Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T17:35:02.531Z Has data issue: false hasContentIssue false
  • English
  • Français

Laser generated Richtmyer–Meshkov and Rayleigh–Taylor instabilities and nonlinear wave-vortex paradigm in turbulent mixing. II. Near-central region of Gaussian spot

Published online by Cambridge University Press:  23 February 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: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Laser-induced three-dimensional (3D) Richtmyer–Meshkov and Rayleigh–Taylor instabilities (RMI and RTI) on metal target in the semi-confined configuration (SCC) show the new paradigm of wave-vortex mixing. The SCC enables extended lifetime of a hot vapor/plasma plume above the target surface and the formation of fast multiple reshocks. This causes – in the central region (CR) of Gaussian-like spot – the evolution of RMI with the spike breakup (Lugomer, 2016b), while in the near CR causes the RMI followed by the RTI. The density interface is transformed into the large-scale broken irregular, quasi-periodic web, which comprises the RTI mushroom-shape spikes and the coherent wave-vortex structures such as the line solitons and vortex filaments. The intensity and direction of reshocks change (due to irregularity of the interface) and cause the formation of domains with the weak and the strong reshocks effects. The weak reshocks affect mushroom-shape spikes only slightly, while the strong ones cause their deformation and symmetry break, bubble collapse, and separation of the horizontal flow into vortex ribbons. Interaction of ribbons with spikes and bubbles causes the ribbon pinning, looping, winding, and formation of knotted and tangled structures. The line solitons, vortex filaments, and ribbons tend to organize into complex large-scale structures with the low wave-vortex turbulent mixing. They represent the new paradigm of 3D RMI and RTI in which the transition to the small-scale turbulent mixing does not appear.

