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Laser generated Richtmyer–Meshkov instability and nonlinear wave paradigm in turbulent mixing: I. Central region of Gaussian spot

Published online by Cambridge University Press:  17 October 2016

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: Stjepan Lugomer, Rudjer Boskovic Institute, Center of Excellence for Advanced Materials and Sensing Devices, Bijenicka c. 54, 10000 Zagreb, Croatia. E-mail: [email protected]
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Abstract

A three-dimensional Richtmyer–Meshkov instability (RMI) was generated on metal target by the laser pulse of Gaussian-like power profile in the semiconfined configuration (SCC). The SCC enables the extended lifetime of a hot vapor/plasma plume above the target surface as well as the fast multiple reshocks. The oscillatory pressure field of the reshocks causes strong bubble shape oscillations giving rise to the complex wave-vortex phenomena. The irregularity of the pressure field causes distortion of the shock wave front observed as deformed waves. In a random flow field the waves solidified around the bubbles form the broken “egg-karton” structure – or the large-scale chaotic web. In the coherent flow field the shape oscillations and collapse of the large bubbles generate nonlinear waves as the line- and the horseshoe-solitons. The line solitons are organized into a polygonal web, while the horseshoe solitons make either the rosette-like web or appear as the individual parabolic-like solitons. The configurations of the line solitons are juxtapositioned with solitons simulated by the Kadomtsev–Petviashvili (KP) equation. For the horseshoe solitons it was mentioned that it can be obtained by the simulation based on the cylindrical KP equation. The line and the horseshoe solitons represent the wave-vortex phenomena in which the fluid accelerated by the shock and exposed to a subsequent series of fast reshocks follows more complex scenario than in the open configuration. The RMI environment in the SCC generates complex fluid dynamics and the new paradigm of wave vortex phenomena in turbulent mixing.

Keywords

Horseshoe solitonsJet-spike breakupKadomtsev–Petviashvili equationLaser ablationLine solitonsRichtmyer–Meshkov instabilityTurbulent mixingWave-vortex phenomena
Type
Research Article
Information
Laser and Particle Beams , Volume 34 , Issue 4 , December 2016 , pp. 687 - 704
Copyright
Copyright © Cambridge University Press 2016 

