Elapsed time ["uts/6]0 0.5 1 1.5

Vor

tex

sepa

ratio

n [d

/6]

0

0.1

0.2

0.3

0.4

0.5

0.670:14060:120Predicted

•  W.C. Wan et. al., “Observation of single-mode, Kelvin-Helmholtz instability in a super-sonic flow," Physical Review Letters, (Volume 115, Issue 14, Pages 145001) 2015.

•  G. Malamud et. al., “A design of a two-dimensional, supersonic KH experiment on OMEGA-EP," High Energy Density Physics, (Volume 9, Issue 4, Pages 672-686) 2013.

•  S.R. Choudhury et. al., “Nonlinear evolution of the Kelvin-Helmholtz instability of supersonic tangential velocity discontinuities,” Journal of Mathematical Analysis and Applications, (Volume 214, Issue 2, Pages 561-586) 1997.

We present two sample pieces of x-ray radiographic data. On the left are raw images of Cu Kα x-ray transmission through the target, at t = 65 and t = 68 ns for the top and bottom image respectively. On the top right, a section of the data has been processed through a contrast-enhancing unsharp mask algorithm. Beneath it, contours from a simulated radiograph with appropriate smearing and noise have been overlaid upon the data. Structure above the diagnostic resolution limit of ~10-15 µm is well-reproduced by 2D simulations .

0.1

0.2

0.2

0.3

0.30.3

0.4

0.40.4

0.5

0.5

0.5

0.50.5

0.60.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

A

Mc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.2

0.4

0.6

0.8

1

1.2

Elapsed time ["uts/6]0 0.5 1 1.5 2

PtV

am

plitu

de [h

/6]

0.1

0.2

0.3

0.4

0.5

0.6

0.7Dominant mode (70:140)Secondary mode (70:140)Dominant mode (60:120)Secondary mode (60:120)Incompressible predictionsCompressible predictions

1.  Produce the first data of the KHI evolving from dual-mode initial conditions in a supersonic flow

2.  Study the vortex merger rate of the KHI

3.  Supplement data on the instability growth inhibition in a supersonic flow

The Kelvin-Helmholtz instability is a fundamental hydrodynamic process that generates vortical structures and turbulence at an interface with shear flow. In a supersonic flow, effects of compression inhibit the vortex merger rate and instability growth rate. We share the results of a laser-driven experiment designed to produce the first observations of the KHI evolving from well-characterized, dual-mode initial conditions in a supersonic flow.

Figure 1: We design scaled experiments to study the the behavior of fluids under extreme temperatures

and pressures, such as those found in fusion experiments and astrophysical systems.

Photocredit: NASA, Voyager I (1979)

We developed a novel experimental platform, firing three 10-ns laser pulses in sequence to sustain a shockwave in carbon foam for roughly 70-ns.

The data support the predicted reduction in the KHI vortex merger rate and instability growth rate. The larger, dominant mode is denoted in blue. The smaller, secondary mode is denoted in red. The dashed lines represent incompressible predictions, while the solid lines represent the compressible predictions.

Figure 5: Top: Data at t = 65 ns, with a seed perturbation of 60 µm : 120 µm

Bottom: Data at t = 68 ns, with a seed perturbation of 70 µm : 140 µm

1.  We applied a novel experimental platform to sustain a supersonic shockwave over a precision-machined, dual-mode foam-plastic interface.

2.  This successfully produced the first experimental measurements of the KHI vortex merger rate from well-characterized initial conditions.

3.  We obtained additional data supporting KHI growth inhibition in a supersonic flow.

This work is funded by the U.S. Department of Energy, through the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, grant number DE-NA0002956, and the National Laser User Facility Program, grant number DE-NA0002719, through the Laboratory for Laser Energetics, University of Rochester by the NNSA/OICF under Cooperative Agreement No. DE-NA0001944, and through by Lawrence Livermore National Laboratory under subcontract B614207 to DE-AC52-07NA27344.

Vortex merger in a dual-mode, supersonic Kelvin-Helmholtz instability experiment W.C. Wan1, G. Malamud1,2, A. Shimony2,3, M.R. Trantham1, S.R. Klein1, D.Shvarts1,2,3, R.P.Drake1, C.C. Kuranz1

1Climate and Space Science and Engineering, University of Michigan, Ann Arbor, MI, USA. 2Nuclear Research Center – Negev, Beer Sheva, Israel. 3Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel.

Introduction

Objectives

Materials and Methods

Results and Discussion

Conclusions

Acknowledgements

References

CRFfoam

PCablator

CHBrinsulator

High-Zshockblocker

CHItracer

PAIplas>c

Transmitted shock

Plastic

Foam

Shockblocker

ShockEntrained ablatorand insulator

Log(ρ[g/cm3])

Figure 2: The ratio of the compressible to incompressible growth rate coefficients is reduced

by about half for this experiment

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ++−−−

Δ=

MMMAuk 22

2 41112)(

γ

Figure 3: Left: Our primary diagnostic is Cu Kα x ray radiography. An unshocked target is shown

Right: 2D simulations are used for both design work and data analysis

Figure 4: The data supports predictions of growth inhibition, until disturbed by the thermal insulator

Dual-modeSingle-mode

Entrainedgold

Foam

Plastic

Entrained CHBrinsulator

Foam

Plastic

Entrained CHBrinsulator

Entrainedgold

a)

b)

Figure 6: Measurements of vortex separation distance vs. time can be reproduced with 2D

simulations