This paper describes the theory of nonlinear internal-solitary waves of the type observed in coastal seas. It also describes a numerical solution of an initial-value problem that leads to an internal solitary-like wave. The equations solved numerically are the Navier-Stokes, diffusion, and continuity equations. The computer solution illustrates that solitary-like waves are easily generated. A comparison with the theory illustrates that the wave is a KdV-like solitary wave. Hence, the computed wave is caused by a near balance between dispersive and nonlinear effects. However, the shape of the fully-nonlinear solitary wave is fore-aft asymmetric with a relatively long, somewhat elevated tail. This feature is characteristic of the computationally derived wave as compared with the fore-aft symmetry of the theoretical wave. (This work is motivated by the fact that internal solitary-like waves have practical importance in the design of offshore structures and on the acoustic properties of the sea, among other environmental consequences.)
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August 2002
Technical Papers
Nonlinear Internal Solitary Wave on a Pycnocline
Daniel T. Valentine,
Daniel T. Valentine
Applied Research Laboratory, Penn State University, State College, PA 16804-0030
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Radica Sipcic
Radica Sipcic
Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699
Search for other works by this author on:
Daniel T. Valentine
Applied Research Laboratory, Penn State University, State College, PA 16804-0030
Radica Sipcic
Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699
Contributed by the OOAE Division of the American Society of Mechanical Engineers for publication in the ASME JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received by the ASME OOAE Division, Nov. 2000; final revision, Nov. 2001. Associate Editor: S. Yim.
J. Offshore Mech. Arct. Eng. Aug 2002, 124(3): 120-124 (5 pages)
Published Online: August 1, 2002
Article history
Received:
November 1, 2000
Revised:
November 1, 2001
Online:
August 1, 2002
Citation
Valentine, D. T., and Sipcic, R. (August 1, 2002). "Nonlinear Internal Solitary Wave on a Pycnocline ." ASME. J. Offshore Mech. Arct. Eng. August 2002; 124(3): 120–124. https://doi.org/10.1115/1.1490380
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