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Bubble re-acceleration behaviours in compressible Rayleigh–Taylor instability with isothermal stratification

Published online by Cambridge University Press:  03 January 2023

Cheng-Quan Fu Open the ORCID record for Cheng-Quan Fu [Opens in a new window] ,
Zhiye Zhao Open the ORCID record for Zhiye Zhao [Opens in a new window] ,
Pei Wang ,
Nan-Sheng Liu Open the ORCID record for Nan-Sheng Liu [Opens in a new window] ,
Zhen-Hua Wan Open the ORCID record for Zhen-Hua Wan [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Cheng-Quan Fu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Zhiye Zhao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Pei Wang
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China
Nan-Sheng Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Zhen-Hua Wan
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email address for correspondence: zzy12@ustc.edu.cn
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Abstract

The highly nonlinear evolution of the single-mode stratified compressible Rayleigh–Taylor instability (RTI) is investigated via direct numerical simulation over a range of Atwood numbers ($A_T=0.1$–$0.9$) and Mach numbers ($Ma=0.1$–$0.7$) for characterising the isothermal background stratification. After the potential stage, it is found that the bubble is accelerated to a velocity which is well above the saturation value predicted in the potential flow model. Unlike the bubble re-acceleration behaviour in quasi-incompressible RTI with uniform background density, the characteristics in the stratified compressible RTI are driven by not only vorticity accumulation inside the bubble but also flow compressibility resulting from the stratification. Specifically, in the case of strong stratification and high $A_T$, the flow compressibility dominates the bubble re-acceleration characters. To model the effect of flow compressibility, we propose a novel model to reliably describe the bubble re-acceleration behaviours in the stratified compressible RTI, via introducing the dilatation into the classical model that takes into account only vorticity accumulation.

