Liu, Z;
Grimshaw, R;
Johnson, E;
(2021)
Resonant coupling of mode-1 and mode-2 internal waves by topography.
Journal of Fluid Mechanics
, 908
(A2)
pp. 1-21.
10.1017/jfm.2020.829.
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Abstract
We consider the resonant coupling of mode-1 and mode-2 internal solitary waves by topography. Mode-2 waves are generated by a mode-1 wave encountering variable topography, modelled by a coupled Korteweg–de Vries (KdV) system. Three cases, namely (A) weak resonant coupling, (B) moderate resonant coupling and (C) strong resonant coupling, are examined in detail using a three-layer density-stratified fluid system with different stratification and topographic settings. The strength of the resonant coupling is determined by the range of values taken by the ratio of linear long-wave phase speeds (c2/c1, where c1 is the mode-1 speed and c2 the mode-2 speed) while the waves are above the slope. In case A the range is from 0.42 (ocean edge) to 0.48 (shelf edge), in case B from 0.58 (ocean) to 0.72 (shelf) and in case C from 0.44 (ocean) to 0.92 (shelf). The feedback from mode-2 to mode-1 is estimated by comparing the coupled KdV system with a KdV model. In case A, a small-amplitude convex mode-2 wave is generated by a depression mode-1 wave and the feedback on the mode-1 wave is negligible. In case B, a concave mode-2 wave of comparable amplitude to that of the depression incident mode-1 wave is formed; strong feedback enhances the polarity change process of the mode-1 wave. In case C, a large-amplitude concave mode-2 wave is produced by an elevation mode-1 wave; strong feedback suppresses the fission of the mode-1 wave. Simulations for a wider range of topographic slopes and three-layer stratifications are then classified in terms of these responses.
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