<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE article SYSTEM "http://www.nonlin-processes-geophys.net/inc/npg/copernicus.dtd">
<article language="en">
	<journal>
		<journal_title>Nonlinear Processes  in Geophysics</journal_title>
		<journal_url>www.nonlin-processes-geophys.net</journal_url>
		<issn>1023-5809</issn>
		<eissn>1607-7946</eissn>
		<volume_number>16</volume_number>
		<issue_number>1</issue_number>
		<publication_year>2009</publication_year>
	</journal>
	<doi>10.5194/npg-16-33-2009</doi>
	<article_url>http://www.nonlin-processes-geophys.net/16/33/2009/</article_url>
	<abstract_html>http://www.nonlin-processes-geophys.net/16/33/2009/npg-16-33-2009.html</abstract_html>
	<fulltext_pdf>http://www.nonlin-processes-geophys.net/16/33/2009/npg-16-33-2009.pdf</fulltext_pdf>
	<start_page>33</start_page>
	<end_page>42</end_page>
	<publication_date>2009-02-05</publication_date>
	<article_title content_type="html">The transformation of an interfacial solitary wave of elevation at a bottom step</article_title>
	<authors>
		<author numeration="1" affiliations="1">
			<name>V. Maderich</name>
		</author>
		<author numeration="2" affiliations="2">
			<name>T. Talipova</name>
		</author>
		<author numeration="3" affiliations="3">
			<name>R. Grimshaw</name>
			<email>r.h.j.grimshaw@lboro.ac.uk</email>
		</author>
		<author numeration="4" affiliations="2,3">
			<name>E. Pelinovsky</name>
		</author>
		<author numeration="5" affiliations="4">
			<name>B. H. Choi</name>
		</author>
		<author numeration="6" affiliations="1">
			<name>I. Brovchenko</name>
		</author>
		<author numeration="7" affiliations="1">
			<name>K. Terletska</name>
		</author>
		<author numeration="8" affiliations="4">
			<name>D. C. Kim</name>
		</author>
	</authors>
	<affiliations>
		<affiliation numeration="1" content_type="html">Department of Marine and River Systems, Institute of Mathematical Machine and System Problems, Kiev, Ukraine</affiliation>
		<affiliation numeration="2" content_type="html">Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod, Russia</affiliation>
		<affiliation numeration="3" content_type="html">Department of Mathematical Sciences, Loughborough University, Loughborough, UK</affiliation>
		<affiliation numeration="4" content_type="html">Department of Civil and Environmental Engineering, Sungkyunwan University, Suwon, Korea</affiliation>
	</affiliations>
	<abstract content_type="html">In this paper we study the transformation of an internal solitary wave at a
bottom step in the framework of two-layer flow, for the case when the
interface lies close to the bottom, and so the solitary waves are elevation
waves. The outcome is the formation of solitary waves and dispersive wave
trains in  both the reflected and transmitted fields. We use a
two-pronged approach, based on numerical simulations of the fully nonlinear
equations using a version of the Princeton Ocean Model on the one hand, and
a theoretical and numerical study of the Gardner equation on the other hand. In the numerical
experiments, the ratio of the initial wave amplitude to the layer thickness
is varied up one-half, and nonlinear effects are then essential. In general,
the characteristics of the generated solitary waves obtained in the fully
nonlinear simulations are in reasonable agreement with the predictions of
our theoretical model, which is based on matching linear shallow-water
theory in the vicinity of a step with solutions of the Gardner
equation for waves far from the step.</abstract>
	<references>
		<reference numeration="1" content_type="text">Bogucki, D. and Redekopp, L.: A mechanism for sediment resuspension by internal solitary waves, Geophys. Res. Lett., 26, 9, 1317–1320, 1999. </reference>
		<reference numeration="2" content_type="text">Bourgault, D., Blokhina, M. D., Mirshak, R., and Kelley, D. E.: Evolution of a shoaling internal solitary wavetrain, Geophys. Res. Lett., 34, L03601, doi:10.1029/2006GL028462, 2007. </reference>
