Difference Frequency QTF

Calculation of second order (wave drift) forces from full Difference-Frequency Quadratic Transfer Function (QTF). The Difference-Frequency QTF gives forces oscillating at the difference of pairs of wave frequencies in the wave spectrum and can therefore excite low-frequency resonant motions of floating bodies.

Difference frequency forces together with sum frequency forces from Sum Frequency QTF gives the full second order wave forces, as described in Second-order wave forces.

By checking the Enable wave-current interaction checkbox, the zero-current QTF will be modified using a version of Aranha’s formula extended to full QTFs.

The QTF modified by current can be plotted based on current velocity and -direction values entered in the plot window. These values only have effect in the plot. During a simulation, the actual current condition is used.

Checking Enable wave-current interaction will only enable the excitation part of the wave-current interaction. To include the damping effect due to body velocities, a wave drift damping model should be added. See also Wave-current correction of second order wave drift force and wave drift damping using an extended Aranha’s formula.

From SIMA 5.0, the Difference Frequency QTF model is changed. The legacy QTF model from SIMA version ≤ 4.8 continues to be supported for backwards compatibility. Users can choose to convert to the new model by right-clicking the QTF model in the model tree and choosing Export/Convert QTF. You will see a warning message in the model tree if you have a legacy QTF model in your SIMA workspace.

The new QTF model refers to QTF data stored on an external file, which can drastically reduce the size of the SIMA workspace and gives overall efficiency improvements in both SIMA and SIMO.

When hydrodynamic data is imported from a SIF file, a new model and associated QTF file is created automatically. However, when hydrodynamic data is imported from WAMIT files, the legacy model is currently created, and it is thus recommended to convert to the new model after importing.

In addition to changing the storage method, the new model corresponds to a new implementation in SIMO. The new implementation will give slightly different results for the following reasons:

  • Different interpolation methods

    • The new implementation uses a combination of linear (close to the main-diagonal) and bi-linear interpolation in the bi-frequency domain

    • The legacy implementation uses a two-step interpolation where step 1 creates a dense QTF by resampling the QTF data with bi-linear interpolation, and step 2 use "nearest neighbor" interpolation on the dense QTF

  • The new implementation applies forces in the low-frequency body-related coordinate system (following low-frequency yaw motions), while the legacy implementation applies forces in the body-related coordinate system (following total yaw motion). Note that both implementations does heading correction based on the low-frequency yaw motion.

The computed force time series can be stored by selecting the Store difference frequency wave force option in the storage section of Dynamic Calculation.

The new implementation also comes with other improvements:

  • The mean wave drift force is now included in static analysis (STAMOD)

  • Body symmetry is now utilized to reduce the number of relative wave headings required in the QTF, and reduce the number of pregenerated time series accordingly

  • The new model avoids generation of forces for vessel headings never experienced ("on-demand" pre-generation)

  • General efficiency improvements

Due to the efficiency improvements, simulations with a full QTF now has approximately the same running time as simulations with wave drift force coefficients (using Newman’s approximation).