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Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability
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10.1063/1.3258668
/content/aip/journal/pof2/21/11/10.1063/1.3258668
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/11/10.1063/1.3258668

Figures

Image of FIG. 1.
FIG. 1.

Difference between the (dimensionless) cylindrical growth rate and its plane counterpart vs for (solid line), (dotted line), (small dashed line), (dashed line), and (long dashed line) for two different Atwood ratios: (a) and (b) .

Image of FIG. 2.
FIG. 2.

Atwood ratio corresponding to critical perturbations vs for (solid line), (dotted line), (small dashed line), and (dashed line).

Image of FIG. 3.
FIG. 3.

Imploding and exploding shock front average radial positions vs . The converging shock travels in air with Mach number of 3.0 at . Superposition of two-dimensional simulation results of cylindrical shock initialized by Chisnell’s solution (crosses) and a power-law least-squares fit for both imploding and exploding shocks (solid line).

Image of FIG. 4.
FIG. 4.

Postshock interface base radial position vs in plane and converging geometries for various . An incident shock impacts the density interface at rest at with an instantaneous Mach number .

Image of FIG. 5.
FIG. 5.

Axial perturbations : dimensionless amplitude (left) and growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for different ; case , , . See details in Sec. ???.

Image of FIG. 6.
FIG. 6.

Axial perturbations : dimensionless amplitude (left) and growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for three different ; case , , . See details in Sec. ???.

Image of FIG. 7.
FIG. 7.

Axial perturbations : dimensionless volume (left) and volume growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for three different ; case , , . See details in Sec. ???.

Image of FIG. 8.
FIG. 8.

Azimuthal perturbations : dimensionless amplitude (left) and growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for different ; case , , . See details in Sec. ???.

Image of FIG. 9.
FIG. 9.

Azimuthal perturbations : dimensionless amplitude (left) and growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for three different ; case , , . See details in Sec. ???.

Image of FIG. 10.
FIG. 10.

Azimuthal perturbations : dimensionless volume (left) and volume growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for three different ; case , , . See details in Sec. ???.

Image of FIG. 11.
FIG. 11.

Dimensionless amplitude (left) and growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for the plane, cylindrical axial, cylindrical azimuthal, and spherical azimuthal perturbations; case , , ; for the plane geometry , for cylindrical axial geometry and , the azimuthal geometry and , and the spherical azimuthal geometry and . See details in Sec. ???.

Image of FIG. 12.
FIG. 12.

Dimensionless volume (left) and volume growth rate (right) vs of the interface perturbation (top), spike front (middle), and bubble front (bottom) plotted for the plane, cylindrical axial, cylindrical azimuthal, and spherical azimuthal perturbations; case , , ; for the plane geometry , for cylindrical axial geometry and , the azimuthal geometry and , and the spherical azimuthal geometry and . See details in Sec. ???.

Tables

Generic image for table
Table I.

Three-parameter least-squares fit for imploding and exploding shocks.

Generic image for table
Table II.

Table of runs for an shock interaction with single mode perturbations of initial amplitude . is computed using Eq. (22) in Ref. 13, while is obtained from Eq. (15). Postshock amplitude and Atwood ratio , and interface velocity are evaluated from the simulation immediately following the shock interaction and depend on the incident shock strength only.

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/content/aip/journal/pof2/21/11/10.1063/1.3258668
2009-11-06
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/11/10.1063/1.3258668
10.1063/1.3258668
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