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Title: Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability

Abstract

Weakly nonlinear (WN) Rayleigh-Taylor instability (RTI) initiated by single-mode cosinusoidal interface and velocity perturbations is investigated analytically up to the third order. Expressions of the temporal evolutions of the amplitudes of the first three harmonics are derived. It is shown that there are coupling between interface and velocity perturbations, which plays a prominent role in the WN growth. When the 'equivalent amplitude' of the initial velocity perturbation, which is normalized by its linear growth rate, is compared to the amplitude of the initial interface perturbation, the coupling between them dominates the WN growth of the RTI. Furthermore, the RTI would be mitigated by initiating a velocity perturbation with a relative phase shift against the interface perturbation. More specifically, when the phase shift between the interface perturbation and the velocity perturbation is {pi} and their equivalent amplitudes are equal, the RTI could be completely quenched. If the equivalent amplitude of the initial velocity perturbation is equal to the initial interface perturbation, the difference between the WN growth of the RTI initiated by only an interface perturbation and by only a velocity perturbation is found to be asymptotically negligible. The dependence of the WN growth on the Atwood numbers and the initialmore » perturbation amplitudes is discussed. In particular, we investigate the dependence of the saturation amplitude (time) of the fundamental mode on the Atwood numbers and the initial perturbation amplitudes. It is found that the Atwood numbers and the initial perturbation amplitudes play a crucial role in the WN growth of the RTI. Thus, it should be included in applications where the seeds of the RTI have velocity perturbations, such as inertial confinement fusion implosions and supernova explosions.« less

Authors:
; ;  [1];  [2]; ; ; ; ; ;  [3]
  1. HEDPS and CAPT, Peking University, Beijing 100871 (China)
  2. (China)
  3. Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China)
Publication Date:
OSTI Identifier:
22068899
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 19; Journal Issue: 11; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; DISTURBANCES; EXPLOSIONS; HARMONICS; IMPLOSIONS; INERTIAL CONFINEMENT; NONLINEAR PROBLEMS; PHASE SHIFT; RAYLEIGH-TAYLOR INSTABILITY; SUPERNOVAE; TIME DEPENDENCE; VELOCITY

