Fully nonlinear internal waves in a system of two fluids. 1: Shallow water configuration; 2: Deep water configuration

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The authors derive model equations that govern the evolution of internal gravity waves at the interface of two immiscible fluids. These models follow from the original Euler equations under the sole assumption that the waves are long compared to the undisturbed thickness of one of the fluid layers. No smallness assumption on the wave amplitude is made. Here the shallow water configuration is first considered, whereby the waves are taken to be long with respect to the total undisturbed thickness of the fluids. In part 2, the authors derive models for the configuration in which one of the two fluids ... continued below

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9 p.

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Choi, W. & Camassa, R. December 31, 1998.

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The authors derive model equations that govern the evolution of internal gravity waves at the interface of two immiscible fluids. These models follow from the original Euler equations under the sole assumption that the waves are long compared to the undisturbed thickness of one of the fluid layers. No smallness assumption on the wave amplitude is made. Here the shallow water configuration is first considered, whereby the waves are taken to be long with respect to the total undisturbed thickness of the fluids. In part 2, the authors derive models for the configuration in which one of the two fluids has a thickness much larger than the wavelength. The fully nonlinear models contain the Korteweg-de Vries (KdV) equation and the intermediate-long-wave (ILW) equation, for shallow and deep water configurations respectively, as special cases in the limit of weak nonlinearity and unidirectional wave propagation. In particular, for a solitary wave of given amplitude, the characteristic wavelength is larger and the wave speed smaller than their counterparts for solitary wave solutions of the weakly nonlinear equations. These features are compared and found in overall good agreement with available experimental data for solitary waves of large amplitude in two-fluid systems.

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9 p.

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OSTI as DE99000637

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  • ASCE engineering mechanics conference, La Jolla, CA (United States), 17-20 May 1998

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  • Other: DE99000637
  • Report No.: LA-UR--98-1231
  • Report No.: CONF-980525--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 304115
  • Archival Resource Key: ark:/67531/metadc684055

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  • December 31, 1998

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  • July 25, 2015, 2:20 a.m.

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  • Feb. 25, 2016, 5:54 p.m.

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Choi, W. & Camassa, R. Fully nonlinear internal waves in a system of two fluids. 1: Shallow water configuration; 2: Deep water configuration, article, December 31, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc684055/: accessed September 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.