Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-04T13:12:47.618Z Has data issue: false hasContentIssue false
  • English
  • Français

Laser-generated Richtmyer–Meshkov and Rayleigh–Taylor instabilities. III. Near-peripheral region of Gaussian spot

Published online by Cambridge University Press:  13 September 2017

Stjepan Lugomer
Stjepan Lugomer*
Affiliation:
Rudjer Boskovic Institute, Center of Excellence for Advanced Materials and Sensing Devices, Bijenicka c. 54, 10000 Zagreb, Croatia
*
*Address correspondence and reprint requests to: S. Lugomer, Rudjer Boskovic Institute, Center of Excellence for Advanced Materials and Sensing Devices, Bijenicka c. 54, 10000 Zagreb, Croatia. E-mail: lugomer@irb.hr
Get access Rights & Permissions [Opens in a new window]

Abstract

Dynamics and organization of laser-generated three-dimensional (3D) Richtmyer–Meshkov (RMI) and Rayleigh–Taylor instabilities (RMI and RTI) on metal target in the semiconfined configuration are different in the central region (CR) (Lugomer, 2016), near central region (NCR) (Lugomer, 2017) and the near periphery region (NPR) of the Gaussian-like spot. The RMI/RTI in the NPR evolve from the shock and series of reshocks associated with lateral expansion and increase of the vapor density, decrease of the Atwood number and momentum transfer. Scanning electron micrographs show irregular (chaotic) web of the base-plane walls, and mushroom spikes on its nodal points with disturbed two-dimensional (2D) lattice organization. Lattice disturbance is caused by the incoherent wavy motion of background fluid due to fast reshocks, which after series of reflections change their strength and direction. Reconstruction of the disturbed lattice reveals rectangular lattice of mushroom spikes with p2mm symmetry. The splitting (bifurcation) of mushroom diameter distribution on the large and small mushroom spikes increases with radial distance from the center of Gaussian-like spot. Dynamics of their evolution is represented by the orbits or stable periods in 2D phase space. The constant mushroom diameter – stable circulation or the stable periodic orbits – are the limit cycles between the unstable spiral orbits. Those with increasing periods represent supercritical Hopf bifurcation, while those leading to decrease and disappearance represent subcritical Hopf bifurcation. The empirical models of RMI, although predict dependence of the growth rate on radial distance (distance the reshocks travel to reach the interface), show many limitations. More appropriate interpretation of the simultaneous growth and lattice organization of small and large spikes give the fundamental model based on the interference of the perturbation modes depending on their amplitude, relative phase, and the symmetry. The late-time instability in the base-plane evolves into line solitons, vortex filaments and wave–vortex structures with chaotic rather than stochastic features.

