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Mass and Momentum Transfer by Solitary Internal Waves in a Shelf Zone : Volume 19, Issue 2 (03/04/2012)

By Gavrilov, N.

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Book Id: WPLBN0003982369
Format Type: PDF Article :
File Size: Pages 8
Reproduction Date: 2015

Title: Mass and Momentum Transfer by Solitary Internal Waves in a Shelf Zone : Volume 19, Issue 2 (03/04/2012)  
Author: Gavrilov, N.
Volume: Vol. 19, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2012
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Gavrilova, K., Liapidevskii, V., & Gavrilov, N. (2012). Mass and Momentum Transfer by Solitary Internal Waves in a Shelf Zone : Volume 19, Issue 2 (03/04/2012). Retrieved from http://hawaiilibrary.net/


Description
Description: Lavrentyev Institute of Hydrodynamics, Novosibirsk, 630090, Russia. The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the swash zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.

Summary
Mass and momentum transfer by solitary internal waves in a shelf zone

Excerpt
Choi, W. and Camassa, R.: Fully nonlinear internal waves in a two-fluid system, J. Fluid Mech., 386, 1–36, 1999.; Derzho, O. G. and Grimshaw, R.: Assymetric internal solitary waves with a trapped core in deep fluids, Phys. Fluids, 19, 096601, doi:10.1063/1.2768507, 2007.; Ermanyuk, E. V. and Gavrilov, N. V.: A note on the propagation speed of a weakly dissipative gravity current, J. Fluid Mech., 574, 393–403, 2007.; Gavrilov, N. V. and Liapidevskii, V. Yu.: Finite-amplitude solitary waves in a two layer fluid, J. Appl. Mech. Tech. Phys., 51, 471–481, 2010.; Gavrilov, N. V., Liapidevskii, V., and Gavrilova, K.: Large amplitude internal solitary waves over a shelf, Nat. Hazards Earth Syst. Sci., 11, 17–25, doi:10.5194/nhess-11-17-2011, 2011.; Green, A. E. and Naghdi, P. M.: A derivation of equations for wave propagation in water of variable depth, J. Fluid Mech., 78, 237–246, 1976.; Helfrich, K. R. and Melville, W. K.: Long nonlinear internal waves, Annu. Rev. Fluid Mech., 38, 395–425, 2006.; Klymak, J. M. and Moum, J. N.: Internal solitary waves of elevation advancing on a shoaling shelf, Geophys. Res. Lett., 30, 2045, doi:10.1029/2003GL017706, 2003.; Lamb, K. G.: Shoaling solitary internal waves:on a criterion for the formation of waves with trapped cores, J. Fluid Mech., 478, 81–100, 2003.; Le Metayer, O., Gavrilyuk, S., and Hank, S.: A numerical scheme for the Green-Naghdi model, J. Comput. Phys., 229, 2034–2045, 2010.; Liapidevskii, V. Yu. and Teshukov, V. M.: Mathematical Models of Long-Wave Propagation in an Inhomogeneous Fluid, Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000 (in Russian).; Maxworthy, T.: On the formation of nonlinear internal waves from the gravity collapse of mixing regions in two and three dimensions, J. Fluid Mech., 96, 47–64, 1980.; Nash, J. D. and Moum, J. N.: River plumes as a source of large-amplitude internal waves in the coastal ocean, Nature, 437, 400–403, doi:10.1038/nature03936, 2005.; Stamp, A. P. and Jacka, M.: Deep-water internal solitary waves, J. Fluid Mech., 305, 347–371, 1995.; Tung, K.-K., Chan, T. F., and Kubota, T.: Large amplitude internal waves of permanent form, Stud. Appl. Math., 66, 1–44, 1982.; Scotti, A. and Pineda, J.: Observation of very large and steep internal waves of elevation near the Massachusetts coast, Geophys. Res. Lett., 31, L22307, 1–5, doi:10.1029/2004GL021052, 2004.; Vlasenko, V. and Hutter, K.: Numerical experiments on the breaking of solitary internal waves over a slope-shelf topography, J. Phys. Oceanography, 32, 1779–1793, 2002.; Wallace, B. C. and Wilkinson D. L.: Run up of internal waves on a gentle slope, J. Fluid Mech., 191, 419–442, 1988.

 

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