		<reference numeration="3" content_type="text">Brovchenko, I., Gorodetska, N., Maderich, V., Nikishov, V., and Terletska, K.: Interaction of internal solitary waves of large amplitude with obstacle, Applied Hydromechanics, 9(81), No 1, 3–7, 2007 </reference>
		<reference numeration="4" content_type="text">Chang, K.-A., Hsu, T.-J., and Liu, P. L.-F.: Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle, Coastal Eng., 44, 13–36, 2001. </reference>
		<reference numeration="5" content_type="text">Chen, C.-Y., Hsu, J. R.-C., Chen, H.-H., Kuo, C.-F., and Cheng, M.-H.: Laboratory observations on internal solitary wave evolution on steep and inverse uniform slopes, Ocean Eng., 34, 157–170, 2007a. </reference>
		<reference numeration="6" content_type="text">Chen, C.-Y., Hsu, J. R.-C., Cheng-Wu Chen, C.-W., Chen, H.-H., Kuo, C.-F., and Cheng, M.-H.: Generation of internal solitary wave by gravity collapse, J. Mar. Sci. Technol., 15, 1–7, 2007b. </reference>
		<reference numeration="7" content_type="text">Chen, C.-Y., Hsu, J. R.-C., Cheng, M.-H., Chen, H.-H., and Kuo, C.-F.: An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slopes, Ocean Eng., 34, 171–184, 2007c. </reference>
		<reference numeration="8" content_type="text">Choi, W. and Camassa, R.: Fully nonlinear internal waves in a two-fluid system, J. Fluid Mech., 396, 1–36, 1999. </reference>
		<reference numeration="9" content_type="text">De Zárate, A. R. and Nashbin, A.: A reduced model for internal waves interacting with topography at intermediate depth, Commun. Math. Sci., 6, 385–396, 2008. </reference>
		<reference numeration="10" content_type="text">Djordjevic, V. and Redekopp, L.: The fission and disintegration of internal solitary waves moving over two-dimensional topography, J. Phys. Ocean., 8, 1016–1024, 1978. </reference>
		<reference numeration="11" content_type="text">Grimshaw, R., Pelinovsky, D., Pelinovsky, E., and Slunyaev, A.: The generation of large- amplitude solitons from an initial disturbance in the extended Korteweg – de Vries equation, Chaos, 12, 1070–1076, 2002a. </reference>
		<reference numeration="12" content_type="text">Grimshaw, R., Pelinovsky, E., and Poloukhina, O.: Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface, Nonlin. Processes Geophys., 9, 221–235, 2002b. </reference>
		<reference numeration="13" content_type="text">Grimshaw, R., Pelinovsky, E., Talipova, T., and Kurkin, A.: Simulation of the transformation of internal solitary waves on oceanic shelves, J. Physical Oceanography, 34, 2774–2779, 2004. </reference>
		<reference numeration="14" content_type="text">Grimshaw, R., Pelinovsky, E., and Talipova, T.: Modeling internal solitary waves in the coastal ocean, Survey in Geophysics, 28, 273–298, 2007 </reference>
		<reference numeration="15" content_type="text">Grimshaw, R., Pelinovsky, E., and Talipova T.: Fission of a weakly nonlinear interfacial solitary wave at a step, Geophysical and Astrophysical Fluid Dynamics, 102, 179–194, 2008. </reference>
		<reference numeration="16" content_type="text">Grue, J., Jensen, A., Rus&amp;aring;s, P.-O., and Sveen, J. K.: Properties of large amplitude internal waves, J. Fluid Mech., 380, 257–278, 1999. </reference>
		<reference numeration="17" content_type="text">Helfrich, K. R.: Internal solitary wave breaking and run-up on a uniform slope, J. Fluid Mech., 243, 133–154, 1992. </reference>
		<reference numeration="18" content_type="text">Helfrich, K. R. and Melville, W. K.: On long nonlinear internal waves over slope-shelf topography, J. Fluid Mech., 167, 285–308, 1986. </reference>
		<reference numeration="19" content_type="text">Holloway, P., Pelinovsky, E., Talipova, T., and Barnes, B.: A Nonlinear Model of Internal Tide Transformation on the Australian North West Shelf, J. Physical Oceanography, 27, 871–896, 1997. </reference>
