skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime

Abstract

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 the 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 ofmore » the formation mechanism for the astrophysical jets, and for the jetlike long spikes in the high energy density physics.« less

Authors:
 [1];  [2];  [1];  [2];  [3]
  1. LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China)
  2. (China)
  3. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083 (China)
Publication Date:
OSTI Identifier:
21371107
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 17; Journal Issue: 5; Other Information: DOI: 10.1063/1.3396369; (c) 2010 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPUTERIZED SIMULATION; INSTABILITY GROWTH RATES; INTERFACES; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; PLASMA DENSITY; RAYLEIGH-TAYLOR INSTABILITY; FLUID MECHANICS; HYDRODYNAMICS; INSTABILITY; MECHANICS; SIMULATION

Citation Formats

Wang, L. F., State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, Ye, W. H., Department of Physics, Zhejiang University, Hangzhou 310027, China and CAPT, Peking University, Beijing 100871, and Li, Y. J. Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime. United States: N. p., 2010. Web. doi:10.1063/1.3396369.
Wang, L. F., State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, Ye, W. H., Department of Physics, Zhejiang University, Hangzhou 310027, China and CAPT, Peking University, Beijing 100871, & Li, Y. J. Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime. United States. doi:10.1063/1.3396369.
Wang, L. F., State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, Ye, W. H., Department of Physics, Zhejiang University, Hangzhou 310027, China and CAPT, Peking University, Beijing 100871, and Li, Y. J. 2010. "Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime". United States. doi:10.1063/1.3396369.
@article{osti_21371107,
title = {Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime},
author = {Wang, L. F. and State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083 and Ye, W. H. and Department of Physics, Zhejiang University, Hangzhou 310027, China and CAPT, Peking University, Beijing 100871 and Li, Y. J.},
abstractNote = {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 the 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.},
doi = {10.1063/1.3396369},
journal = {Physics of Plasmas},
number = 5,
volume = 17,
place = {United States},
year = 2010,
month = 5
}
  • The two-dimensional Rayleigh-Taylor instability (RTI) with and without thermal conduction is investigated by numerical simulation in the weakly nonlinear regime. A preheat model {kappa}(T)={kappa}{sub SH}[1+f(T)] is introduced for the thermal conduction [W. H. Ye, W. Y. Zhang, and X. T. He, Phys. Rev. E 65, 057401 (2002)], where {kappa}{sub SH} is the Spitzer-Haerm electron thermal conductivity coefficient and f(T) models the preheating tongue effect in the cold plasma ahead of the ablation front. The preheating ablation effects on the RTI are studied by comparing the RTI with and without thermal conduction with identical density profile relevant to inertial confinement fusionmore » experiments. It is found that the ablation effects strongly influence the mode coupling process, especially with short perturbation wavelength. Overall, the ablation effects stabilize the RTI. First, the linear growth rate is reduced, especially for short perturbation wavelengths and a cutoff wavelength is observed in simulations. Second, the second harmonic generation is reduced for short perturbation wavelengths. Third, the third-order negative feedback to the fundamental mode is strengthened, which plays a stabilization role. Finally, on the contrary, the ablation effects increase the generation of the third harmonic when the perturbation wavelengths are long. Our simulation results indicate that, in the weakly nonlinear regime, the ablation effects are weakened as the perturbation wavelength is increased. Numerical results obtained are in general agreement with the recent weakly nonlinear theories as proposed in [J. Sanz, J. Ramirez, R. Ramis et al., Phys. Rev. Lett. 89, 195002 (2002); J. Garnier, P.-A. Raviart, C. Cherfils-Clerouin et al., Phys. Rev. Lett. 90, 185003 (2003)].« less
  • Harmonic growth in classical Rayleigh-Taylor instability (RTI) on a spherical interface is analytically investigated using the method of the parameter expansion up to the third order. Our results show that the amplitudes of the first four harmonics will recover those in planar RTI as the interface radius tends to infinity compared against the initial perturbation wavelength. The initial radius dramatically influences the harmonic development. The appearance of the second-order feedback to the initial unperturbed interface (i.e., the zeroth harmonic) makes the interface move towards the spherical center. For these four harmonics, the smaller the initial radius is, the faster theymore » grow.« less
  • 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 wouldmore » 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.« less
  • The effect of compressibility and of density variation on Rayleigh-Taylor and Richtmyer-Meshkov instability of the temporal development of two fluid interfacial structures such as bubbles and spikes have been investigated. It is seen that the velocity of the tip of the bubble or spike increases (destabilization) if the local Atwood number increases due to density variation of either of the fluids. The opposite is the result, i.e., the bubble or spike tip velocity decreases (stabilization) if the density variation leads to lowering of the value of the local Atwood number. The magnitude of stabilization or destabilization is an increasing functionmore » of the product of the wave number k and interfacial pressure p{sub 0}. The effect of compressibility is quite varied. If the heavier (upper) fluid alone is incompressible ({gamma}{sub h}{yields}{infinity}), but the lighter fluid is compressible the growth rate is higher (destabilization) than when both the fluids are incompressible. Moreover the heavier fluid remaining incompressible the growth rate decreases (stabilization) as {gamma}{sub l} (finite) increases and ultimately tends to the incompressible limit value as {gamma}{sub l}{yields}{infinity}. With {gamma}{sub l}{yields}{infinity} but {gamma}{sub h} finite the growth increases (destabilization) as {gamma}{sub h} increases. When both {gamma}{sub h} and {gamma}{sub l} are finite (density {rho}{sub h}>density {rho}{sub l}) the growth is reduced when {gamma}{sub h}<{gamma}{sub l} compared to that when both fluids are incompressible and enhanced when {gamma}{sub h}>{gamma}{sub l}. The set of nonlinear equations describing the dynamics of bubbles and spikes in the presence of fluid density variations are not analytically integrable in closed form. The results derived by numerical solution methods are represented and interpreted in corresponding figures.« 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