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Vortex sheet motion in incompressible Richtmyer–Meshkov and Rayleigh–Taylor instabilities with surface tension
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10.1063/1.3231837
/content/aip/journal/pof2/21/9/10.1063/1.3231837
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/9/10.1063/1.3231837
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Interfacial profiles, circulation , and sheet strength in the RM instability for and at 1.2, [(b) and (e)] 3.0, and [(c) and (f)] 4.1. The dashed and solid lines in (d)–(f) denote the circulation and sheet strength , respectively. An enlarged view of the circled region in (c) is shown in Fig. 2.

Image of FIG. 2.
FIG. 2.

Enlarged view of circled region in Fig. 1(c).

Image of FIG. 3.
FIG. 3.

Interfacial profiles in the RM instability for at various : (a) and , (b) and , and (c) and , where (d)–(f) are curvature profiles corresponding to (a)–(c), respectively.

Image of FIG. 4.
FIG. 4.

Interfacial profiles in the RM instability for various Atwood numbers: (a) and , (b) and , and (c) and , where for all calculations. All circled regions in (a)–(c) do not self-intersect.

Image of FIG. 5.
FIG. 5.

Growth rate (velocity) of bubbles and spikes at the linear stage. The solid, dashed, and dot-dashed lines show the cases of , 0.5, and 1.0, respectively, with finite surface tension parameters. The solid line with the circle shows the case of with .

Image of FIG. 6.
FIG. 6.

Stable finite amplitude standing wave solution in the RM instability with large : (a) interfacial profiles and (b) growth rate (velocity) of a bubble and spike for . The solid and dashed lines in (b) indicate the bubble and spike, respectively. (c) The maximum sheet strength for various surface tension coefficients . The Atwood number is set to for all calculations.

Image of FIG. 7.
FIG. 7.

Analytical interfacial profiles in the RM instability for and .

Image of FIG. 8.
FIG. 8.

Comparison of analytical and numerical results in the RT instability: (a) numerical interfacial profiles, (b) analytical interfacial profiles, and (c) temporal evolution of the amplitude of a bubble and spike, where the parameters used in the calculations are , , and .

Image of FIG. 9.
FIG. 9.

Unstable finite amplitude standing wave solution in the RM instability: (a) interfacial profiles and (b) curvature profiles, where and . The solid, dashed, dot-dashed, and solid-with-circle lines in (a) show the interface at , 25.0, 40.0, and 51.9, respectively. The curvatures at and 51.9 are shown in (b).

Image of FIG. 10.
FIG. 10.

Temporal evolution of an interface in the RT instability for , , and , where (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 11.
FIG. 11.

Growth rate (velocity) of a bubble and spike in the RT instability for , , and . The solid and dashed lines denote the absolute values of bubble and spike velocities, respectively.

Image of FIG. 12.
FIG. 12.

Critical motion in the RT instability; (a) temporal evolution of an interface, (b) sheet strength , (c) absolute value of growth rate (velocity) of a bubble and spike, and (d) semilog plot of (c) for , , and , where the solid, dashed, dot-dashed, and solid-with-circle lines in (a) and (b) depict , 28.0, 32.0, and 34.3, respectively.

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/content/aip/journal/pof2/21/9/10.1063/1.3231837
2009-09-25
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Vortex sheet motion in incompressible Richtmyer–Meshkov and Rayleigh–Taylor instabilities with surface tension
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/9/10.1063/1.3231837
10.1063/1.3231837
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