Keywords

Hopf bifurcationLaser ablationLattice of mushroom spikesRayleigh–Taylor instabilityRichtnyer–Meshkov instabilitySmall and large mushroom spikesSolitary wavesWave–vortex phenomena
Type
Research Article
Information
Laser and Particle Beams , Volume 35 , Issue 4 , December 2017 , pp. 597 - 609
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abarzhi, S.I. (2008). Coherent structures and pattern formation in Rayleigh–Taylor turbulent mixing. Phys. Scr. 78, 015401.CrossRefGoogle Scholar
Abarzhi, S.I. & Hermann, M. (2003). New Type of the Interface Evolution in the RMI. Annual Res. Briefs 2003, Center for Turbulence Research, Defense Tech. Inform. Center. (173–183). http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADP014801 Google Scholar
Alon, U., Ofer, D. & Shvarts, D. (1996). Scaling Laws of Nonlinear RT and RM Instabilities, Proc. 5th Int.Workshop on Compressible Turbulent Mixing, ed. R. Young, J. Glimm and B. Boston, World Scientific. http://www.damtp.cam.ac.uk/iwpctm9/proceedings/.../Alon_Ofer_Shvarts.pdf Google Scholar
Anuchina, N.N., Volkov, V.I., Gordeychuk, V.A., Es'kov, N.S., Ilyutina, O.S. & Kozyrev, O.M. (2004). Numerical simulation of R–T and R–M instability using MAH-3 code. J. Comput. Appl. Math. 168, 11–20.CrossRefGoogle Scholar
Balakumar, B.J., Orlicz, G.C., Tomkins, C.D. & Prestridge, K.P. (2008). Dependence of growth patterns and mixing width on initial conditions in Richtmyer–Meshkov unstable fluid layers. Phys. Scr. T 132, 014013.CrossRefGoogle Scholar
Bressan, A. (2014). Math 417 – Qualitative theory of ODEs. https://www.math.psu.edu/bressan/PSPDF/M417-review4.pdf Google Scholar
Bromwick, A.K. & Abarzhi, S.I. (2016). Richtmyer–Meshkov unstable dynamics influenced by pressure fluctuations. Phys. Plasmas 23, 112702.Google Scholar
Brouilette, M. & Sturtevant, B. (1994). Experiments on the Richtmyer–Meshkov instability: Single-scale perturbations on continuum interface. J. Fluid Mech. 263, 71–292.Google Scholar
Cohen, R.H., Dennevik, W.P., Dimits, A.M., Eliason, D.E., Mirin, A.A., Zhou, Y., Porter, D.H. & Woodward, P.R. (2002). Three-dimensional simulation of a RM instability with two-scale initial perturbation. Phys. Fluids 14, 3692–3709.CrossRefGoogle Scholar
Craford, J.D. (1991). Introduction to bifurcation theory. Rev. Mod. Phys. 63, 991–1035.CrossRefGoogle Scholar
Dimotakis, P.E. (2000). The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Kartoon, D., Oron, D., Arazi, I. & Shvartz, D. (2003). Three-dimensional Rayleigh-Taylor and Richrmyer–Meskhow instabilities at all density ratios. Laser Part. Beams 21, 327–334.Google Scholar
Leighton, T.G., Walton, A.J. & Pickworth, M.J.W. (1990). Primary Bjerknes forces. Eur. J. Phys. 11, 47–50.CrossRefGoogle Scholar
Leinov, E., Malamud, G., Elbaz, Y., Levin, L.A., Ben-Dor, G., Shvarts, D. & Sadot, O. (2009). Experimental and numerical investigation of the RM instability under re-shock conditions. J. Fluid Mech. 626, 449–475.CrossRefGoogle Scholar
Long, C.C., Krivets, V.V., Greenough, J.A. & Jacobs, J.W. (2009). Shock tube 3D-experiments and numerical simulation of the single-mode, 3D RM instability. Phys. Fluids 21, 114104.CrossRefGoogle Scholar
Lugomer, S. (2016). Laser generated Richtmyer–Meshkov instability and nonlinear wave paradigm in turbulent mixing. I. Central region of Gaussian spot. Laser Part. Beams 34, 687–704.CrossRefGoogle Scholar
Lugomer, S. (2017). Laser generated Richtmyer–Meshkov instability and nonlinear wave paradigm in turbulent mixing. II. Near-central region of Gaussian spot. Laser Part. Beams 35, 210–225.CrossRefGoogle Scholar
Ma, Q.I., Motto-Ros, V., Boueri, M., Bai, X.S., Zheng, L.J., Zheng, H.P. & Yu, J. (2010). Temporal and spatial dynamics of laser-induced Al plasma in Ar background at atmospheric pressure: Interplay with the ambient gas. Spectrocim. Acta B 65, 896–907.CrossRefGoogle Scholar
Meshkov, E.E. (1969). Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.Google Scholar
Mikelian, K.O. (1989). Turbulent mixing generated by RT and RM instabilities. Physica D 36, 343–347.CrossRefGoogle Scholar
