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Convex and Concave Types of Second Baroclinic Mode Internal Solitary Waves : Volume 17, Issue 6 (02/11/2010)

By Yang, Y. J.

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Book Id: WPLBN0003978648
Format Type: PDF Article :
File Size: Pages 10
Reproduction Date: 2015

Title: Convex and Concave Types of Second Baroclinic Mode Internal Solitary Waves : Volume 17, Issue 6 (02/11/2010)  
Author: Yang, Y. J.
Volume: Vol. 17, Issue 6
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Fang, Y. C., Tang, T. Y., Ramp, S. R., & Yang, Y. J. (2010). Convex and Concave Types of Second Baroclinic Mode Internal Solitary Waves : Volume 17, Issue 6 (02/11/2010). Retrieved from

Description: Department of Marine Science, Naval Academy, Kaohsiung, Taiwan. Two types of second baroclinic mode (mode-2) internal solitary waves (ISWs) were found on the continental slope of the northern South China Sea. The convex waveform displaced the thermal structure upward in the upper layer and downward in the lower layer, causing a bulge in the thermocline. The concave waveform did the opposite, causing a constriction. A few concave waves were observed in the South China Sea, marking the first documentation of such waves. On the basis of the Korteweg-de Vries (K-dV) equation, an analytical three-layer ocean model was used to study the characteristics of the two mode-2 ISW types. The analytical solution was primarily a function of the thickness of each layer and the density difference between the layers. Middle-layer thickness plays a key role in the resulting mode-2 ISW. A convex wave was generated when the middle-layer thickness was relatively thinner than the upper and lower layers, whereas only a concave wave could be produced when the middle-layer thickness was greater than half the water depth. In accordance with the K-dV equation, a positive and negative quadratic nonlinearity coefficient, Α2, which is primarily dominated by the middle-layer thickness, resulted in convex and concave waves, respectively. The analytical solution showed that the wave propagation of a convex (concave) wave has the same direction as the current velocity in the middle (upper or lower) layer. Analysis of the three-layer ocean model properly reproduced the characteristics of the observed mode-2 ISWs in the South China Sea and provided a criterion for the existence of convex or concave waves. Concave waves were seldom seen because of the rarity of a stratified ocean with a thick middle layer. This analytical result agreed well with the observations.

Convex and concave types of second baroclinic mode internal solitary waves

Gill, A. E.: Atmosphere-Ocean Dynamics, Academic Press, San Diego, 662 pp., 1982; Grimshaw, R.: Evolution equations for long nonlinear waves in stratified shear flow, Stud. Appl. Math., 65, 159–188, 1981.; Gear, J. and Grimshaw, R.: A second-order theory for solitary waves in shallow fluids, Phys. Fluids, 26, 14–29, 1983.; Akylas, T. and Grimshaw, R.: Solitary internal waves with oscillatory tails, J. Fluid Mech., 242, 279–298, 1992.; Alpers, W.: Theory of radar imaging of internal waves, Nature, 314, 245–247, 1985.; Apel, J. R.: A new analytical model for internal solitons in the ocean, J. Phys. Oceanogr., 33, 2247–2269, 2003.; Antenucci, J. P., Imberger, J., and Saggio, A.: Seasonal evolution of basin-scale internal wave field in a large stratified lake, Limnol. Oceanogr., 45, 1621–1638, 2000.; Apel, J. R., Ostrovsky, L. A., Stepanyants, Y. A., and Lynch, J. F.: Internal solitons in the ocean and their effect on underwater sound, J. Ascust. Soc. Am., 121, 695–722, 2007.; Apel, J. R., Badiey, M., Chiu, C.-S., Finette, S., Headrick, R., Kemp, J., Lynch, J. F., Newhall, A., Orr, M. H., Pasewark, B. H., Tielbuerger, D., Turgut, A., von der Heydt, K., and Wolf, S.: An overview of the 1995 SWARM Shallow-Water Internal Wave Acoustic Scattering Experiment, IEEE J. Oceanic Eng., 22, 465–500, 1997.; Benjamin, T. B.: Internal waves of permanent form in fluids of great depth, J. Fluid Mech., 29, 559–592, 1967.; Benny, D. J.: Long non-linear waves in fluid flow, J. Math. Phys., 45, 52–63, 1966.; Boegman, L., Imberger, J., Ivey, G. N., and Antenucci, J. P.: High-frequency internal waves in large stratified lakes, Limnol. Oceanogr., 48, 895–919, 2003.; Bogucki, D. J., Redekopp, L. G., and Barth, J.: Internal solitary waves in the Coastal Mixing and Optics 1996 experiment: Multimodal structure and resuspension, J. Geophys. Res., 110, C02024, doi:10.1029/2003JC002253, 2005.; Chang, M.-H., Lien, R.-C., Yang, Y. J., Tang, T. Y., and Wang, J.: A composite view of surface signatures and interior properties on nonlinear internal waves: Observations and applications, J. Atmos. Ocean. Tech., 25, 1218–1227, 2008.; Davis, R. E. and Acrivos, A.: Solitary internal waves in deep water, J. Fluid Mech., 29, 593–607, 1967.; Duda, T. F., Lynch, J. F., Irish, J. D., Beardsley, R. C., Ramp, S. R., Chiu, C.-S., Tang, T. Y., and Yang, Y. J.: Internal tide and nonlinear internal wave behavior at the continental slope in the northern South China Sea, IEEE J. Oceanic Eng., 29, 1105–1130, 2004; Farmer, D. M. and Smith, J. D.: Tidal interaction of stratified flow with a sill in Knight Inlet, Deep-Sea Res., 27A, 239–254, 1980.; Grimshaw, R., Pelinovsky, E., and Talipova, T.: The modified Korteweg – de Vries equation in the theory of large – amplitude internal waves, Nonlin. Processes Geophys., 4, 237–250, doi:10.5194/npg-4-237-1997, 1997.; Helfrich, K. R. and Melville, W. K.: Long nonlinear internal waves, Annu. Rev. Fluid Mech., 38, 395–425, 2006.; Honji, H., Matsunaga, N., Sugihara, Y., and Sakai, K.: Experimental observation of internal symmetric solitary waves in a two-layer fluid, Fluid Dyn. Res., 15, 89–102, 1995.; Kao, T. W. and Pao, H.-P.: Wake collapse in the thermocline and internal solitary waves, J. Fluid Mech., 97, 115–127, 1980.; Konyaev, K. V., Sabinin, K. D., and Serebryany, A. N.: Large-amplitude internal waves at the Mascarene Ridge in the Indian Ocean, Deep-Sea Res. Pt. I, 42, 2075–2091, 1995.; Lee, C.-Y. and Beardsley, R. C.: The generation of long nonlinear internal waves in a weakly stratified shear flow, J. Geophys. Res., 79, 453–462, 1974.; Liu, A. K., Chang, Y. S., Hsu, M.-K., and Liang, N. K.: Evolution of nonlinear internal waves in the East and South China Seas, J. Geophys. Res., 103, 7995–8008, 1998.; Maslowe, S. A. and Redekopp, L. G.: Long nonlinear waves in stratified shear flows, J. Fluid Mech., 101, 321–348, 1980.; Maxworthy, T.: On the formation of nonlinear internal waves from the gravitational collapse of mixed


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