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Idealized numerical simulation of breaking water wave propagating over a viscous mud layer
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10.1063/1.4768199
/content/aip/journal/pof2/24/11/10.1063/1.4768199
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/11/10.1063/1.4768199

Figures

Image of FIG. 1.
FIG. 1.

Schematics of water wave over a mud layer.

Image of FIG. 2.
FIG. 2.

Time history of turbulent velocity fluctuation in the three-dimensional simulation of case NBW-B1 with initial turbulence seed added.

Image of FIG. 3.
FIG. 3.

Time history of (a) the amplitude of the surface wave a normalized by its initial value a 0 and (b) the ratio of interfacial wave amplitude to surface wave amplitude b/a. Prediction of DL’s theory for case NBW-B0 (——), case NBW-B1 (– – –), and case NBW-B2 (– · – · –). DNS results for case NBW-A1 (△), case NBW-B0 (▽), case NBW-B1 (○), case NBW-B2 (◊), and case NBW-C1 (•).

Image of FIG. 4.
FIG. 4.

Instantaneous flow fields on the xy cross section at the center of the computational domain (i.e., z = 0) with contours of u at (a) t = 0.78T, (b) t = 0.99T, (c) t = 1.53T, and (d) t = 2.25T. The distribution of ε in the mud layer is also shown. Here, u is normalized by a 0σ and ε is normalized by . The water–mud interface is marked by (– – –). The arrow at the water surface denotes the wave propagation direction.

Image of FIG. 5.
FIG. 5.

Time history of (a) total mechanical energy in water and mud, (b) total mechanical energy in water, and (c) total mechanical energy in mud of case BW-A1 (——), case BW-A2 (– – –), case BW-B1 (– · – · –), and case BW-C1 (· · · · · ·). (a) The theoretical prediction for non-breaking water waves is also shown (with symbol).

Image of FIG. 6.
FIG. 6.

Vertical transport terms in the horizontally-averaged kinetic energy budget equation in the water region for (a) non-breaking wave and (b) breaking wave: (——), transport due to advection ; (– – –), transport due to pressure ; (– · · – · · –), transport due to viscous diffusion . The results are normalized by E va σ. Here, the superscript “va” denotes the volume-averaged value. For the non-breaking wave, case NBW-B1 at ak = 0.15 is shown. For the breaking wave, case BW-A1 at t = 2.25T is shown. Note that the scales are different between the two figures.

Image of FIG. 7.
FIG. 7.

Vertical transport terms in the horizontally-averaged kinetic energy budget equation in the mud region for (a) non-breaking wave and (b) breaking wave: (——), transport due to advection ; (– – –), transport due to pressure ; (– · · – · · –), transport due to viscous diffusion ; (· · · · · ·), viscous dissipation . The results are normalized by E va σ. For the non-breaking wave, case NBW-B1 at ak = 0.15 is shown. For the breaking wave, case BW-A1 at t = 2.25T is shown.

Image of FIG. 8.
FIG. 8.

Time history of (a) the viscous dissipation in water, (b) the viscous dissipation in mud, (c) the work done at the water–mud interface, (d) the work done by pressure at the water–mud interface, and (e) the ratio of kinetic energy between mud and water for case BW-A1 (——), case BW-A2 (– – –), case BW-B1 (– · – · –), and case BW-C1 (· · · · · ·).

Tables

Generic image for table
Table I.

Parameters considered in the present study. The “NBW” stands for non-breaking water wave; “BW” stands for breaking water wave. The a 0 is the initial wave amplitude.

Generic image for table
Table II.

Energy dissipated through the viscous dissipation in water and mud, the energy transfer at water–mud and air–water interfaces, and the energy loss during the wave breaking.

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/content/aip/journal/pof2/24/11/10.1063/1.4768199
2012-11-26
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Idealized numerical simulation of breaking water wave propagating over a viscous mud layer
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/11/10.1063/1.4768199
10.1063/1.4768199
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