Miles, A.R., Blue, B., Edwards, M.J., Greenough, J.A., Hansen, F., Robey, H., Drake, R.P., Kuranz, C. & Leibrandt, R. (2005). Transition to turbulence and effect of initial conditions on 3D compressible mixing in planar blast-wave-driven systems. Phys. Plasmas 12, 056317.CrossRefGoogle Scholar
Pandian, A., Stellingwerf, R.F. & Abarzhi, S.I. (2017). Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows. Phys. Fluids 2, 073903.CrossRefGoogle Scholar
Probyn, M. & Thornber, B. (2013). Reshock of self-similar multimode RMI at high Atwood number in heavy-light and light-heavy configurations. 14th European Turbulence Conf., Lyon, France. etc14.ens-lyon.fr/openconf//request.php? Google Scholar
Reckinger, S. (2006). Development and applications of important interfacial Instabilities Rayleigh-Taylor, Rchtmyer–Meskhov, and Kelvin–Helmholtz, sales.colorado.edu/reckinger/Pubs/a1_fluids.pdf Google Scholar
Richtmyer, R.D. (1960). Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math 13, 297–319.Google Scholar
Shvarts, D., Sadot, O., Oron, D., Kishony, R., Srebro, Y., Rikanati, A., Kartoon, D., Yedvab, Y., Elbaz, Y., Yosef-Hai, A., Alon, U., Levin, L.A., Sarid, E., Arazi, L. & Ben-Dor, G. (2001). Studies in the Evolution of Hydrodynamic Instabilities and their Role in Inertial Confinement Fusion, IAEA, IF/7. www-pub.iaea.org/mtcd/publications/pdf/csp_008c/html/node263.htm Google Scholar
Srebro, Y., Elbaz, Y., Sadot, O., Arazi, L. & Shvarts, D. (2003). A general buoyancy-drag model for the evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Laser Part. Beams 21, 347–353.CrossRefGoogle Scholar
Statsenko, V.P., Sin'kova, O.G. & Yanilkin, Y.V. (2006). Direct 3D numerical simulation of turbulent mixing in a buoyant jet (in Russian). VANT Ser. MMFP 1, 39–49.Google Scholar
Statsenko, V.P., Yanilkin, Y., Sin'kova, O.G. & Toporova, O.O. (2014). Numerical modeling of development of regular local perturbations and turbulent mixing for the shock waves of various intenisties. (in Russian). VANT ser. Math. Model. Phys. Process. 1, 3–17.Google Scholar
Stellingwerf, R., Pandian, A. & Abarzhi, S.I. (2016 a). Wave interference in Richtmyer–Meshkov flows. 69th Annual Meeting of the APS Division of Fluid Dynamics, November 20–22, 2016; Portland, Oregon, Vol. 61, Number 20. http://meetings.aps.org/Meeting/DFD16/Session/R18.6 Google Scholar
Stellingwerf, R., Pandian, A. & Abarzhi, S.I. (2016 b). Wave interference in Richtmyer–Meshkov flows. 58th Annual Meeting of the APS Division of Fluid Dynamics, October 31–November 4, 2016; San Jose, California, Vol. 61, http://meetings.aps.org/Meeting/DPP16/Session/YP10.52 Google Scholar
Suponitsky, V., Barsky, S. & Froese, A. (2014). On the collapse of a gas cavity by an imploding molten lead shell and Richtmyer–Meshkov instability. Comput. Fluids 89.20, 1–19. Science Direct. Web. 17 May 2014CrossRefGoogle Scholar
Suponitsky, V., Froese, A. & Barsky, S. (2013). A parametric study examining the effects of re-shock in RMI. Soft Condens. Matter 2013, 1–43. Arxiv. Web. 17 May 2014.Google Scholar
Ukai, S., Balakrishnan, K. & Menon, S. (2011). Growth rate predictions of single- and multi-mode RM instability with reshock. Shock Waves 21, 533–546.CrossRefGoogle Scholar
Unverdi, S.O. & Trygvason, G. (1992). A front-tracking method for viscous, incmpressible multi-fluid flows. J. Comput. Phys. 100, 25–37.CrossRefGoogle Scholar
Wouchuk, J.G. & Nishihara, K. (1996). Linear growth at a shocked interface. Phys. Plasmas 3, 3761–3776.Google Scholar
Yang, X., Zabusky, N.J. & Chern, I.L. (1990). Breakthrought via dipolar-vortx formation in shock-accelerated density-stratified layers. Phys. Fluids A2, 892–895.Google Scholar
Youngs, D.I. (2013). The density ratio dependence of self-similar Rayleigh–Taylor mixing. Philos. Transact. R. Soc. A 371, 20120173.Google Scholar
Zabusky, N.J. (1999). Vortex paradigm for accelerated inhomogeneous flows: Visiometrics for the RT and RM environments. Ann. Rev. Fluid Dyn. 31, 495–536.Google Scholar
Zhang, Q. (1998). Analytical solutions of Lazer-type approach to unstable interfacial fluid mixing. Phys. Rev. Lett. 81, 3391–3394.Google Scholar