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Internal solitary wave transformation over a bottom step: Loss of energy
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10.1063/1.4797455
/content/aip/journal/pof2/25/3/10.1063/1.4797455
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/3/10.1063/1.4797455

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the numerical tank for simulation of ISW transformation over a bottom step: (a) for a depression ISW, (b) for an elevation ISW.

Image of FIG. 2.
FIG. 2.

The energy loss δ for waves of elevation versus the height of the bottom layer after the step (a) and δ versus ratio /| | (b) for various amplitudes of an incident wave. The regimes of ISW interaction with the step (I–V) separated by dashed lines are shown in the right panel. The half-shaded symbols indicate interaction when the minimum Richardson number . The filled symbols indicate presence of supercritical flow with the composite Froude number .

Image of FIG. 3.
FIG. 3.

The relative energy loss δ for the waves of depression versus height of the bottom layer after the step (a) for various amplitudes of the incident wave and δ versus ratio /| | (b). The regimes of ISW interaction with step (I–V) separated by dashed lines are shown in the right panel. The half-shaded symbols indicate interaction with the minimum Richardson number . The filled symbols indicate presence of supercritical flow with the composite Froude number .

Image of FIG. 4.
FIG. 4.

The relative energy difference Δ in the waves of elevation (a) and depression (b) versus the ratio /| |. The regimes of ISW interaction with step are separated by dashed lines and shown by Roman numbers.

Image of FIG. 5.
FIG. 5.

The relative difference Δ between transmitted and reflected waves for waves of elevation versus (a) for waves of elevation at / = 0.4 and (b) for a wave of depression at / = 7. The solid line is an analytical estimate (6) for Δ

Image of FIG. 6.
FIG. 6.

The salinity field in the vicinity of the step shows KH instability for an incident elevation ISW (a) and depression ISW (b) with amplitude 8.8 cm and different /| | at the same time moments.

Image of FIG. 7.
FIG. 7.

Maximal values of composite Froude number, , at the step versus ratio /| | for incident elevation ISW type (a) and depression ISW type (b).

Image of FIG. 8.
FIG. 8.

Velocity vectors superimposed on the vorticity field in the vicinity of the step to show the formation of jet and vortices in the wave of elevation (a) and in the wave of depression (b) with amplitude 8.8 cm.

Image of FIG. 9.
FIG. 9.

Snapshots of the salinity field show the interaction with a step of an elevation ISW for an incident wave amplitude 4.2 cm (1) /| | = 0.25; (2) /| | = 0.12; (3) /| | = 0; (4) /| | = −0.12; (5) /| | = −1 at successive times (a) − = 0, (b) − = 13 c, (c) − = 38 c.

Image of FIG. 10.
FIG. 10.

Snapshots of the salinity field show the interaction with a step of a depression ISW for an incident wave of amplitude 8.8 cm (1) /| | = 2; (2) /| | = 1.36; (3) /| | = 0.2; (4) /| | = 0 at successive times (a) = 0; (b) = 10 s; (c) = 22 s.

Image of FIG. 11.
FIG. 11.

Zoom of Fig. 10 for the case 3 (left panel) at various time moments and a comparison of the wave after the step with the KdV and Gardner solitons (right panel) corresponding to snapshots in the left panel.

Image of FIG. 12.
FIG. 12.

Salinity field snapshots show KH billows appearing in the reflected wave from a vertical wall; ISW of elevation (a) and depression (b) with initial amplitude of 8.8 cm.

Image of FIG. 13.
FIG. 13.

Energy loss δ for wave scattering by an obstacle versus /| | for an incident wave of elevation (a) and an incident wave of depression (b), in comparison with laboratory experiments for two-layer flow by Wessels and Hutter and Chen.

Tables

Generic image for table
Table I.

Parameters of the computational tank.

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/content/aip/journal/pof2/25/3/10.1063/1.4797455
2013-03-29
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Internal solitary wave transformation over a bottom step: Loss of energy
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/3/10.1063/1.4797455
10.1063/1.4797455
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