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.
Enlarged view of circled region in Fig. 1(c).
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.
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.
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 .
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.
Analytical interfacial profiles in the RM instability for and .
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 .
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).
Temporal evolution of an interface in the RT instability for , , and , where (a) , (b) , (c) , (d) , (e) , and (f) .
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.
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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