Skip to main content
SpringerLink
Log in

Water Wave Impulse Response Function on Moving Point with Constant Speed in Head Wave

  • Original Article
  • Published:
Water Waves Aims and scope Submit manuscript

Abstract

Accurate wave prediction is essential for moving ships at forward speed under head wave conditions. To achieve precise short-term wave predictions, the direct convolution integral of the measured wave elevation with an impulse response function can be employed, which has recently been proven as an efficient tool for static conditions. Comparatively, much research has not been conducted on moving conditions yet; however, it is essential to predict encounter water waves for ships at forward speed. This paper presents the analytical solution of the impulse response function on the moving point at a constant speed in head waves based on the finite-depth dispersion relation. The impulse response function is divided into three time domains, named small, middle, and large time domains. For each domain, the impulse response functions are derived, respectively. Additionally, the optimal limit of the proposed solution has been investigated in terms of speeds and distances. It has been observed that the proposed solution is valid within the optimal region, and the influence of non-causality is small. The analytical solution is compared with a numerical solution derived using the inverse discrete Fourier transform (IDFT). Towing tank experiments were conducted for different distances and speeds to validate the proposed solution by predicting regular and irregular water waves. For all cases, the comparison between experimental and predicted wave elevations shows good agreement, ensuring the prediction accuracy of the proposed analytical solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Data Availability

Data will be made available on reasonable request.

References

  1. Prislin, I., Zhang, J., Seymour, R.J.: Deterministic decomposition of deep water short-crested irregular gravity waves. J. Geophys. Res. Oceans 102(C6), 12677–12688 (1997). https://doi.org/10.1029/97JC00791

    Article  Google Scholar 

  2. Ferrier, B., Baitis, A., Manning, A.: Evolution of the landing period designator (lpd) for shipboard air operations. Naval Eng J 112, 297–316 (2000). https://doi.org/10.1111/j.1559-3584.2000.tb03338.x

    Article  Google Scholar 

  3. Ferrier, B., Duncan, J., Belmont, M., Curnow, A., Crossland, P.: Using simulation to justify and develop quiescent period prediction systems for the royal navy, vol. 2, pp. 99–107 (2013)

  4. Klein, M., Dudek, M., Clauss, G., Ehlers, S., Behrendt, J., Hoffmann, N., Onorato, M.: On the deterministic prediction of water waves. Fluids 5(1), 9 (2020). https://doi.org/10.3390/fluids5010009

    Article  Google Scholar 

  5. Edgar, D., Horwood, J.M.K., Thurley, R., Belmont, M.: Effects of parameters on the maximum prediction time possible in short term forecasting of the sea surface shape. Int. Shipbuild. Prog. 47, 287–301 (2000)

    Google Scholar 

  6. Halliday, J., Dorrell, D., Wood, A.: The application of short-term deterministic wave prediction to offshore electricity generation. Renew. Energy Power Qual. J. 1 (2005). https://doi.org/10.24084/repqj03.271

  7. Law, Y.Z., Santo, H., Chua, K.H.: Wave-field prediction based on radar snapshots taken on a moving vessel. J. Phys. Conf. Ser. 2311(1), 012022 (2022). https://doi.org/10.1088/1742-6596/2311/1/012022

    Article  Google Scholar 

  8. Naaijen, P., Huijsmans, R.: Real Time Wave Forecasting for Real Time Ship Motion Predictions. In: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, vol. 4, pp. 607–614 (2008). https://doi.org/10.1115/OMAE2008-57804

  9. Naaijen, P., Huijsmans, R.: Real time prediction of second order wave drift forces for wave force feed forward in dp. In: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, vol. 4, pp. 357–364 (2010). https://doi.org/10.1115/OMAE2010-20618

  10. Naaijen, P., Oosten, K., Roozen, K., Veer, R.: Validation of a deterministic wave and ship motion prediction system. In: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, vol. 7B (2018). https://doi.org/10.1115/OMAE2018-78037

  11. Susaki, H., Hirakawa, Y., Takayama, T., Hirayama, T.: Acquisition and prediction of wave surface by marine radar for the safety of small ships. In: Proceeding of the 16th International Ship Stability Workshop, 5-7 June, Belgrade, Serbia (2017)

  12. Al-Ani, M., Belmont, M., Christmas, J.: Sea trial on deterministic sea waves prediction using wave-profiling radar. Ocean Eng. 207, 107297 (2020). https://doi.org/10.1016/j.oceaneng.2020.107297

