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TECHNICAL PAPERS

Nonlinear Internal Solitary Wave on a Pycnocline

[+] Author and Article Information
Daniel T. Valentine

Applied Research Laboratory, Penn State University, State College, PA 16804-0030e-mail: clara@clarkson.edu

Radica Sipcic

Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699e-mail: radica.sipcic@awo.com

J. Offshore Mech. Arct. Eng 124(3), 120-124 (Aug 01, 2002) (5 pages) doi:10.1115/1.1490380 History: Received November 01, 2000; Revised November 01, 2001; Online August 01, 2002
Copyright © 2002 by ASME
Topics: Waves
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References

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Osborne, A. R., et al., 1978, “The Influence of Internal Waves on Deep-Water Drilling,” J. Pet. Technol., JPTCAZpp. 1497–1504.
Headrick,  R. H., , 2000, “Acoustic Normal Mode Fluctuation Statistics in the 1995 SWARM Internal Wave Scattering Experiment,” J. Acoust. Soc. Am., 107, pp. 201–220.
Kao,  T. W., , 1985, “Internal Solitons on the Pycnocline: Generation, Propagation, and Shoaling on Breaking Over a Slope,” J. Fluid Mech., 159, pp. 19–53.
Saffarinia,  K., and Kao,  T. W., 1996, “A Numerical Study of the Breaking of an Internal Soliton and its Interaction with a Slope,” Dyn. Atmos. Oceans, 23, pp. 379–391.
Keulegan,  G. H., 1953, “Characteristics of Internal Solitary Waves,” J. Res. Natl. Bur. Stand., 51, pp. 133–140.
Benjamin,  T. B., 1967, “Internal Waves of Permanent Form in Fluids of Great Depth,” J. Fluid Mech., 29, pp. 559–592.
Benney,  D. J., 1966, “Long Non-linear Waves in Fluid Flows,” J. Math. Phys., 45, pp. 52–63.
Korteweg,  D. J., and de Vries,  G., 1895, “On the Change of the Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves,” Philos. Mag., 39, pp. 422–443.
Choi,  W., and Camassa,  R., 1999, “Fully Nonlinear Internal Waves in a Two-Fluid System,” J. Fluid Mech., 396, pp. 1–36.
Wu, T. Y., 1999, “On Modeling Unsteady Fully Nonlinear Dispersive Interfacial Waves,” Chap. 13, Fluid Dynamics at Interfaces W. Shyy and R. Narayanan (eds.), Cambridge Univ. Press, pp. 171–178.
Valentine, D. T., 1988, “Control-Volume Finite Difference Schemes to Solve Convection Diffusion Problems,” ASME Computers in Engineering, III , pp. 543–551.
Terez,  D. E., and Knio,  O. M., 1998, “Numerical simulations of large-amplitude internal solitary waves,” J. Fluid Mech., 362, pp. 53–82.
Valentine, D. T., et al., 1999, “Large Amplitude Solitary Wave on a Pycnocline and Its Instability,” Fluid Dynamics at Interfaces, Chap. 15, W. Shyy and R. Narayanan (eds.), Cambridge Univ. Press, pp. 227–239.

Figures

Grahic Jump Location
The density-difference ratio as a function of depth illustrating the shape of the pycnocline density structure
Grahic Jump Location
The left side of a rectangular basin illustrating the initial variation of the reference density-difference ratio, θ̄(z), including the shape of the pycnocline on which the solitary wave propagates and the shape of the displaced pool used to generate it
Grahic Jump Location
Flow properties of the leading solitary wave: (a) The θ=0.5 isopycnal; (b) The distortion of the pycnocline caused by the wave—Nine equally-spaced contours in the range 0.1≤θ≤0.9; (c) The streamline pattern—Twenty equally-spaced contours in the range −0.0757≤ψ≤0.0202; and (d) Vorticity field—Seventy-two equally-spaced contours in the range −60.8≤ζ≤30,9 (the four contors in the center of the wave are for ζ=1.16, 2.40, 3.64 and 4.88 with the largest value closest to the center of the pattern)
Grahic Jump Location
Velocity profile at the horizontal location of the peak of the leading solitary wave; x=18.45
Grahic Jump Location
The stream function versus time at the location (x,z)=(17.5,0.725): the solid line is the computational prediction; the dash-dot line is the KdV theory solitary wave (Inset: The spatial shape of the leading solitary wave as depicted by the θ=0.5 isopycnal)

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