Abstract
The Richtmyer-Meshkov instability (RMI) occurs when an initially perturbed density interface between two different fluids is impulsively accelerated [1, 2]. As a planar incident shock impacts a perturbed interface, the interface is accelerated and compressed at the initial stage, baroclinic vorticity is generated due to the misalignment between the pressure gradient across the shock and density gradient at the interface. The perturbation of the interface is expected to grow linearly with time in the early stage, while in the late stage, the growth of the perturbation amplitude becomes nonlinear with spikes and bubbles of the interface evolving asymmetrically, as well as the emergence of Kelvin-Helmholtz instabilities. The RMI has been attractive during the past decades to researchers owing to its significant applications in the fields such as inertial confinement fusion [3], supernova explosions [4], and supersonic combustion [5].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Richtmyer, R.D.: Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319 (1960)
Meshkov, E.E.: Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104 (1969)
Lindl, D.L., McCrory, R.L., Campbell, E.M.: Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today 45, 32–40 (1992)
Arnett, W.D., Bahcall, J.N., Kirshner, R.P., Woosley, S.E.: Supernova 1987{A}. Annu. Rev. Astron. Astrophys. 27, 629–700 (1989)
Marble, F., Hendricks, G., Zukoski, E.: Progress toward shock enhancement of supersonic combustion processes. 23rd AIAA, SAE, ASME, and ASEE, Joint Propulsion Conference, San Diego, CA, June 29–July 2 1987 (American Institute of Aeronautics and Astronautics, New York, 1987). 1–8, (2004)
Ranjan, D., Oakley, J., Bonazza, R.: Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140 (2011)
Zhang, Q., Sohn, S.I.: Quantitative theory of Richtmyer-Meshkov instability in three dimensions. Z. Angew. Math. Phys. 50, 1–46 (1999)
Yosef-Hai, A., Sadot, O., Kartoon, D., Oron, D., Levin, L.A., Sarid, E., Elbaz, Y., Ben-Dor, G., Shvarts, D.: Late-time growth of the Richtmyer-Meshkov instability for different Atwood numbers and different dimensionalities. Laser Part. Beams 21, 363–368 (2003)
Chapman, P.R., Jacobs, J.W.: Experiments on the three-dimensional incompressible Richtmyer-Meshkov instability. Phys. Fluids 18, 074101 (2006)
Leinov, E., Malamud, G., Elbaz, Y., Levin, L.A., Ben-Dor, G., Shvarts, D., Sadot, O.: Experimental and numerical investigation of the Richtmyer-Meshkov instability under re-shock conditions. J. Fluid Mech. 626, 449–475 (2009)
Long, C.C., Krivets, V.V., Greenough, J.A., Jacobs, J.W.: Shock tube experiments and numerical simulation of the single-mode. Three-dimensional Richtmyer-Meshkov instability. Phys. Fluids 21, 114104 (2009)
Luo, X., Wang, X., Si, T.: The Richtmyer-Meshkov instability of a three-dimensional air/SF6 interface with a minimum-surface feature. J. Fluid Mech. 722, R2 (2013)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)
Wang, C.W., Liu, T.G., Khoo, B.C.: A real ghost fluid method for the simulation of multimedium compressible flow. SIAM J. Sci. Comput. 28, 278–302 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Guan, B., Luo, X. (2017). On the Richtmyer-Meshkov Instability of a Three-Dimensional Single-Mode Interface: Effect of Initial Interfacial Principal Curvatures. In: Ben-Dor, G., Sadot, O., Igra, O. (eds) 30th International Symposium on Shock Waves 2. Springer, Cham. https://doi.org/10.1007/978-3-319-44866-4_55
Download citation
DOI: https://doi.org/10.1007/978-3-319-44866-4_55
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44864-0
Online ISBN: 978-3-319-44866-4
eBook Packages: EngineeringEngineering (R0)