1. Computations of Force and Motion Response to Arbitrary Fluid Motions around Stationary Vessels
J.A. Pinkster

2. Developments initially stimulated by:
Need to predict motions of moored vessels on inland waters due to passing fast passenger catamarans (Effect of wash waves)
Need to predict additional passing ship effects on large moored tankers and container vessels of seiches generated by large vessels passing in restricted waters .This will not be treated further here.

3. Wash Waves

4. Subcritical speeds : Transverse and diverging waves

5. Supercritical speeds : Diverging waves only

6. Basis for computational procedure:
Forces on moored vessel (first and second order) to be computed using linear 3-d diffraction code, preferably using well-tried frequency-domain code.
Duration of passing maneuver is short (a few minutes)
Special problem posed by the fluid motions and pressures of the incoming wave field ; i.e. generally no analytical expressions available such as is the case of long-crested regular waves. Only numerical data for discrete locations based on other codes . For instance the RAPID code (Raven, MARIN).

7. Wash Waves computed by RAPID (MARIN). Sub-critical speed

8. Steps in the computational procedure:
Compute time records of velocity components and pressure of undisturbed wave at location of all collocation points of the panel model of the vessel (and harbour)
Using FFT compute complex amplitudes of frequency components of velocities and pressures for all frequencies up to maximum frequency
For each frequency solve the diffraction problem using the data from the FFT operation
Transform all frequency domain output back to time domain using IFFT
Compute second order force terms dependent on products of first order quantities in the time domain

9. Propagation of waves outside RAPID domain
Some options:
1. Use disturbance of ship computed within RAPID domain as input to a numerical wave-maker
Numerical wave-maker (line of wave-making sources) generates waves at the location of the moored ship
2. Match to time domain wave model such as TRITON (WL|Delft Hydraulics) based on Boussinesq equations.
3. Compute ‘wave-cut’ inside RAPID domain and extend wave field by application of linear wave theory . (This can also be applied to a measured wave-cut from model tests or full scale)

10. Real Wavemaker MARIN basin generating oblique waves.
The numerical method ‘mimics’ the multi-segmented wave maker.

11. ‘RAPID’ wave at wave maker
Numerical wave maker extending
the wave field generated by RAPID
Moored ship
Numerical wave makers
‘RAPID’ wave at wave maker

12. Computational scheme Time domain (real world)
Disturbance from waves
Ship Response
Moored ship
FFT
IFFT
3-D diffraction comp.
Wave
maker
Moored ship
Frequency domain (computational world)

13. Example : Wash effect on a ship moored in a harbour due to a vessel passing at sub-critical speed

14. Ship moored in a harbour
Direction of
Passing ship
100 m
Moored ship in
Harbour
100 m

15. 3-D panel models of ship and harbour

17. Analysis of measured or simulated wave record (wave-cut)
Decomposition in regular, long-crested wave components, each with own amplitude, phase and direction, for computation of ship responses. Implemented in DELWASH

18. Measured (or computed) wave-cut
Measured (or computed) wave-cut. Extend with zeros as required in order to obtain sufficient total duration. Total number of points is a power of 2 (for efficient FFT)

19. Fourier analysis of wave-cut

20. Wave frequency, number and phase velocity

21. Wave direction
WAVE CREST U y c a

22. An example: Fast Ferry Wash
Measurements of wash waves of a new Fast Ferry concept in MARIN’s Shallow Water Basin, and application to the simulation of the behaviour of a moored inland barge.

26. Forces on a captive container vessel (‘Scheur’)
Simulation of wash waves of a passing ship using the (real) wave maker.
Model tests carried out in the Vinje Basin of WL| Delft Hydraulics
Wave propagation computations using TRITON, a time-domain, non-linear code based on the Boussinesq equations

27. Captive model in Vinje Basin of WL| Delft Hydraulics

28. Wave maker generating the ‘wash wave’ of a ship
travelling at supercritical speed

29. Calculations of waves using TRITON (Boussinesq eqn.)

30. Measured and computed forces and moments on captive model

31. Compare results with results obtained using undisturbed wave-cut measured at the location of the model

33. Predicted forces based on measured wave-cut and DELWASH

34. Now: Long-duration simulations of 3 hours or more for arbitrary irregular sea conditions (long-crested or directionally spread)
Of interest for changing coastal topography which results in complex combinations of directionally spread short waves with an even more complex bound, free and reflected sub-harmonic wave field
Codes such as those based on Boussinesq eqn. can generate the required wave field and fluid kinematics
Note : Diffracted waves are all free waves (linear theory)

35. Long duration simulations:
Problem:
Number of input frequencies for diffraction computations is extremely large in the direct application of FFT to the complete record
Solution :
Cut the time-record into shorter, overlapping segments of equal duration resulting in less frequencies.
Input data from the segments are treated as so many RHS vectors (Compare with different wave directions in standard diffraction codes)

36. Two long-duration (3 hours) examples:
Irregular long-crested waves
Irregular short-crested waves

37. Use wave kinematics and pressure as input to diffraction computations
Long-crested waves
Two approaches:
Use wave kinematics and pressure as input to diffraction computations
Use computed undisturbed wave elevation at the location of the vessel combined with DELWASH. (waves with fixed direction this time)

38. The computed wave record at the location of the vessel

39. Heave and Sway force time records

40. Irregular directional seas
Results based on input from TRITON only

41. Wave field simulation: Directional spectrum prescribed at boundary of TRITON domain

42. Some results of forces on the vessel ; 10 time segments

43. Same waves, more segments , larger overlap

44. Mean and Low-frequency , second order forces
Last but not Least:
Mean and Low-frequency , second order forces
Case 1: 200 kdwt tanker in regular wave group in head waves in shallow water
Some comparisons between present approach and ‘conventional’ QTF results

45. Second Order Surge Force

46. Second order Surge Force in a regular wave group , components I through IV only. Dashed red line : QTF-based results

47. Case 2 : Sway drift force on container vessel in irregular directional seas . Sum of components I through IV

48. Conclusions
Coupling of linear 3-d diffraction code to different codes generating fluid motions at the location of the vessel has been realized
First- and second order forces compare well with results of ‘conventional’ computations
Long-duration simulations using input from non-linear time domain wave codes such as TRITON allow the generation of first- and second order wave forces for complex wave conditions