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An Asymptotic Method in Ship Hydrodynamics

In: Differential Equations Theory, Numerics and Applications

Author

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  • A. J. Hermans

    (TU Delft, Department of Applied Mathematics and Computer Science)

Abstract

In the field of diffraction of acoustic, electro-magnetic and elastic waves the ray method has proven to be a powerful tool to obtain reliable results for the behaviour of short waves. In ship hydrodynamics where the generation of short waves by a slowly sailing vessel and the diffraction of short surface waves by these vessels is of importance recently the ray method is applied successfully. In this presentation we present two cases, each with its own free surface condition, treated with this method. In the first part we derive the asymptotic results for the wave pattern generated by a ship with a blunt bow and stern (for instance VLCC’s). The dimensionless forward velocity, Fn = U/(gL)1/2, of these ships is small. After an appropriate linearisation of the free surface condition is carried out, approximation for large wave numbers can be obtained. We derive equations for the ray pattern and for the wave ampitude. The wave excitation coefficients are obtained by the asymptotic evaluation of an approximate integral formulation. Results for the wave resistance are obtained by a ray tracing algorithm. In the second part we derive an asymptotic theory for the diffraction of free surface waves by a very large floating flexible platform (floating airport) and the deflection of this platform. In the case of total reflection the evanescent mode will be shown. Also the deflection due to a landing airplane and its take off is considered.

Suggested Citation

  • A. J. Hermans, 1997. "An Asymptotic Method in Ship Hydrodynamics," Springer Books, in: E. van Groesen & E. Soewono (ed.), Differential Equations Theory, Numerics and Applications, pages 103-123, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5157-3_5
    DOI: 10.1007/978-94-011-5157-3_5
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