Keywords

coherent structureslaser ablationRayleigh–Taylor instabilityRichtnyer–Meshkov instabilitysolitary wavesturbulent mixingvortex filamentswave-vortex phenomena
Type
Research Article
Information
Laser and Particle Beams , Volume 35 , Issue 2 , June 2017 , pp. 210 - 225
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. (2000). Regular and singularlate-timeasymptotes of potential motion of fluuid with afree boundary. Phys. Fluids 12, 3112–3120.CrossRefGoogle Scholar
Abarzhi, S.I. (2008). Review of nonlinear dynamics of the unstable fluid interface: Consrvation laws and group theory. Phys. Scr. T132, 014012 (1–18).CrossRefGoogle Scholar
Abarzhi, S.I. (2010). Review of theoretical modelling approaches of Rayleigh-Taylor instabilities and turbulent mixing. Phil. Trans. R. Soc. A 368, 1809–1828.Abarzhi, S.I. (2016). Private communication.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, (Young, R., Glimm, J. and Boston, B., eds.) World Scientific. 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.Google Scholar
Biondini, G. (2007). Line soliton interactions of the Kadomtsev–Petviashvili equation. Phys. Rev. Lett. 99, 064103 (1–4).Google Scholar
Blatter, G., Geshkenbein, V.B. & Koopmann, J.A.G. (2004). Weak to strong pinning crossover. Phys. Rev. Lett. 92, 067009–067013.Google Scholar
Calini, A.M. & Ivey, T. (2001). Knot types, Floquet spectra, and finite-gap solutions of the vortex filament equation. Math. Comput. Simul. 55, 341–250.Google Scholar
Chapman, P.R. & Jacobs, J.W. (2006). Experiments on the 3D incompressible R–M instability. Phys. Fluids 18, 074101 (1–12).CrossRefGoogle Scholar
Cohen, R.H., Dennevik, W.P., Dimits, A.M., Eliason, D.E., Mirin, A.A., Zhou, Ye., 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
Dimotakis, P.E. (2000). The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Fukumoto, Y. (1997). Stationary configurations of a vortex filament in background flows. Proc. R. Soc. Lond. A 453, 1205–1232.Google Scholar
He, X., Zhang, R., Chen, S. & Doolen, G.D. (1999). On the three-dimensional R–T instability. Phys. Fluids 11, 1143–1152.Google Scholar
Hua, J. & Lou, J. (2007). Numerical simulation of bubble rising in viscous liquid. J. Comput. Phys. 222, 769–795.Google Scholar
Ivy, T. (2005). Geometry and topology of finite-gap vortex filaments, in Seventh Int. Conf. on Geometry, Integrability and Quantification, June (2005). Varna, Bulgaria. SOFTEX, Sofia, p. 1–16. Editors, I.M. Miladinov and M. De Leon.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.CrossRefGoogle Scholar
Khusnutdinova, K.R., Klein, C., Matveev, V.B. & Smirnov, A.O. (2013). On the elliptic cylindrical Kadomtsev–Petviashvili equation. Chaos 23, 013126 (1–14).Google Scholar
Klein, C., Matveev, V.B. & Smirnov, A.O. (2007). Cylindrical Kadomtsev–Petviashvili equation: Old and new results. Theor. Math. Phys. 152, 1132–1144.Google Scholar
Kodama, Y. (2004). Young diagram and N-soliton solutions of the KP equation. J. Phys. A: Math. Gen. 37, 11169–11190.CrossRefGoogle Scholar
Koochesfahani, M.M. & Dimotakis, P.E. (1986). Mixing and chemical reactions in a turbulent liquid mixing layer. J. Fluid Mech. 170, 83–112.Google Scholar
Lazer, D. (1955). On the instability of superposed fluids in a gravitational filed. Astrophys. J. 122, 1–12.Google 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 (1–9).Google Scholar
Lugomer, S. (2016 a). Laser-matter interactions: Inhomogeneous Richtmyer–Meshkov and Rayleigh–Taylor instabilities. Laser Part. Beams 34, 123–135.Google Scholar
Lugomer, S. (2016 b). Laser generated Richtmyer–Meshkov and Rayleigh–Taylor instabilities and nonlinear wave paradigm in turbulent mixing. I. Central region of Gaussian spot. Laser Part. Beams 34, 687–704.CrossRefGoogle Scholar
Lugomer, S. & Fukumoto, Y. (2010). Generation of ribbons, helikoids, and complex Scherk surfacesin laser–matter interactions. Phys. Rev. E 81, 036311 (1–11).Google Scholar
Lugomer, S., Fukumoto, Y., Farkas, B., Szorenyi, T. & Toth, A. (2007). Supercomplex wave-vortex multiscale phenomena induced in laser–matter interactions. Phys. Rev. E 76, 1–15.CrossRefGoogle ScholarPubMed
Lugomer, S., Maksimovic, A., Geretovszky, Z. & Szorenyi, T. (2013). Nonlinear waves generated on liquid silicon layer by femtosecond laser pulses. Appl. Surf. Sci. 28, 588–600.Google 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 (1–10).CrossRefGoogle Scholar
Oikawa, M. & Tsuji, H. (2006). Oblique interactions of weakly nonlinear long waves in dispersive systems. Fluid Dyn. Res. 38, 868–898.Google Scholar
Pandian, A., Stellingwerf, R.E. & Abarzhi, S.I. (2016). Effect of wave interference on nonlinear dynamics of Richtmyer–Meshkov flows. Phys. Fluids accepted.Google Scholar
Pedrizzetti, G. (1992). Close interaction between a vortex filament and a rigid sphere. J. Fluid Mech. 245, 701–722.Google Scholar
Pazo, D., Kramer, L., Pumir, A., Kanani, S., Efimov, I. & Krinsky, V. (2004). Pinning force in active media. Phys. Rev. Lett. 93, 168303–168307.CrossRefGoogle ScholarPubMed
Schwarz, K.W. (1985). Three-dimensional vortex dynamics in superfluid He4: Line-line and line-boundary interactions. Phys. Rev. B 31, 5782.Google Scholar
Shu, S. & Yang, N. (2013). Direct numerical simulation of bubble dynamics using phase-field model and lattice Boltzmann method. Ind. Eng. Chem. Res. 52, 11391–11403.Google Scholar
Sin'kova, O.G., Statsenko, V.P. & Yanilkin, Yu. (2007). Numerical Study of the turbulent mixing development of the air-SF6 interface at the shock-wave propagation with large Mach numbers. (in Russian). VANT, Ser. TPF 2/3, 3–17.Google Scholar
Statsenko, V.P., Yanilkin, Yu. & Zmaylo, V.A. (2014). Direct numerical simulation of turbulent mixing. Philos. Trans. R. Soc. A 371, 20120216 (1–19).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, 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, 1–19.Google Scholar
Suponitsky, V., Froese, A. & Barsky, S. (2013). A parametric study examining the effects of re-shock in RMI. Soft Condensed Matter 2013, 1–43. Arxiv. Web. 17 May 2014.Google Scholar
Thomas, J.H., Weissl, N.O., Tobias, S.M. & Brummel, N.H. (2002). Downward pumping of magnetic flux as the cause of filamentary structures in sunspot penumbrae. Nature, London, 420, 390–393.CrossRefGoogle ScholarPubMed
Tonomura, A., Kasai, H., Kamimura, O., Matsuda, T., Harada, K., Nayakama, Y., Shimoyama, J., Kishio, K., Hanaguri, T., Kitazawa, K., Sasase, M. & Okayasu, S. (2001). Observation of individual vortices along columnar defects in high temperature superconductors. Nature, London, 412, 620–622.Google Scholar
Tsukruk, V.V., Ko, H. & Peleshanko, S. (2004). Nanotube surface arrays: Weaving, bending, and assembling on patterned silicon. Phys. Rev. Lett. 92, 065502–065506.Google Scholar
Unverdi, S.O. & Trygvason, G. (1992). A front-tracking method for viscous, incmpressible multi-fluid flows. J. Comput. Phys. 100, 25–37.Google Scholar
Zabusky, N.J., Lugomer, S. & Zhang, S. (2005). Micro-fluid dynamics via laser metal surface interactions: Wave-vortex interpretation of emerging multiscale coherent structures. Fluid Dyn. Res. 36, 291.Google Scholar
Zhang, Q. (1998). Analytical solutions of Lazer-type approach to unstable interfacial fluid mixing. Phys. Rev. Lett. 81, 3391–3394.Google Scholar
Zhang, Y.-T., Shu, C-W. & Zhou, Ye. (2006). Effects of shock waves on R–T instability. Phys. Plasmas 13, 062705 (1–13).Google Scholar
Zhou, Ye., Remington, B.A., Robey, H.F., Cook, A.W., Glendinning, S.G., Dimits, A., Buckingham, A.C., Zimmerman, G.B., Burke, E.W., Peyser, T.A., Cabot, W. & Eliason, D. (2003). Progress in understanding turbulent mixing induced by RT and RM instabilities. Phys. Plasmas 10, 1883–1896.CrossRefGoogle Scholar
Youngs, D.I. (2013). The density ratio dependence of self-similar Rayleigh–Taylor mixing. Philos. Trans. R. Soc. A 371, 20120173 (1–15).Google Scholar