynamic simulation.

Kinematics can be pre-generated at the static positions of the selected kinematics nodes.
Alternatively, kinematics can be calculated at the dynamic position of the selected kinematics nodes by summing cosine terms at each generation time step.

The kinematics at a generation time step are calculated using the dynamic position at the previous generation time step. Kinematics at simulation time steps (between the generated time steps) are found using linear interpolation. The generation time step should be small enough that the change in dynamic position between generation steps is negligible and that the highest frequency wave components with significant contributions are well represented. Om the other hand, a short generation time step will lead to frequent calculation of kinematics, which will make a time-consuming simulation.

Selecting kinematics calculated during the simulation for a linear time domain simulation with Wilson’s integration method will result in the calculation of kinematics at two generation time steps each time a new generation time step is reached.

The option Kinematics at static position calculated during simulation should give the same results as Kinematics at static position, but take several times longer. It is primarily implemented for for testing.

The possible combinations are described below.

1. Default procedure on, default Z lower/upper, Nodestep = 1

This is the recommended default option in SIMA and will apply wave kinematics at all nodes between:

  • The water depth entered under Location (lower limit)

  • Four times the square of the standard deviation of the total wave elevation (upper limit)

2. Default procedure on, Z Lower and Upper given by user

If Z Lower and Z Upper is set to editable, the user may manually limit the nodes where wave kinematics will be applied in the dynamic analysis. Wave kinematics will not be applied to nodes outside this range. This range will be applied to all lines in the system.

3. Default procedure on, Nodestep != 1

If Nodestep is set to an integer value different from 1, the value will be used as nodestep for calculating wave kinematics. Linear interpolation will be used for intermediate nodes. A nodestep of 2 will for example result in calculation of kinematics at every other node and linear interpolation for intermediate nodes.

4. Default procedure on, Nodestep < 1

A negative integer value may be given for nodestep. The distance between Z upper/lower is then divided into 4 equal intervals and nodestep is increased gradually giving the following nodesteps:

  • |nodestep| in the upper interval

  • 2 * |nodestep| in the second interval

  • 4 * |nodestep| in the third interval

  • 8 * |nodestep| in the fourth interval

This option is intended to reduce computation time when generating timeseries of wave kinematics. The option should be used with care as the resulting response is dependent on element length, water depth and system type. Nodestep < –1 is therefore not recommended.

5. Default procedure on, diffracted wave kinematics at selected nodes

If a transfer function file for wave kinematics is included, the default kinematics will be replaced for the specified nodes.

  • If one node is specified, diffracted kinematics will be applied at this node.

  • If several nodes are specified, diffracted kinematics will be calculated at these nodes and linear interpolation of diffracted kinematics will be applied to intermediate nodes.

6. Default procedure on, Nodestep specified for selected lines

Nodestep may be specified for individual lines. This specification will replace the default specification for the selected line.

7. Default procedure off, Nodestep specified for selected lines

Wave kinematics will only be applied to the lines that are specified with a nodestep.

Z Upper, Z Lower, and nodestep given under default procedure are now dummy values.

8. Default procedure off, Diffracted wave kinematics at selected nodes

Diffracted wave kinematics will only be applied to the nodes that are specified.

  • If one node is specified, diffracted kinematics will be applied at this node.

  • If several nodes are specified, diffracted kinematics will be calculated at these nodes and linear interpolation of diffracted kinematics will be applied to intermediate nodes.

9. Wave kinematics specified for selected nodes

Wave kinematics may be read from file and applied at specified nodes. The wave kinematics file must contain wave elevation, velocities in the global X, Y and Z directions and accelerations in the global X, Y and Z directions for each position which will be used.

  • If one node is specified, the input kinematics will be applied at this node.

  • If several nodes are specified, the input kinematics will be applied at these nodes and linear interpolation of kinematics will be applied to intermediate nodes.

10. Second Order Wave Kinematics

Second-order Stokes wave theory for finite water depth may be used to calculate fluid velocities and accelerations below the water surface if the second order wave kinematics option is chosen. The first order wave elevation and mean water depth are input to the calculation. A second order, non-linear contribution to the wave elevation is calculated and added to the first order elevation. The second order contribution grows with increasing wave steepness, leading to a flattening of troughs and sharpening of crests. Fluid velocities and accelerations are calculated from the velocity potential, up to and including second order. Currently, second order wave kinematics are only available for long-crested sea-states.

Wave kinematics theory manual