Research Papers: Fundamental Issues and Canonical Flows

The Effect of a Dominant Initial Single Mode on the Kelvin–Helmholtz Instability Evolution: New Insights on Previous Experimental Results

[+] Author and Article Information
Assaf Shimony

Department of Physics,
Beer-Sheva 84190, Israel;
Department of Physics,
Beer-Sheva 84015, Israel
e-mail: shimonya@gmail.com

Dov Shvarts, Guy Malamud

Department of Physics,
Beer-Sheva 84190, Israel;
Department of Atmospheric,
Oceanic, and Space Sciences,
University of Michigan,
Ann Arbor, MI 48109

Carlos A. Di Stefano

Department of Atmospheric,
Oceanic, and Space Sciences,
University of Michigan,
Ann Arbor, MI 48109;
Los Alamos National Laboratory,
Los Alamos, NM 87507

Carolyn C. Kuranz, R. P. Drake

Department of Atmospheric,
Oceanic, and Space Sciences,
University of Michigan,
Ann Arbor, MI 48109

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 31, 2015; final manuscript received August 15, 2015; published online April 12, 2016. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 138(7), 070902 (Apr 12, 2016) (7 pages) Paper No: FE-15-1075; doi: 10.1115/1.4032530 History: Received January 31, 2015; Revised August 15, 2015

This paper brings new insights on an experiment, measuring the Kelvin–Helmholtz (KH) instability evolution, performed on the OMEGA-60 laser facility. Experimental radiographs show that the initial seed perturbations in the experiment are of multimode spectrum with a dominant single-mode of 16 μm wavelength. In single-mode-dominated KH instability flows, the mixing zone (MZ) width saturates to a constant value comparable to the wavelength. However, the experimental MZ width at late times has exceeded 100 μm, an order of magnitude larger. In this work, we use numerical simulations and a statistical model in order to investigate the vortex dynamics of the KH instability for the experimental initial spectrum. We conclude that the KH instability evolution in the experiment is dominated by multimode, vortex-merger dynamics, overcoming the dominant initial mode.

Copyright © 2016 by ASME
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Grahic Jump Location
Fig. 4

Map of the plastic's volume fraction from the DAFNA simulation of the dominant single-mode initial conditions at different times: (a) t = 0, (b) t = 2.4 ns, (c) t = 5 ns, (d) t = 10 ns, and (e) t = 20 ns. The initial perturbation was taken from Fig. 2(b).

Grahic Jump Location
Fig. 3

Map of the plastic's volume fraction from the DAFNA simulation of the dominant single-mode initial conditions in two resolutions (Δx is the size of the smallest cell in the simulation) at two different times: (a) t = 2.4 ns, Δx = 0.5 μm; (b) t = 2.4 ns, Δx = 0.25 μm; (c) t = 20 ns, Δx = 0.5 μm; and (d) t = 20 ns, Δx = 0.25 μm

Grahic Jump Location
Fig. 7

Histogram of the vortex length at the end of the experiment obtained by the statistical model

Grahic Jump Location
Fig. 8

MZ width versus evolution time by different numerical methods: statistical model (with the dominant single-mode initial conditions) and DAFNA simulations with multimode (three different scans) and dominant single-mode initial conditions in solid, dotted, and dashed lines, respectively, comparing to the experimental results (presented by the circles). The dashed-dotted line presents the saturation width of the 16 μm wavelength mode, 9 μm.

Grahic Jump Location
Fig. 2

The initial conditions: spectra from the two different measuring methods: (a) Fourier transform of the surface scan, showing multimode initial conditions and (b) Fourier transform of the experimental radiograph, showing dominant single-mode initial conditions; and the experimental radiograph picture (c) (© 2014 by AIP, reproduced from Ref. [11].)

Grahic Jump Location
Fig. 1

A scheme of the physical relevant components in the experimental target and the main shock waves

Grahic Jump Location
Fig. 5

Map of the plastic's volume fraction from the DAFNA simulation of the multimode initial conditions at different times: (a) t = 5 ns, (b) t = 10 ns, (c) t = 20 ns, and (d) t = 35 ns. The initial perturbation for the simulation was taken from Fig. 2(a).

Grahic Jump Location
Fig. 6

Map of the plastic's volume fraction from the DAFNA simulation of the dominant single-mode initial conditions in comparison to the multimode initial conditions at different times: (a) t = 2.4 ns, dominant mode; (b) t = 2.4 ns, multimode; (c) t = 10 ns, dominant mode; (d) t = 10 ns, multimode; (e) t = 20 ns, dominant mode; and (f) t = 20 ns, multimode




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