Journal of Ocean Engineering and Technology (한국해양공학회지)

Korean Society of Ocean Engineers (한국해양공학회)
권호 표지

On the Wave Source Identification of an Wave Maker Problem

  • JANG TAEK-SOO (Department of Naval Architecture and Ocean Engineering, Pusan National University)
  • Published : 2003.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

The question of wave source identification in a wave maker problem is the primary objective of the this paper. With the observed wave elevation, the existence of the wave maker velocity is discussed with the help of the mathematical theory of inverse problems. Utilizing the property of the Strum-Liouville system and compactness, the uniqueness and the ill-posedness(in the sense of stability) for the identification are proved.

Keywords

References

  1. Bassanini, P. and Elcrat, A.R. (1997). A Theory and Applications of Partial Differential Equations, Plenum Press, New York
  2. Chakrabarti, S.K. (1994). Fluid Structure Interaction in Offshore Engineering, Computational Mechanics Publications, New York
  3. Crapper, G.D. (1984). Introduction to Water Waves, Ellis Horwood Limited, New York
  4. Groetsch, C. W. (1993). Inverse Problems in the Mathematical Sciences, Vieweg, Braunschweig
  5. Hocking, L.M. and Mahdmina, D. (1991). "Capillary-Gravity Waves Produced by a Wavemaker", J. Fluid Mech, Vol 224, pp 217-226 https://doi.org/10.1017/S0022112091001726
  6. Hulme, A. (1984). "Some Applications of Maz'ja's Uniqueness Theorem to a Class of Linear Water Wave Problems", J. Fluid Mech., Vol 95, pp 165-174
  7. Isakov, V. (1998). Inverse Problems for Partial Differential Equations, Springer Verlag, Berlin
  8. Jang, T. S., Choi, H. S. and Kinoshita, T. (2000a). "Solution of an Unstable Inverse Problem:Wave Source Evaluation from Observation of Velocity Distribution", J. Mar. Sci. Technol., Vol 5, No 4, pp 181-188 https://doi.org/10.1007/s007730070004
  9. Jang. T. S., Choi, H. S. and Kinoshita, T. (2000b). "Numerical Experiments on an Ill-posed Inverse Problem for a Given Velocity Around a Hydrofoil by Iterative and Noniterative Regularizations", J. Mar Sci. Technol., Vol 5, No, 3 pp 107-111 https://doi.org/10.1007/s007730070007
  10. John, F. (1950). "On the Motion of Floating Bodies", Math. Proc. Camb. Phil. Soc., Vol 95, pp 165-174 https://doi.org/10.1017/S0305004100061417
  11. Joo, S.W., Schultz, W.W. and Messiter, A.F. (1990). "An Analysis of the Initial-Value Wavemaker Problem.", J. Fluid Mech., Vol 214, pp 161-183 https://doi.org/10.1017/S002211209000009X
  12. Kirsch, A. (1996). An Introduction to the Mathematical Theory of Inverse Problems, Springer Verlag, Berlin
  13. Kreisel, G. (1949). Surface Waves, Q. Appl. Math., Vol 7, pp 21-24
  14. Miles, J. (1991). "On the Initial-Value Problem of a Wavemaker", J. Fluid Mech., Vol 229, pp 589-601 https://doi.org/10.1017/S002211209100318X
  15. Simon, M.J. and Ursell, F. (1984). "Uniqueness in Linearized Two-Dimensional Water-Wave Problems", J. Fluid Mech., Vol 148, pp 137-154 https://doi.org/10.1017/S0022112084002287
  16. Stakgold, I. (1967). Boundary Value Problems of Math. Physics, Vol 1, Macmillan, London