Skip to main content
Log in

The Green function for potential flow in a rectangular channel

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

The evaluation of the Green function is considered for the three-dimensional Laplace equation, in the interior of a rectangular channel subject to homogeneous Neumann conditions on the boundaries. To complement the Fourier eigenfunction expansion which is effective in the far-field, a near-field algorithm is developed based on the simpler Green function for a channel of infinite width, using images to account for the channel sides. Examples are given of numerical applications including the added mass of a sphere in a square channel, and the interaction force between a ship and an adjacent canal wall.

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

Access this article

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

  1. S.R.Breit, The potential of a Rankine source between parallel planes and in a rectangular cylinder. J. Engg. Math. 25 (1991) 151–163.

    Article  MATH  Google Scholar 

  2. J.N. Newman, The approximation of free-surface Green functions, Meeting in honour of Professor Fritz Ursell, University of Manchester, in Wave Asymptotics, Cambridge University Press (1991).

  3. I.S.Gradshteyn and I.M.Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York (1965).

    Google Scholar 

  4. F.T. Korsmeyer, C.-H. Lee and J.N. Newman, The computation of ship-interaction forces in restricted waters, submitted to J. Ship Research.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Newman, J.N. The Green function for potential flow in a rectangular channel. J Eng Math 26, 51–59 (1992). https://doi.org/10.1007/BF00043225

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00043225

Keywords

Navigation