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Simulations and model of the nonlinear Richtmyer–Meshkov instability
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10.1063/1.3276269
/content/aip/journal/pof2/22/1/10.1063/1.3276269
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/1/10.1063/1.3276269

Figures

Image of FIG. 1.
FIG. 1.

Configuration and nomenclature for RM instability before and after the interaction of shock with material interface.

Image of FIG. 2.
FIG. 2.

Amplitudes and images at for simulations of a representative case with , , , , and . The numbers represent the number of zones per wavelength for each simulation.

Image of FIG. 3.
FIG. 3.

Scaled amplitude vs scaled time for NOVA experiment, FLASH simulations (black line), and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27). NOVA data taken with face-on (circles) and side-on (diamonds) x-ray radiographs on many different shots.

Image of FIG. 4.
FIG. 4.

Scaled average amplitude vs scaled time for air/SF6 shock tube experiments of SEA (gray circles) and Jacobs (gray diamonds) with . The lines represent the FLASH simulations (black line) and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27) for , , and .

Image of FIG. 5.
FIG. 5.

Scaled amplitude of bubbles and spikes vs scaled time for air/SF6 shock tube experiments of SEA (gray circles) with . The lines represent the FLASH simulations (black line) and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27) for .

Image of FIG. 6.
FIG. 6.

Scaled amplitude of bubbles and spikes vs scaled time for the incompressible experiments of NJ (gray diamonds). The lines represent the FLASH simulations (black line) and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27) for .

Image of FIG. 7.
FIG. 7.

Scaled velocity [(a) and (b)] and amplitude [(c) and (d)] for bubbles [(b) and (d)] and spikes [(a) and (c)] for and (37). The lines represent the FLASH simulations (black line) and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27).

Image of FIG. 8.
FIG. 8.

Scaled velocity [(a) and (b)] and amplitude [(c) and (d)] for bubbles [(b) and (d)] and spikes [(a) and (c)] for and (40). The lines represent the FLASH simulations (black line) and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27).

Image of FIG. 9.
FIG. 9.

Interface profiles at selected times for cases in Figs. 7 and 8 with and (a) and 1 (b).

Image of FIG. 10.
FIG. 10.

Scaled velocity for spikes (a) and bubbles (b) for and (22). The lines represent the FLASH simulations (black line) and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27).

Image of FIG. 11.
FIG. 11.

Scaled velocity [(a) and (b)] and amplitude [(c) and (d)] for bubbles [(b) and (d)] and spikes [(a) and (c)] for and (23). The lines represent the FLASH simulations (black line) and models due to SEA (green), MIK (blue), ZS (brown), and our Eqs. (2.24)–(2.27).

Image of FIG. 12.
FIG. 12.

Interface profiles at selected times for cases in Figs. 10 and 11 with and (a) and 1 (b).

Image of FIG. 13.
FIG. 13.

Scaled velocity [(a) and (b)] and amplitude [(c) and (d)] for bubbles [(b) and (d)] and spikes [(a) and (c)] for and (37 black), 0.94 (43 red), 0.88 (34 green), 0.75 (44 blue), 0.5 (45 brown), and 0.25 (46 magenta). Solid lines are from FLASH simulations and dashed lines are our model equations (2.24)–(2.27).

Image of FIG. 14.
FIG. 14.

Peak spike velocity taken from Fig. 13 vs Atwood number for . Black lines with diamonds are FLASH simulations and colored lines are SEA (green), MIK (blue), ZS (brown), and our model equations (2.24)–(2.27) (red). The magenta point is due to Zhang [Eq. (2.11)] at .

Image of FIG. 15.
FIG. 15.

Scaled velocity [(a) and (b)] and amplitude [(c) and (d)] for bubbles [(b) and (d)] and spikes [(a) and (c)] for and (black), 0.25 (red), 0.5 (green), 1 (blue), 2 (brown), and 4 (magenta) (37–42). Solid lines are from FLASH simulations and dashed lines are our model equations (2.24)–(2.27).

Image of FIG. 16.
FIG. 16.

Peak spike velocity taken from Fig. 15 vs at . Black lines with diamonds are FLASH simulations and colored lines are SEA (green), MIK (blue), ZS (brown), and our model equations (2.24)–(2.27) (red). The magenta point is due to Zhang [Eq. (2.11)] at .

Image of FIG. 17.
FIG. 17.

Scaled velocity for spikes (a) and bubbles (b) for and (black), 0.25 (red), 0.5 (green), 1 (blue), 2 (brown), and 4 (magenta) (22–24a). Solid lines are from FLASH simulations and dashed lines are our model equations (2.24)–(2.27).

Image of FIG. 18.
FIG. 18.

Scaled velocity of bubbles vs scaled time to asymptotic values for at (23), 0.5 (45a), 0.87 (26), and 0.98 (40). Black lines with diamonds are FLASH simulations and colored lines are SEA (green), MIK (blue), ZS (brown), and our model equations (2.24)–(2.27) (red). Dashed black line shows a slope of expected from potential flow. Conditions for each case are summarized in Table II.

Image of FIG. 19.
FIG. 19.

Scaled velocity of spikes vs scaled time to asymptotic values for at (23), 0.5 (45a), 0.87 (26), and 0.98 (40). Black lines with diamonds are FLASH simulations and colored lines are SEA (green), MIK (blue), ZS (brown), and our model equations (2.24)–(2.27) (red). Dashed black line shows a slope of expected from potential flow. Conditions for each case are summarized in Table II.

Image of FIG. 20.
FIG. 20.

Diamonds are the initial velocity required to fit the simulation result to our model [Eqs. (2.24)–(2.27)] scaled to linear growth rate (from simulations with ) vs initial amplitude. Solid line is from Padé approximant of VD and dashed line is our approximation equation (2.27).

Image of FIG. 21.
FIG. 21.

Initial growth rate scaled by the linear growth rate vs . Points are from SEA (circles) (Ref. 30), Aleshin et al. (diamonds) (Refs. 20 and 21), and Dimonte et al. (squares) (Refs. 22 and 23). Solid black line is the Padé approximant of VD and dashed (dotted) black line is our model equation (2.24)–(2.27) evaluated at for (0). The red line is given by our nonlinear impulsive model equation (3.3).

Tables

Generic image for table
Table I.

Parameters associated with experiments in Figs. 3–6. The values in parenthesis are only estimates used in the associated FLASH simulations which require , , , , and as input.

Generic image for table
Table II.

Simulation parameters for Figs. 18 and 19 with .

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/content/aip/journal/pof2/22/1/10.1063/1.3276269
2010-01-21
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Simulations and model of the nonlinear Richtmyer–Meshkov instability
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/1/10.1063/1.3276269
10.1063/1.3276269
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