Journal of Engineering Mathematics

, Volume 70, Issue 1–3, pp 67–91 | Cite as

Unsteady three-dimensional sources for a two-layer fluid of finite depth and their applications

  • Thai C. Nguyen
  • Ronald W. Yeung
Open Access


To our friend Ernie Tuck, in celebration of his multi-faceted talents. The velocity potentials of various unsteady point sources are derived in this paper for a two-layer fluid of finite depth. Two-layer fluids are often used to study effects of density stratification on hydrodynamics of marine systems. The sources here are restricted to the upper fluid layer and the potentials of the induced flows are given for the whole fluid domain. The velocity potentials of a transient source of arbitrary strength and in arbitrary three-dimensional motion are derived first. The potentials of a time-harmonic source without forward speed, and then with forward speed, are obtained from the transient source by specifying the appropriate source strength and motion. These potentials are fundamental to the analyses of various types of body motion in finite water depths under the influence of surface and interfacial waves. As a sample application, a numerical solution of the radiation and diffraction problem for a floating rectangular barge is presented. The results indicate that internal waves can have a strong effect on the motions of the floating barge over a wide range of incident-wave frequencies.


Floating systems Free-surface flow Ship motion Source function Stratified fluid Unsteady flow Wave motion 



The first author would like to acknowledge the support of the ILIR Program of the Naval Surface Warfare Center, Panama City Division. Partial support of this work, conducted under Office of Naval Research Grant No. N00014-09-1-1086 at The University of California at Berkeley is also gratefully acknowledged.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Naval Surface Warfare CenterPanama CityUSA
  2. 2.Ocean Engineering Group, Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA

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