    Article  Google Scholar 

  13. Tucker, M.J., Pitt, E.G.: Waves in Ocean Engineering, 1st edn. Elsevier Ocean Engineering, vol. 5. Elsevier Science, Amsterdam (2001)

  14. Nomiyama, D.H., Tsugukiyo, H.: Evaluation of marine radar as an ocean-wave-field detector through full numerical simulation. J. Mar. Sci. Technol. 8(2), 88–98 (2003). https://doi.org/10.1007/s00773-003-0160-8

    Article  Google Scholar 

  15. Nishimura, K., Hirayama, T., Nomiyama, D.H., Hirakawa, Y., Takayama, T.: A navigation system for dangerous-wave-avoidance maneuver as an application of marine radar and motion simulation technique. In: Conference Proceedings The Society of Naval Architects of Japan, vol. 4, pp. 91–92 (2004). https://doi.org/10.14856/zosenconf.4.0_91

  16. Nishimura, K., Hirayama, T., Takayama, T., Hirakawa, Y., Nomiyama, D.H.: Unsteady rolling due to turning manoeuvre in waves-ii : motion simulation based on encounter wave prediction by wave radar. J. Jpn. Inst. Navig. 112, 307–314 (2005)

    Google Scholar 

  17. Belmont, M.R., Christmas, J., Dannenberg, J., Hilmer, T., Duncan, J., Duncan, J.M., Ferrier, B.: An examination of the feasibility of linear deterministic sea wave prediction in multidirectional seas using wave profiling radar: Theory, simulation, and sea trials. J. Atmos. Ocean. Technol. 31(7), 1601–1614 (2014). https://doi.org/10.1175/JTECH-D-13-00170.1

    Article  Google Scholar 

  18. Belmont, M.R., Horwood, J.M.K., Thurley, R.W.F., Baker, J.: Shallow angle wave profiling lidar. J. Atmos. Ocean. Technol. 24(6), 1150–1156 (2007). https://doi.org/10.1175/JTECH2032.1

    Article  Google Scholar 

  19. Naaijen, P., Wijaya, A.: Phase resolved wave prediction from synthetic radar images. In: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, vol. 8A (2014). https://doi.org/10.1115/OMAE2014-23470

  20. Hilmer, T., Thornhill, E.: Observations of predictive skill for real-time deterministic sea waves from the WaMoS 2. OCEANS 2015 - MTS/IEEE Washington, 1–7 (2015). https://doi.org/10.23919/OCEANS.2015.7404496

  21. Al-Ani, M., Christmas, J., Belmont, M.R., Duncan, J.M., Duncan, J., Ferrier, B.: Deterministic sea waves prediction using mixed space-time wave radar data. J. Atmos. Ocean. Technol. 36(5), 833–842 (2019). https://doi.org/10.1175/JTECH-D-17-0146.1

    Article  Google Scholar 

  22. Davis, M., Zarnick, E.E.: Testing ship models in transient waves. Technical report, David taylor model basin washington dc hydromechanics lab (1966)

  23. Falnes, J.: On non-causal impulse response functions related to propagating water waves. Appl. Ocean Res. 17(6), 379–389 (1995). https://doi.org/10.1016/S0141-1187(96)00007-7

    Article  Google Scholar 

  24. Falnes, J.: Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction. Cambridge University Press, Cambridge (2002). https://doi.org/10.1017/CBO9780511754630

    Book  Google Scholar 

  25. Belmont, M.R., Horwood, J.M.K., Thurley, R.W.F., Baker, J.: Filters for linear sea-wave prediction. Ocean Eng. 33(17), 2332–2351 (2006). https://doi.org/10.1016/j.oceaneng.2005.11.011

    Article  Google Scholar 

  26. Minoura, M., Hayatsu, N.: Spatial and Temporal Impulse Response Function of Propagating Wave. In: International Ocean and Polar Engineering Conference (2019)

  27. Korde, U.A., Coe, R.G., Bacelli, G.: Deterministic incident-wave elevation prediction in intermediate water depth. J. Ocean Eng. Mar. Energy 6(4), 359–376 (2020). https://doi.org/10.1007/s40722-020-00177-5

    Article  Google Scholar 

  28. Iida, T., Minoura, M.: Analytical solution of impulse response function of finite-depth water waves. Ocean Eng. 249, 110862 (2022). https://doi.org/10.1016/j.oceaneng.2022.110862

    Article  Google Scholar 

  29. Iida, T.: Decomposition and prediction of initial uniform bi-directional water waves using an array of wave-rider buoys. Renew. Energy 217, 119137 (2023). https://doi.org/10.1016/j.renene.2023.119137

