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Nonlin. Processes Geophys., 24, 751-762, 2017
https://doi.org/10.5194/npg-24-751-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
22 Dec 2017
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 a 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 trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly non-linear waves without trapped cores, (ii) stable strongly non-linear waves with trapped cores, and (iii) shear unstable strongly non-linear waves. The wave phase shift of the colliding waves with equal amplitude grows as the amplitudes increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum run-up amplitude, normalized by the amplitude of the waves, over the sum of the amplitudes of the equal colliding waves increases almost linearly with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The colliding waves of class (ii) lose fluid trapped by the wave cores when amplitudes normalized by the thickness of the pycnocline are in the range of 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 instability. The dependence of loss of energy on the wave amplitude is not monotonic. 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., 24, 751-762, https://doi.org/10.5194/npg-24-751-2017, 2017.
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Short summary
When near-surface or near-bottom layers in the ocean are stratified, 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, internal solitary waves...
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