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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2017-31
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
13 Jul 2017
Review status
This discussion paper is a preprint. A revision of this manuscript was accepted for the journal Nonlinear Processes in Geophysics (NPG) and is expected to appear here in due course.
Head-on collision of internal waves with trapped cores
Vladimir Maderich1, Kyung Tae Jung2, Kateryna Terletska1, and Kyeong Ok Kim2 1Institute of Mathematical Machine and System Problems, Glushkov av., 42, Kiev 03187, Ukraine
2Korea Institute of Ocean Science and Technology, 787, Haean-ro, Ansan 426-744 Republic of Korea
Abstract. The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in thin pycnocline were studied numerically within the framework of the Navier-Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves the trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly nonlinear waves without trapped cores, (ii) stable strongly nonlinear waves with trapped cores, and (iii) shear unstable strongly nonlinear waves. The wave phase shift grows as the amplitudes of the interacting waves increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum runup amplitude over the sum of the amplitudes of colliding waves almost linearly increases with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The waves of class (ii) with a normalized on thickness of pycnocline amplitude lose fluid trapped by the wave cores in the range approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of three-dimensional instability and turbulence. The dependence of loss of energy on the wave amplitude is not monotonous. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.

Citation: Maderich, V., Jung, K. T., Terletska, K., and Kim, K. O.: Head-on collision of internal waves with trapped cores, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2017-31, in review, 2017.
Vladimir Maderich et al.
Interactive discussionStatus: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version      Supplement - Supplement
 
RC1: 'Manuscript Review', Anonymous Referee #1, 12 Sep 2017 Printer-friendly Version Supplement 
 
RC2: 'Please see attached.', Oliver Fringer, 20 Sep 2017 Printer-friendly Version Supplement 
 
AC1: 'Final Response', Vladimir Maderich, 30 Oct 2017 Printer-friendly Version Supplement 
 
EC1: 'Response to reviewers', Marek Stastna, 31 Oct 2017 Printer-friendly Version 
Vladimir Maderich et al.
Vladimir Maderich et al.

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Short summary
When near-surface or near-bottom layers in the ocean are stratified, then internal solitary waves (ISWs) of large amplitude can trap and transport fluid in their cores. The dynamics and energetics of a head-on collision of ISWs with trapped cores for a wide range of amplitudes and stratifications are studied numerically. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions. The interaction can trigger local wave instability of ISWs.
When near-surface or near-bottom layers in the ocean are stratified, then internal solitary...
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