JFM classification

Convection: Buoyancy-driven instability

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A16
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© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Banerjee, R., Mandal, L., Roy, S., Khan, M. & Gupta, M.R. 2011 Combined effect of viscosity and vorticity on single mode Rayleigh–Taylor instability bubble growth. Phys. Plasmas 18, 022109.10.1063/1.3555523CrossRefGoogle Scholar
Betti, R. & Sanz, J. 2006 Bubble acceleration in the ablative Rayleigh–Taylor instability. Phys. Rev. Lett. 97, 205002.10.1103/PhysRevLett.97.205002CrossRefGoogle ScholarPubMed
Bian, X., Aluie, H., Zhao, D.-X., Zhang, H. & Livescu, D. 2020 Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity. Physica D 403, 132250.10.1016/j.physd.2019.132250CrossRefGoogle Scholar
Burrows, A. 2000 Supernova explosions in the universe. Nature 403, 727–733.10.1038/35001501CrossRefGoogle ScholarPubMed
Cabot, W.H. & Cook, A.W. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae. Nat. Phys. 2, 562–568.10.1038/nphys361CrossRefGoogle Scholar
Fu, C.-Q., Zhao, Z.-Y., Xu, X., Wang, P., Liu, N.-S., Wan, Z.-H. & Lu, X.-Y. 2022 Nonlinear saturation of bubble evolution in a two-dimensional single-mode stratified compressible Rayleigh–Taylor instability. Phys. Rev. Fluids 7, 023902.10.1103/PhysRevFluids.7.023902CrossRefGoogle Scholar
Goncharov, V.N. 2002 Analytical model of nonlinear, single-mode, classical Rayleigh–Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett. 88, 134502.10.1103/PhysRevLett.88.134502CrossRefGoogle ScholarPubMed
Houseman, G.A. & Molnar, P. 1997 Gravitational (Rayleigh–Taylor) instability of a layer with non-linear viscosity and convective thinning of continental lithosphere. Geophys. J. Intl 128, 125–150.10.1111/j.1365-246X.1997.tb04075.xCrossRefGoogle Scholar
Hu, Z.-X., Zhang, Y.-S. & Tian, B.-L. 2020 Evolution of Rayleigh–Taylor instability under interface discontinuous acceleration induced by radiation. Phys. Rev. E 101, 043115.10.1103/PhysRevE.101.043115CrossRefGoogle ScholarPubMed
Hu, Z.-X., Zhang, Y.-S., Tian, B.-L., He, Z.-W. & Li, L. 2019 Effect of viscosity on two-dimensional single-mode Rayleigh–Taylor instability during and after the reacceleration stage. Phys. Fluids 31, 104108.Google Scholar
Layzer, D. 1955 On the instability of superposed fluids in a gravitational field. Astrophys. J. 122, 1–12.10.1086/146048CrossRefGoogle Scholar
Li, H.-F., He, Z.-W., Zhang, Y.-S. & Tian, B.-L. 2019 On the role of rarefaction/compression waves in Richtmyer–Meshkov instability with reshock. Phys. Fluids 31, 054102.Google Scholar
Livescu, D. 2004 Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids. Phys. Fluids 16, 118–127.10.1063/1.1630800CrossRefGoogle Scholar
Luo, T.-F. & Wang, J.-C. 2021 Effects of Atwood number and stratification parameter on compressible multi-mode Rayleigh–Taylor instability. Phys. Fluids 33, 115111.10.1063/5.0071437CrossRefGoogle Scholar
Luo, T.-F., Wang, J.-C., Xie, C.-Y., Wan, M.-P. & Chen, S.-Y. 2020 Effects of compressibility and Atwood number on the single-mode Rayleigh–Taylor instability. Phys. Fluids 32, 012110.Google Scholar
Ramaprabhu, P., Dimonte, G., Woodward, P., Fryer, C., Rockefeller, G., Muthuraman, K., Lin, P.H. & Jayaraj, J. 2012 The late-time dynamics of the single-mode Rayleigh–Taylor instability. Phys. Fluids 24, 074107.10.1063/1.4733396CrossRefGoogle Scholar
Ramaprabhu, P., Dimonte, G., Young, Y.N., Calder, A.C. & Fryxell, B. 2006 Limits of the potential flow approach to the single-mode Rayleigh–Taylor problem. Phys. Rev. E 74, 066308.10.1103/PhysRevE.74.066308CrossRefGoogle Scholar
Rayleigh, Lord 1882 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. R. Math. Soc. s1-14, 170–177.10.1112/plms/s1-14.1.170CrossRefGoogle Scholar
Reckinger, S.J., Livescu, D. & Vasilyev, O.V. 2012 Simulations of compressible Rayleigh–Taylor instability using the adaptive wavelet collocation method. In Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii.Google Scholar
Reckinger, S.J., Livescu, D. & Vasilyev, O.V. 2016 Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh–Taylor instability. J. Comput. Phys. 313, 181–208.10.1016/j.jcp.2015.11.002CrossRefGoogle Scholar
Swisher, N.C., Kuranz, C.C., Arnett, D., Hurricane, O., Remington, B.A., Robey, H.F. & Abarzhi, S.I. 2015 Rayleigh–Taylor mixing in supernova experiments. Phys. Plasmas 22, 102707.10.1063/1.4931927CrossRefGoogle Scholar
Taylor, G.I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201, 192–196.Google Scholar
Wang, J.C., Yang, Y.T., Shi, Y.P., Xiao, Z.L., He, X.T. & Chen, S.Y. 2013 Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505.10.1103/PhysRevLett.110.214505CrossRefGoogle ScholarPubMed
Wei, T. & Livescu, D. 2012 Late-time quadratic growth in single-mode Rayleigh–Taylor instability. Phys. Rev. E 86, 046405.10.1103/PhysRevE.86.046405CrossRefGoogle ScholarPubMed
Wieland, S.A., Hamlington, P.E., Reckinger, S.J. & Livescu, D. 2019 Effects of isothermal stratification strength on vorticity dynamics for single-mode compressible Rayleigh–Taylor instability. Phys. Rev. Fluids 4, 093905.10.1103/PhysRevFluids.4.093905CrossRefGoogle Scholar
Wilcock, W.S.D. & Whitehead, J.A. 1991 The Rayleigh–Taylor instability of an embedded layer of low-viscosity fluid. J. Fluid Mech. 96, 12193–12200.Google Scholar
Wilkinson, J.P. & Jacobs, J.W. 2007 Experimental study of the single-mode three-dimensional Rayleigh–Taylor instability. Phys. Fluids 19, 124102.10.1063/1.2813548CrossRefGoogle Scholar
Yan, R., Betti, R., Sanz, J., Aluie, H., Liu, B. & Frank, A. 2016 Three-dimensional single-mode nonlinear ablative Rayleigh–Taylor instability. Phys. Plasmas 23, 022701.10.1063/1.4940917CrossRefGoogle Scholar
Zhang, H., Betti, R., Yan, R. & Aluie, H. 2020 Nonlinear bubble competition of the multimode ablative Rayleigh–Taylor instability and applications to inertial confinement fusion. Phys. Plasmas 27, 122701.10.1063/5.0023541CrossRefGoogle Scholar
Zhao, D.-X., Betti, R. & Aluie, H. 2022 Scale interactions and anisotropy in Rayleigh–Taylor turbulence. J. Fluid Mech. 930, A29.10.1017/jfm.2021.902CrossRefGoogle Scholar
Zhao, Z.-Y., Liu, N.-S. & Lu, X.-Y. 2020 a Kinetic energy and enstrophy transfer in compressible Rayleigh–Taylor turbulence. J. Fluid Mech. 904, A37.10.1017/jfm.2020.700CrossRefGoogle Scholar
Zhao, Z.-Y., Wang, P., Liu, N.-S. & Lu, X.-Y. 2020 b Analytical model of nonlinear evolution of single-mode Rayleigh–Taylor instability in cylindrical geometry. J. Fluid Mech. 900, A24.10.1017/jfm.2020.526CrossRefGoogle Scholar
Zhao, Z.-Y., Wang, P., Liu, N.-S. & Lu, X.-Y. 2021 Scaling law of mixing layer in cylindrical Rayleigh–Taylor turbulence. Phys. Rev. E 104 (5), 055104.10.1103/PhysRevE.104.055104CrossRefGoogle ScholarPubMed
Zhou, Y. 2017 Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Phys. Rep. 720, 1–136.Google Scholar