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References

REFERENCES

Abarzhi, S.I. (1998). Stable steady flows in RT instability. Phys. Rev. Lett. 81, 337–340.Google Scholar
Abarzhi, S.I. (2008). Coherent structures and pattern formation in Rayleigh-Taylor turbulent mixing. Phys. Scripta 78(1–9), 015401.Google Scholar
Abarzhi, S.I. (2010). Review of theoretical modeling approaches of Rayleigh-Taylor instabilities and turbulent mixing. Philos Trans. R. Soc. A 368, 1809–1828.CrossRefGoogle ScholarPubMed
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
Ablowitz, M.J. & and Clarkson, P.A. (1992). Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge: Cambridge Univ. Press.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
Andreae, A., Ballman, J., Muller, S., Vos, A. (2003). Dynamics of Collapsing Bubbles near walls. http://www.igpm.rwth-aachen.de/Download/reports/pdf/IGPM220.pdf Google Scholar
Berger, K.M. & Milewski, P.A. (2000). The generation and evolution of lump solitary waves in surface-tension-dominated flows. SIAM J. Appl. Math. 61, 731–750.Google Scholar
Biondini, G. (2007). Line soliton interactions of the Kadomtsev-Petviashvili equation. Phys. Rev. Lett. 99(1–4), 064103.Google Scholar
Biondini, G. & Kodama, Y. (2003). On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy. J. Phys. A: Math. Gen. 36(1–), 1051910536.Google Scholar
Brujan, E.A., Vogel, A. & Blake, J.R. (2002). The final stage of the collapse of a cavitation bubble close to a rigid boundary. Phys. Fluids 14, 85–92.Google Scholar
Chakravarty, S. & Kodama, Y. (2008). Classification of the line-soliton solutions of KPII. J. Phys. A: Math. Theor. 41(1–30), 275209.Google Scholar
Chakravarty, S., Lewkow, T. & Maruno, K.-I. (2010). On the construction of the KP line-solitons and their interactions. Appl. Analysis 89, 529–545.Google Scholar
Chakravarty, S., Maruno, K.-I., Oikawa, M. & Tsuji, H. (2009). Soliton interactions ofb the Kadomtsev-Petviashvili equation and generation of large-amplitude water waves. Studies Appl. Math. 122, 377–394.Google 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.Google Scholar
Ionin, A., Kudryashov, S.I. & Seleznev, L.V. (2010). Near-critical phase explosion promoting breakdown plasma ignition during laser ablation of graphite. Phys. Rev. E 82(1–9), 016404.Google Scholar
Johnsen, E. & Colonius, T. (2009). Numerical simulations of non-spherical bubble collapse. J. Fluid. Mech. 629, 231–262.Google Scholar
Kartoon, D., Oron, D., Arazi, L., Rikanti, A., Sadot, O., Yosef-Hai, A., Alon, U., Ben-Dor, G. & Svarts, D. (2001). Three-dimensional multi-mode RT and RM instabilities at all density ratios, http://www.damp.cam.ac.uk Google Scholar
Khusnutdinova, K.R., Klein, C., Matveev, V.B. & Smirnov, A.O. (2013). On the elliptic cylindrical Kadomtsev-Petviashvili equation. Chaos 23(1–14), 013126.Google Scholar
Kim, T.-H. & Kim, H.-Y. (2014). Disruptive bubble behavior leding to microstructure danmage in an ultrasonic filed. J. Fluid Mech. 750, 355–371.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.Google Scholar
Lauterborn, W. & Kurz, T. (2010). Physics of bubble oscillations. Rep. Prog. Phys. 73(1–88), 106501.Google Scholar
Lazer, D. (1955). On the instability of superposed fluids in a gravitational filed. Astrophys. J. 122, 1–12.Google Scholar
Lee, H.C., Vuillon, J., Zeituon, D., Marine, W., Sentis, M. & Dreyfus, R.W. (1996). 2D modeling of laser-induced plume expansion near the plasma ignition threshold). Appl. Surf. Sci. 96–98, 76–81.Google Scholar
Leighton, T.G. (1994). The Acoustic Bubble. London: Acad. Press.Google Scholar
Leighton, T.G., Walton, A.J. & Pickworth, M.J.W. (1990). Primary Bjerknes forces. Eur. J. Phys. 11, 47–50.Google Scholar
Li, J., Zhang, H.-Q., Xu, T., Zhang, Ya.-X., Hu, W. & Tian, B. (2007). Symbolic computation on the multi-soliton-like solutions of the Cylindric Kadomtsev-Petviashvili equation from dusty plasmas. J. hys. A: Math. Theor. 40, 7643–7657.Google Scholar
Lim, K.Y., Quinto-su, P.A., Klaseboer, E., Khoo, B.C., Venugopalan, V. & Ohl, C.D. (2010). Nonspherical laser-induced cavitation bubbles. Phys. Rev. E 81(1–9), 016308.Google Scholar
Lugomer, S. (2007). Micro-fluid dynamics via laser-matter interactions: Vortex filament structures, helical instability, reconnection, merging, and undulation. Phys. Lett. A 361, 87–97.Google Scholar
Lugomer, S. (2016). Laser-Matter interactions: Inhomogeneous Richtmyer- Meshkov and Rayleigh-Taylor Instabilities. Laser Part. Beams 34, 123–136.Google Scholar
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
