Skip to main content
SpringerLink
Log in

A free surface frequency domain green function with viscous dissipation and partial reflections from side walls

  • Research Papers
  • Published:
Journal of Marine Science and Application Aims and scope Submit manuscript

Abstract

The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves. In the context of inviscid potential flow, hydrodynamic problems such as multi-body interaction and tank side wall effect cannot be properly dealt with based on the traditional free-surface frequency domain Green function method, in which the water viscosity is omitted and the energy dissipation effect is absent. In this paper, an open-sea Green function with viscous dissipation was presented within the theory of visco-potential flow. Then the tank Green function with a partial reflection from the side walls in wave tanks was formulated as a formal sum of open-sea Green functions representing the infinite images between two parallel side walls of the source in the tank. The new far-field characteristics of the tank Green function is vitally important for improving the validity of side-wall effects evaluation, which can be used in supervising the tank model tests.

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

Similar content being viewed by others

References

  • Abramowitz M, Stegun IA (1964). Handbook of mathematical functions. Dover Publications, New York.

    MATH  Google Scholar 

  • Chen Xiaobo (1994). On the side wall effects upon bodies of arbitrary geometry in wave tanks. Applied Ocean Research, 16, 337–345.

    Article  Google Scholar 

  • Chen Xiaobo (2004). Hydrodynamics in offshore and naval applications-Part I. Keynote Lecure at the 6th International Conference on Hydrodynamics, Perth, Australia.

  • Chen Xiaobo, Dias F (2010). Visco-potential flow and time-harmonic ship waves. 25th IwwwFB, Harbin, China.

  • Chen Xiaobo, Lu Dongqiang (2009). Time-harmonic ship waves with the effect of surface tension and fluid viscosity. 24th IwwwFB, Zelenogork, Russia.

  • Dias F, Dyachenko AF, Zakharov VE (2008). Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions. Physics letters, A, 372, 1297–1302.

    Article  MATH  Google Scholar 

  • Dutykh D, Dias F (2007). Viscous potential free-surface in a fluid layer of finite depth. C. R. Acad. Sci. Paris, Ser. I, 345, 113–118.

    MathSciNet  MATH  Google Scholar 

  • Evans DV (1990). The use of porous screens as wave dampers in narrow wave tanks. Journal of Engineering Mathematics, 24, 203–212.

    Article  Google Scholar 

  • John F (1950). On the motion of floating bodies II:simple harmonic motions. Communications on Pure and Applied Mathematics, 3, 45–101.

    Article  MathSciNet  Google Scholar 

  • Kashiwagi M (1991). Radiation and diffraction forces acting on an offshore-structure model in a towing tank. International Journal of Offshore and Polar Engineering, 1(2), 101–107.

    Google Scholar 

  • Linton CM (1993). On the free-surface Green’s function for channel problems. Applied Ocean Research, 15, 263–267.

    Article  Google Scholar 

  • Linton CM, Evans DV (1992). The radiation and scattering of surface waves by a vertical circular cylinder in a channel. Phil. Trans. R. Soc. Lond. A., 338, 325–357.

    Article  MATH  Google Scholar 

  • McIver P (1993). The wave field scattered by a vertical cylinder in narrow wave tank. Applied Ocean Research, 15, 25–37.

    Article  Google Scholar 

  • McIver P, Benneett GS (1993). Scattering of water waves by axisymmetric bodies in a channel. Journal of Engineering Mathematics, 27, 1–29.

    Article  MathSciNet  MATH  Google Scholar 

  • Newman JN (1984). Double precision evaluation of the oscillatory source potential. Journal of Ship Research, 28(3), 151–154.

    Google Scholar 

  • Qin Hongde, Shen Jing (2010). Green function with dissipation and side wall effect in wave tanks. 25th IwwwFB, Harbin, China.

  • Shen Jing, Qin Hongde (2011). Tank Green function with partial reflections from side walls. 26th IwwwFB, Athens (Greece).

  • Taylor RE, Hung SM (1985). Mean drift forces on an articulated column oscillating in a wave tank. Applied Ocean Research, 7(2), 66–78.

    Article  Google Scholar 

  • Vazquez JH, Williams AN (1994). Hydrodynamic loads on a three-dimensional body in a narrow tank. Journal of Offshore Mechanics and Arctic Engineering, 116, 117–121.

    Article  Google Scholar 

  • Xia Jinzhu (2002). Some insight into the Green function of the channel problem. 17th IwwwFB, Cambridge, UK.

  • Yeung RW, Sphaier SH (1989). Wave-interference effects on a truncated cylinder in a channel. Journal of Engineering Mathematics, 23(2), 95–117.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, China

    Hongde Qin & Jing Shen

  2. Research Department, Bureau Veritas, 92570, Neuilly-Sur-Seine, France

    Xiaobo Chen

Authors
  1. Hongde Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaobo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongde Qin.

Additional information

Foundation item: Supported by NSFC Project (51009037) and “111” Program (B07019).

Hongde Qin was born in 1976. He is an associate professor at Harbin Engineering University. His main focus is on hydro-structure response of ships and offshore structures.

Jing Shen was born in 1984. She is a PhD candidate at Harbin Engineering University. Her current research is focused on ship and offshore structure hydrodynamics.

Xiaobo Chen was born in 1961. He is responsible for the development and maintenance of HydroStar software in the Bureau Veritas research department. His research interests are focused on ship and offshore structure hydrodynamics.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qin, H., Shen, J. & Chen, X. A free surface frequency domain green function with viscous dissipation and partial reflections from side walls. J. Marine. Sci. Appl. 10, 259–264 (2011). https://doi.org/10.1007/s11804-011-1067-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11804-011-1067-0

Keywords

Search

Navigation