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Volume 25, issue 1 | Copyright

Special issue: Extreme internal wave events

Nonlin. Processes Geophys., 25, 1-17, 2018
https://doi.org/10.5194/npg-25-1-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 17 Jan 2018

Research article | 17 Jan 2018

On the interaction of short linear internal waves with internal solitary waves

Chengzhu Xu and Marek Stastna Chengzhu Xu and Marek Stastna
  • Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Abstract. We study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent waves are short in comparison to the solitary wave width, the interaction leads to an almost complete destruction of the short waves. For mode-1 short waves in the packet, as the wavelength increases, a cutoff is reached, and for larger wavelengths the waves in the packet are able to maintain their structure after the interaction. This cutoff corresponds to the wavelength at which the phase speed of the short waves upstream of the solitary wave exceeds the maximum current induced by the solitary wave. For mode-2 waves in the packet, however, no corresponding cutoff is found. Analysis based on linear theory suggests that the destruction of short waves occurs primarily due to the velocity shear induced by the solitary wave, which alters the vertical structure of the waves so that significant wave activity is found only above (below) the deformed pycnocline for overtaking (head-on) collisions. The deformation of vertical structure is more significant for waves with a smaller wavelength. Consequently, it is more difficult for these waves to adjust to the new solitary-wave-induced background environment. These results suggest that through the interaction with relatively smaller length scale waves, internal solitary waves can provide a means to decrease the power observed in the short-wave band in the coastal ocean.

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This work contributes to the understanding of the interaction between internal waves of different length scales. A key finding is that, when the disparity in length scales between the participating waves is large, the interaction may lead to an almost complete destruction of the waves that have a relatively smaller length scale. This result suggests that the wavelengths of internal waves observed in the coastal oceans are likely to be deficient in short waves.
This work contributes to the understanding of the interaction between internal waves of...
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