Lugomer, S., Maksimovic, A., Karacs, A. & Toth, L.A. (2009). Nano- structuring of silicon surface by laser redeposition of Si vapor. J. Appl. Phys. 106(1–14), 114309.Google Scholar
Matsuoka, C., Nishihara, K. & Fukuda, Y. (2003). Nonlinear evolution of an interface in the Richtmyer-Meshkow instability. Phys. Rev. E 67(1–14), 036301.Google Scholar
Meshkov, E.E. (1969). Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104.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(1–10), 056317.Google Scholar
Nevmerzhitsky, N.V. (2013). Some peculiarities of turbulent mixing growth and perturbations at hydrodynamic instabilities. Phylos. Trans. R. Soc. A 371(1–13), 2012091.Google Scholar
Nishihara, K., Ishizaki, R., Wouchuk, J.G., Fukuda, Y. & Shimuta, Y. (1998). Hydrodynamic perturbation growth in start-up phase in laser implosion. Phys. Plasmas 5, 1945–1952.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
Ong, C.T., King, T.W., Bin Mohhamad, M.N., Abd Aziz, Z.B. & Kamis, I. (2005). KP Nonlinear Waves Identification, Final Report RMC Research VOT 75023, Dept. of Math, Faculty of Science, University of Technology, Skudai, Malaysia.Google Scholar
Ong, C.T. & Tiong, W.K. Solitons interactions of two triads of the KP equation. http://www.ims.nus.edu.sg/Programs/ocean07/files/ongct,pdf Google Scholar
Osborne, A.R. (1994). Shallow water cnoidal wave interactions, Nonlinear Processes in Geophysics, Copernicus Publishers: Bahnhofsalle 1e, 37081 Gotingen, Germany.Google Scholar
Peng, G., Zabusky, N.J. & Zhang, S. (2003). Jet and vortex flows in a shock hemispherical bubble-on-wall configuration. Laser Part. Beams 21, 449–453.Google Scholar
Prestridge, K., Orlicz, G., Balasubramanian, S. & Balakumar, B.J. (2013). Experiments in the RM instability. Phil. Trans. R. Soc. A 371(1–9), 20120165.Google Scholar
Probyn, M. & Thornber, B. (2013). Reshock of self-similar multimode RMI at high Atwood number in heavy-light and light-heavy configurations. 14th Eu. 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
Shimamura, K., Michigami, K., Wang, B. & Komurasaki, K. (2011). 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida. (p. 1–8).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. http://www-pub.iaea.org/mtcd/publications/pdf/csp_008c/html/node263.htm 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
Smalyuk, V.A., Sadot, O., Betti, R., Goncharov, V.N., Delettrez, J.A., Meyerhofer, D.D., Regan, S.P., Sangster, T.C. & Shavrts, D. (2006). Rayleigh-Taylor grwoth measurements of three-dimensional modulations in a nonlinear regime. Phys. Plasmas 13(1–7), 056312.Google Scholar
Statsenko, V.P., Sin'kova, O.G. & Yanilkin, Yu.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, Yu., 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
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 2014.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
Vogel, A., Bush, S. & Parlitz, U. (1996). Shock wave emission and cavitation bubble generation by picosecond and nanosecond optical breakdown in water. J. Acoust. Soc. Am. 100, 148–165.Google Scholar
Wouchuk, J.G. & Nishihara, K. (1996). Linear growth at a shocked interface. Phys. Plasmas 3, 3761–3776.Google Scholar
Wu, P.K., Miranda, R.F. & Faeth, G.M. (1994). Effects of initial flow conditions on primary breakup on nonturbulent and turbulent liquid jets, AIAA, 94–561, Aerospace Sci. Meeting, 32 Reno, NV. http://hdl.handle.net/202742/77013 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
Zabusky, N.J., Lugomer, S. & Zhang, S. (2005). Micro-fluid dynamics via laser metal surface interactions: Wave-vortex interpretation of emerging multiscale coherent structurres. Fluid Dyn. Res. 36, 291–299.Google Scholar
Zhang, S. & Duncan, J.H. (1994). The behavior of a cavitation bubble near a rigid wall. In Bubble Dynamics and Interface Phenomena, (Blake, J. et al. , Eds.), pp. 429–436. Dordrecht, the Netherlands: Kluwer Academic Publishers.Google Scholar
Zhang, S. & Zabusky, N.J. (2003). Shock-planar curtain interactions: Strong secondary baroclinic deposition and emergence of vortex projectiles and late-time inhomogeneous turbulence. Laser Part. Beams 21, 463–470.Google Scholar
Zhang, S., Zabusky, N.J. & Nishihara, K. (2003). Vortex structures and turbulence emerging in a supernova 1987 configuration: Interactions of “complex” blast waves and cylindrical/spherical bubbles. Laser Part. Beams 21, 471–477.Google Scholar
Yang, X., Zabusky, N.J. & Chern, Li.I. (1990). Breakthrought via dipolar-vortx formation in shock-accelerated density-stratified layers. Phys. Fluids A2, 892–895.Google Scholar
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