    Article  Google Scholar 

  30. Clauss, G.F., Testa, D., Kosleck, S., Stück, R.: Forecast of Critical Wave Groups From Surface Elevation Snapshots. In: International Conference on Offshore Mechanics and Arctic Engineering, vol. 2, pp. 79–88 (2007). https://doi.org/10.1115/OMAE2007-29090

  31. Clauss, G.F., Kosleck, S., Testa, D.: Critical situations of vessel operations in short crested seas-forecast and decision support system. J. Offshore Mech. Arct. Eng. 134(3) (2012). https://doi.org/10.1115/1.4004515

  32. Kosleck, S.: Prediction of wave-structure interaction by advanced wave field forecast. PhD thesis (2013). https://doi.org/10.14279/depositonce-3528

  33. Duan, W., Ma, X., Huang, L., Liu, Y., Duan, S.: Phase-resolved wave prediction model for long-crest waves based on machine learning. Comput. Methods Appl. Mech. Eng. 372, 113350 (2020). https://doi.org/10.1016/j.cma.2020.113350

    Article  MathSciNet  Google Scholar 

  34. Kotowski, A.: The method of frequency determination of impulse response components based on cross-correlation vs. fast fourier transform. Diagnostyka 17(1), 59–64 (2016)

    Google Scholar 

  35. Kaiser, M.S., Iida, T.: Moving point prediction of linear irregular water waves using numerical impulse response function. Int. Ocean Polar Eng. Conf. (2022)

  36. Phelps, B.P., Science, D., (Australia), T.O., Aeronautical, (Australia), M.R.L.: Ship Structural Response Analysis : Spectra and Statistics / B.P. Phelps. DSTO Aeronautical and Maritime Research Laboratory Melbourne, Melbourne (1995)

  37. Venezian, G.: Direct solution of wave dispersion equation, by JN Hunt. J. Waterw. Port Coast. Ocean Eng. Div. Proc. ASCE (106), 501–502 (1980)

  38. Fenton, J.D., McKee, W.D.: On calculating the lengths of water waves. Coast. Eng. 14(6), 499–513 (1990). https://doi.org/10.1016/0378-3839(90)90032-R

    Article  Google Scholar 

  39. Scorer, R.S.: Numerical evaluation of integrals of the form \(I=\int _{x_1}^{x_2}e^{i\phi (x)}dx\) and the tabulation of the function \({{\rm Gi}}(z)=\frac{1}{\pi }\sin (uz+\frac{1}{3}u^3)\). Q. J. Mech. Appl. Math. 3(1), 107–112 (1950). https://doi.org/10.1093/qjmam/3.1.107

    Article  MathSciNet  Google Scholar 

  40. Tsiklauri, M., Zvonkin, M., Fan, J., Drewniak, J., Chen, Q.B., Razmadze, A.: Causality and delay and physics in real systems. In: IEEE International Symposium on Electromagnetic Compatibility (EMC), pp. 961–966 (2014). https://doi.org/10.1109/ISEMC.2014.6899107

  41. Xiao, X., White, E.P., Hooten, M.B., Durham, S.L.: On the use of log-transformation vs. nonlinear regression for analyzing biological power laws. Ecology 92(10), 1887–1894 (2011). https://doi.org/10.1890/11-0538.1

    Article  Google Scholar 

  42. Zakharov, V.E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190–194 (1968). https://doi.org/10.1007/BF00913182

    Article  Google Scholar 

  43. Hasimoto, H., Ono, H.: Nonlinear Modulation of Gravity Waves. J. Phys. Soc. Jpn. 33(3), 805–811 (1972). https://doi.org/10.1143/JPSJ.33.805

    Article  Google Scholar 

  44. Hilmer, T., Thornhill, E.: Deterministic wave predictions from the WaMos II. OCEANS 2014 - TAIPEI, 1–8 (2014). https://doi.org/10.1109/OCEANS-TAIPEI.2014.6964526

Download references

Acknowledgements

This work was supported by JSPS KAKENHI under Grant No. JP23K13504.

Author information

Author notes

  1. M. S. Kaiser, T. Iida, contributed equally to this work.

Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, Osaka University, Suita, Osaka, 5650871, Japan

    Md Shahidullah Kaiser & Takahito Iida

Authors
  1. Md Shahidullah Kaiser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takahito Iida
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takahito Iida.

Ethics declarations

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaiser, M.S., Iida, T. Water Wave Impulse Response Function on Moving Point with Constant Speed in Head Wave. Water Waves (2024). https://doi.org/10.1007/s42286-024-00091-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42286-024-00091-5

Keywords

Search

Navigation