W. H. Ye

Interface width effect on the classical Rayleigh–Taylor instability in the weakly nonlinear regime

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, 0.1λ. 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 suppre...

Destabilizing effect of density gradient on the Kelvin–Helmholtz instability

In this paper, we derive explicit analytic formulas for the linear growth rate and frequency of the Kelvin–Helmholtz instability in fluids with the density gradient. The analytic formulas are in excellent agreement with the results of two-dimensional numerical simulation. We found that the density gradient effect enforces (destabilizes) the Kelvin–Helmholtz instability by increasing its linear growth rate in the direction normal to the perturbed interface. The frequency is reduced (stabilized) by the density gradient effect, i.e., the density gradient decreases the transmission of the perturbation in the direction along to the perturbed interface. In most cases, the combined effect of density and velocity gradients stabilizes the Kelvin–Helmholtz instability.

Combined effect of the density and velocity gradients in the combination of Kelvin–Helmholtz and Rayleigh–Taylor instabilities

We have derived explicit analytic formulas for the linear growth rate and the frequency in the combination of Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instabilities in fluids with continuous density and velocity profiles. It is found that the density gradient effect (i.e., the density transition layer) decreases the linear growth rate in the RT instability (RTI), especially for the short perturbation wavelength. The linear growth rate for the KH instability (KHI) is increased by the density gradient effect but decreased by the velocity gradient effect (i.e., the velocity transition layer). The frequency in the KHI is reduced by both the density gradient effect and the velocity gradient effect. In most cases, both the linear growth rate and the frequency are decreased by the combination of density and velocity transition layers, i.e., the combined effect of density and velocity gradients stabilizes the KHI. The density gradient effect has an opposite influence on the linear growth rates of the RTI an...

A hybrid-drive nonisobaric-ignition scheme for inertial confinement fusion

A new hybrid-drive (HD) nonisobaric ignition scheme of inertial confinement fusion (ICF) is proposed, in which a HD pressure to drive implosion dynamics increases via increasing density rather than temperature in the conventional indirect drive (ID) and direct drive (DD) approaches. In this HD (combination of ID and DD) scheme, an assembled target of a spherical hohlraum and a layered deuterium-tritium capsule inside is used. The ID lasers first drive the shock to perform a spherical symmetry implosion and produce a large-scale corona plasma. Then, the DD lasers, whose critical surface in ID corona plasma is far from the radiation ablation front, drive a supersonic electron thermal wave, which slows down to a high-pressure electron compression wave, like a snowplow, piling up the corona plasma into high density and forming a HD pressurized plateau with a large width. The HD pressure is several times the conventional ID and DD ablation pressure and launches an enhanced precursor shock and a continuous compression wave, which give rise to the HD capsule implosion dynamics in a large implosion velocity. The hydrodynamic instabilities at imploding capsule interfaces are suppressed, and the continuous HD compression wave provides main pdV work large enough to hotspot, resulting in the HD nonisobaric ignition. The ignition condition and target design based on this scheme are given theoretically and by numerical simulations. It shows that the novel scheme can significantly suppress implosion asymmetry and hydrodynamic instabilities of current isobaric hotspot ignition design, and a high-gain ICF is promising.

Spike deceleration and bubble acceleration in the ablative Rayleigh-Taylor instability

The nonlinear evolutions of the Rayleigh-Taylor instability (RTI) with preheat is investigated by numerical simulation (NS). A new phase of the spike deceleration evolution in the nonlinear ablative RTI (ARTI) is discovered. It is found that nonlinear evolution of the RTI can be divided into the weakly nonlinear regime (WNR) and the highly nonlinear regime (HNR) according to the difference of acceleration velocities for the spike and the bubble. With respect to the classical RTI (i.e., without heat conduction), the bubble first accelerates in the WNR and then decelerates in the HNR while the spike holds acceleration in the whole nonlinear regime (NR). With regard to the ARTI, on the contrary, the spike first accelerates in the WNR and then decelerates in the HNR while the bubble keeps acceleration in the whole NR. The NS results indicate that it is the nonlinear overpressure effect at the spike tip and the vorticity accumulation inside the bubble that lead to, respectively, the spike deceleration and bubble acceleration, in the nonlinear ARTI. In addition, it is found that in the ARTI the spike saturation velocity increases with the perturbation wavelength.

Preheating ablation effects on the Rayleigh–Taylor instability in the weakly nonlinear regime

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 κ(T)=κSH[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 κSH is the Spitzer–Harm 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 fusion 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 gene...

Nonlinear saturation amplitudes in classical Rayleigh-Taylor instability at arbitrary Atwood numbers

In this research, nonlinear saturation amplitudes (NSAs) of the first two harmonics in Rayleigh-Taylor instability(RTI) for irrotational, incompressible, and inviscid fluids, with a discontinuous profile at arbitrary Atwood numbers, are investigated analytically, by considering nonlinear corrections up to the tenth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth. The NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the higher-order correction (HOC) and the Atwood number (A) play an important role in the NSA of the RTI. It is found that the NSA of the fundamental mode decreases with increasing A. And when the HOC effects are considered, the NSA of the fundamental mode is significantly larger than the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. We find that the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the NSAs of the first two harmonics demonstrate the trend of convergence as the order of corrections increases. Thus, it should be included in applications where the NSAs play a role, such as inertial confinement fusion ignition target design.

Nonlinear saturation amplitude in the Rayleigh-Taylor instability at arbitrary Atwood numbers with continuous profiles

We present an approximate method to derive an analytic formula for the Nonlinear Saturation Amplitude (NSA, ηs), in the two-dimensional Rayleigh-Taylor Instability (RTI) for incompressible fluids, with sharp density profiles, to analyze the Atwood number (AT) effects. Our analytic formula indicates that the Atwood number effects remarkably affect the NSA of the RTI. The density gradient effects (i.e., the effects of interface width) on the NSA are investigated by the Direct Numerical Simulation (DNS). In our DNS, it is found that the NSA is fundamentally dependent on kL, where L=min(ρ/|dρ/dx|) is the minimum density gradient scale length and k is the perturbation wave number. For fixed AT, kηs increases with kL, and for fixed L, kηs increases with kL. The results of DNS show that our analytic formula , is recovered, when kL→0. In our DNS, for large kL, the NSA can approach and even exceed its wavelength, which cannot be predicted by the classical estimation, 0.1λ (Jacobs J. W. and Catton I., J. Fluid Mech., 187 (1988) 329).

Weakly nonlinear analysis on the Kelvin-Helmholtz instability

A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability in two-dimensional incompressible fluids. The second- and third-harmonic generation effects of single-mode perturbation, as well as the nonlinear correction to the exponential growth of the fundamental modulation are analyzed. An important resonance in the mode-coupling process is found. The nonlinear saturation time depends on the initial perturbation amplitude and the density ratio of the two fluids, but the nonlinear saturation amplitude depends only on the initial perturbation amplitude. The weakly nonlinear result is supported by numerical simulation. The practical system of boundary layer containing thermal conductivity is analyzed. Their nonlinear saturation amplitude can be predicted by our weakly nonlinear model.

Numerical investigation on the ablative Kelvin-Helmholtz instability

The ablative effect on the Kelvin-Helmholtz instability is attemptly analyzed by numerical simulation. One-dimensional ablative effect is analyzed and some typical profiles are introduced for the two-dimensional simulations. We found that the linear growth rate and frequency are reduced by the ablative effect. The heat conduction stabilize the Kelvin-Helmholtz instability by suppressing the growth and transmission of the perturbation. In the weakly nonlinear regime, the ablative effect suppresses the appearance and growth of the second and third harmonics.