Citation Formats

Wang, L. F., Ye, W. H., He, X. T., Institute of Applied Physics and Computational Mathematics, Beijing 100088, Wu, J. F., Fan, Z. F., Zhang, W. Y., Dai, Z. S., Gu, J. F., and Xue, C. Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability. United States: N. p., 2012. Web. doi:10.1063/1.4766165.
Wang, L. F., Ye, W. H., He, X. T., Institute of Applied Physics and Computational Mathematics, Beijing 100088, Wu, J. F., Fan, Z. F., Zhang, W. Y., Dai, Z. S., Gu, J. F., & Xue, C. Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability. United States. doi:10.1063/1.4766165.
Wang, L. F., Ye, W. H., He, X. T., Institute of Applied Physics and Computational Mathematics, Beijing 100088, Wu, J. F., Fan, Z. F., Zhang, W. Y., Dai, Z. S., Gu, J. F., and Xue, C. 2012. "Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability". United States. doi:10.1063/1.4766165.
@article{osti_22068899,
title = {Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability},
author = {Wang, L. F. and Ye, W. H. and He, X. T. and Institute of Applied Physics and Computational Mathematics, Beijing 100088 and Wu, J. F. and Fan, Z. F. and Zhang, W. Y. and Dai, Z. S. and Gu, J. F. and Xue, C.},
abstractNote = {Weakly nonlinear (WN) Rayleigh-Taylor instability (RTI) initiated by single-mode cosinusoidal interface and velocity perturbations is investigated analytically up to the third order. Expressions of the temporal evolutions of the amplitudes of the first three harmonics are derived. It is shown that there are coupling between interface and velocity perturbations, which plays a prominent role in the WN growth. When the 'equivalent amplitude' of the initial velocity perturbation, which is normalized by its linear growth rate, is compared to the amplitude of the initial interface perturbation, the coupling between them dominates the WN growth of the RTI. Furthermore, the RTI would be mitigated by initiating a velocity perturbation with a relative phase shift against the interface perturbation. More specifically, when the phase shift between the interface perturbation and the velocity perturbation is {pi} and their equivalent amplitudes are equal, the RTI could be completely quenched. If the equivalent amplitude of the initial velocity perturbation is equal to the initial interface perturbation, the difference between the WN growth of the RTI initiated by only an interface perturbation and by only a velocity perturbation is found to be asymptotically negligible. The dependence of the WN growth on the Atwood numbers and the initial perturbation amplitudes is discussed. In particular, we investigate the dependence of the saturation amplitude (time) of the fundamental mode on the Atwood numbers and the initial perturbation amplitudes. It is found that the Atwood numbers and the initial perturbation amplitudes play a crucial role in the WN growth of the RTI. Thus, it should be included in applications where the seeds of the RTI have velocity perturbations, such as inertial confinement fusion implosions and supernova explosions.},
doi = {10.1063/1.4766165},
journal = {Physics of Plasmas},
number = 11,
volume = 19,
place = {United States},
year = 2012,
month =
}
  • In this paper, the interface width effects (i.e., the density gradient effects or the density transition layer effects) on the Rayleigh-Taylor instability (RTI) in the weakly nonlinear (WN) regime are investigated by numerical simulation (NS). It is found that the interface width effects dramatically influence the linear growth rate in the linear growth regime and the mode coupling process in the WN growth regime. First, the interface width effects decrease the linear growth rate of the RTI, particularly for the short perturbation wavelengths. Second, the interface width effects suppress (reduce) the third-order feedback to the fundamental mode, which induces themore » nonlinear saturation amplitude (NSA) to exceed the classical prediction, 0.1lambda. The wider the density transition layer is, the larger the NSA is. The NSA in our NS can reach a half of its perturbation wavelength. Finally, the interface width effects suppress the generation and the growth of the second and the third harmonics. The ability to suppress the harmonics' growth increases with the interface width but decreases with the perturbation wavelength. On the whole, in the WN regime, the interface width effects stabilize the RTI, except for an enhancement of the NSA, which is expected to improve the understanding of the formation mechanism for the astrophysical jets, and for the jetlike long spikes in the high energy density physics.« less
  • Understanding the Rayleigh--Taylor instability, which develops at an interface where a low density fluid pushes and accelerates a higher density fluid, is important to the design, analysis, and ultimate performance of inertial confinement fusion targets. Existing experimental results measuring the growth of two-dimensional (2-D) perturbations (perturbations translationally invariant in one transverse direction) are adequately modeled using the 2-D hydrodynamic code LASNEX [G. B. Zimmerman and W. L. Kruer, Comments Plasma Phys. Controlled Fusion {bold 11}, 51 (1975)]. However, of ultimate interest is the growth of three-dimensional (3-D) perturbations such as those initiated by surface imperfections or illumination nonuniformities. Direct simulationmore » of such 3-D experiments with all the significant physical processes included and with sufficient resolution is very difficult. This paper addresses how such experiments might be modeled. A model is considered that couples 2-D linear regime hydrodynamic code results with an analytic model to allow modeling of 3-D Rayleigh--Taylor growth through the linear regime and into the weakly nonlinear regime. The model is evaluated in 2-D by comparison with LASNEX results. Finally the model is applied to estimate the dynamics of a hypothetical 3-D foil.« less
  • Weakly nonlinear stage of the ablative Rayleigh-Taylor instability has been studied by perturbation theory. Mode coupling of linear growing waves with wavenumbers {ital k}{sub {ital A}} and {ital k}{sub {ital B}} drives new excited waves with wavenumbers {ital k}{sub 0}(={ital k}{sub {ital A}}{plus_minus}{ital k}{sub {ital B}},2{ital k}{sub {ital A}},2{ital k}{sub {ital B}}). We have investigated time evolution of the excited waves and found that the ablation effect plays an important role even in nonlinear stage to reduce amplitude of the excited waves. Differences between an ablation surface and a classical contact surface have been discussed. Dependence of the excited wavemore » amplitude on the wavenumber {ital k}{sub 0}, the ablation velocity {ital v}{sub {ital a}}, and the effective gravity {ital g} is also investigated. {copyright} {ital 1996 American Institute of Physics.}« less
  • A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in presence of ablation and thermal transport. The nonlinear effects for a single-mode disturbance are computed, included the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed by a statistical approach. The exponential growth of the linear regime is shown to be reduced by the nonlinear mode coupling. The saturation amplitude is around 0.1{lambda} for long wavelengths, but higher for short instable wavelengths in the ablative regime.
  • Stuart's weakly nonlinear theory is generalized to study single-mode ablative Rayleigh-Taylor instability (ARTI) at a broad ablation front caused by preheating. The thickness effect of the ablation front is considered and the spatial amplitude distributions of density, temperature, and velocity for harmonic modes are obtained in the present model. It is confirmed that the modified Lindl formula [W. H. Ye et al., Phys. Rev. E 65, 057401 (2002)] is valid for predicting the linear growth rate when the ablation front is broad. It is shown by the present model that the mass ablation of the shell is enhanced obviously duemore » to the generation of harmonics while the harmonics' effect on the mass asymmetry of the shell is weaker than the expectation given by the classical theory. It is also indicated by the present model that ARTI is stabilized by the nonlinear correction for all modes. This conclusion is physical and different from the sharp boundary model where ARTI is enhanced by the nonlinear correction for the short wavelength case. The reason for this difference is due to the thickness effect of the ablation front.« less