		<reference numeration="20" content_type="text">Holloway, P., Pelinovsky, E., and Talipova, T.: A Generalized Korteweg – de Vries Model of Internal Tide Transformation in the Coastal Zone, J. Geophys. Res., 104(C8), 18333–18350, 1999 </reference>
		<reference numeration="21" content_type="text">Kakutani, T. and Yamasaki, N. Solitary waves on a two-layer fluid, J. Phys. Soc., Japan, 45, 674–679, 1978. </reference>
		<reference numeration="22" content_type="text">Kanarska, Y. and Maderich, V.: A non-hydrostatic numerical model for calculating of free-surface stratified flows, Ocean Dynam., 51, 176–185, 2003. </reference>
		<reference numeration="23" content_type="text">Lamb, K. G.: A numerical investigation of solitary internal waves with trapped cores formed via shoaling, J. Fluid Mech., 451, 109–144, 2002. </reference>
		<reference numeration="24" content_type="text">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. </reference>
		<reference numeration="25" content_type="text">Lin, P.: A numerical study of solitary wave interaction with rectangular obstacles, Coastal Eng., 51, 35–51, 2004. </reference>
		<reference numeration="26" content_type="text">Liu, P. L.-F. and Cheng, Y.: A numerical study of the evolution of a solitary wave over a shelf, Physics Fluids, 13, 1660–1667, 2001. </reference>
		<reference numeration="27" content_type="text">Mellor, G. L.: An equation of state for numerical models of ocean and estuaries, J. Atmos. Ocean. Tech., 8, 609–611, 1991. </reference>
		<reference numeration="28" content_type="text">Orr, M. H. and Mignerey, P.C.: Nonlinear internal waves in the South China Sea: observation of the conversion of depression internal waves to elevation internal waves, J. Geophys. Res., 108(C3), 3064, doi:10.1029/2001JC001163, 2003. </reference>
		<reference numeration="29" content_type="text">Ramp, S. R., Tang, T. Y., Duda, T. F., Lynch, J. F., Liu, A. K., Chiu, C.-S., Bahr, F. L., Kim, H.-R., and Yang, Y.-J.: Internal Solitons in the Northeastern South China Sea Part I: Sources and Deep Water Propagation, IEEE J. Oceanic Eng., 29, 1157–1181, 2004. </reference>
		<reference numeration="30" content_type="text">Ribbe, J. and Holloway, P.: A model of suspended sediment transport by internal tides, Cont. Shelf Res., 21, 395–422, 2001. </reference>
		<reference numeration="31" content_type="text">Seabra-Santos, F. J., Renouard, D. P., and Temperville, A. M.: Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle, J. Fluid Mech., 176, 117–134, 1987. </reference>
		<reference numeration="32" content_type="text">Stastna, M. and Lamb, K. G.: Sediment resuspension mechanisms associated with internal waves in coastal waters, J. Geophys. Res., 113, C10016, doi:10.1029/2007JC004711, 2008. </reference>
		<reference numeration="33" content_type="text">Vlasenko, V. I. and Hutter, K.: Generation of second mode solitary waves by the interaction of a first mode soliton with a sill, Nonlin. Processes Geophys., 8, 223–239, 2001. </reference>
		<reference numeration="34" content_type="text">Vlasenko, V. and Stashchuk, N.: Three-dimensional shoaling of large-amplitude internal waves, J. Geophys. Res., 112, C11018, doi:10.1029/2007JC004107, 2007. </reference>
		<reference numeration="35" content_type="text">Vlasenko, V., Stashchuk, N., and Hutter, K.: Baroclinic tides: theoretical modeling and observational evidence, Cambridge Univ. Press, 2005. </reference>
		<reference numeration="36" content_type="text">Zhao, Z., Klemas, V. V., Zheng, Q., and Yan, X.-H.: Satellite observation of internal solitary waves converting polarity, Geophys. Res. Lett., 30(19), 1988, doi:10.1029/2003GL018286, 2003. </reference>
		<reference numeration="37" content_type="text">Zheng, Q., Klemas, Q., Yan, X-H., and Pan, J.: Nonlinear evolution of ocean internal solitons propagating along an inhomogeneous thermocline, J. Geophys. Res., 106(C7), 14083–14094, 2001. </reference>
	</references>
</article>

