Numerical modeling of ship wave generation using Green’s functions based on linear dispersive wave theory

ABSTRACT

In this study, an efficient numerical model for predicting ship waves was developed using Green’s functions. Avoiding detailed description of the complex boundary conditions around a ship, this model simply used an inversion technique for estimating the wave source induced by a ship as a function of the navigation route and adjacent measured water level fluctuations. The Green’s functions were determined as linear summations of the water level fluctuations generated from discrete points along the navigation route. At each point, a time-varying wave source was determined as a linear summation of Gaussian pulses introduced at segments along the longitudinal direction of the ship. The linear inversion was then applied for estimating the optimum combinations of the magnitudes of these Gaussian pulses. Linear dispersive wave theory was applied to compute the water level fluctuations generated by a single Gaussian pulse so that the model can reproduce the dispersive characteristics of ship waves. The developed model was tested against experimental data and showed satisfactorily predictive skills of water level fluctuations for cases not used in the inversion. The present model was also found to be robust in that the estimated best-fitted wave source was not sensitive to changes in the conditions of the measured data used for the inversion.

KEYWORDS:

• Ship waves
• Green’s functions
• linear inversion
• dispersive wave
• Gaussian pulse

Acknowledgments

Authors appreciate the support from the JSPS JP17K18898, JP18H01539, and the STINT Grant JA2017-7011 provided within the framework of the Joint Japan–Sweden Collaboration.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science [JP18H01539]; Japan Society for the Promotion of Science [JP17K18898]; Swedish Foundation for International Cooperation in Research and Higher Education [JA2017-7011].