Unsteady threedimensional sources for a twolayer fluid of finite depth and their applications
 Thai C. Nguyen,
 Ronald W. Yeung
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Abstract
To our friend Ernie Tuck, in celebration of his multifaceted talents. The velocity potentials of various unsteady point sources are derived in this paper for a twolayer fluid of finite depth. Twolayer 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 threedimensional motion are derived first. The potentials of a timeharmonic 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 incidentwave frequencies.
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 Title
 Unsteady threedimensional sources for a twolayer fluid of finite depth and their applications
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Journal of Engineering Mathematics
Volume 70, Issue 13 , pp 6791
 Cover Date
 20110701
 DOI
 10.1007/s106650109439z
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Floating systems
 Freesurface flow
 Ship motion
 Source function
 Stratified fluid
 Unsteady flow
 Wave motion
 Industry Sectors
 Authors

 Thai C. Nguyen ^{(1)}
 Ronald W. Yeung ^{(2)}
 Author Affiliations

 1. Naval Surface Warfare Center, Panama City, FL, 32407, USA
 2. Ocean Engineering Group, Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA, 947201740, USA