A unified theoretical model for spatiotemporal development of Rayleigh–Taylor and Richtmyer–Meshkov fingers

Liu, Changwen; Zhang, Yousheng; Xiao, Zuoli

doi:10.1017/jfm.2022.1000

Cited by 6 publications

(37 citation statements)

References 54 publications

(93 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1995; Zhang & Sohn 1996; Mikaelian 1998; Zhang 1998; Goncharov 2002; Abarzhi, Glimm & Lin 2003; Mikaelian 2003; Sohn 2003; Zhang & Guo 2016; Zhang, Deng & Guo 2018; Guo & Zhang 2020; Zhao et al. 2020; Zhang & Guo 2022; Liu, Zhang & Xiao 2023). Then, it was extended by Hecht et al.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, Liu et al. (2023) introduced a dual-source (DS) model within the LPM framework to accurately predict interfacial fingers at all density ratios in two and three dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…According to Liu et al. (2023), such an unphysical assumption accounts for the distinct inaccuracy in attempts to catch the concavity and convexity of the fingertip-growth curve as well as the so-called ‘overshoot’ phenomenon (shown in figure 1). Therefore, shape evolution can be crucial to describe the entire evolution of interfacial perturbations accurately.…”

Section: Introductionmentioning

confidence: 99%

“…To this end, Liu et al. (2023) introduced a DS potential function and coupled the solution of growth rate with that of shape curvature.…”

Section: Introductionmentioning

confidence: 99%

“…The DS model (Liu et al. 2023) accurately predicts growth rate and shape evolution, and reveals the nonlinear coupling interaction between them. It is also found that such nonlinear interaction leads to a time delay for the emergence of extreme values in the growth rate and shape curvature.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A decoupled mechanism of interface growth in single-mode hydrodynamic instabilities

Liu,

Wu-Wang,

Zhang

et al. 2023

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

One of the most significant issues in hydrodynamic interfacial instabilities is the growth rate of the interfacial perturbations, which plays an important role in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). Yet the underlying mechanisms of such flow phenomena remain unclear or controversial. In this paper the decoupled mechanisms of two effects are found to dominate the interface growth of the single-mode Rayleigh–Taylor instability (RTI) and Richtmyer–Meshkov instability (RMI) via Layzer's potential-flow model. One is the inertial effect induced by the interfacial density gradient and the acceleration, and the other is the frontal distortion effect stemming from interface shape evolution. The former determines the dominant features of interface evolution, while the latter influences the local concavity and convexity of growth rate such as the overshoot phenomenon. These two effects can be approximated as a linearly decoupled analytical solution if their nonlinear interaction term is neglected. With the decoupled solution, the theoretical growth rates agree well with high-fidelity numerical simulation results. The present result indicates that the long-time evolution of fluid interface in both RTI and RMI at all density ratios can be accurately predicted if both inertia and frontal distortion effects are taken into account. Furthermore, the strong dependence of instability evolution on initial amplitude is quantified based on the effects of decoupling, which sheds light on the physical origin of the overshoot phenomenon.

show abstract

Section: Introductionmentioning

confidence: 99%

“…More recently, Liu et al. (2023) introduced a dual-source (DS) model within the LPM framework to accurately predict interfacial fingers at all density ratios in two and three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…To this end, Liu et al. (2023) introduced a DS potential function and coupled the solution of growth rate with that of shape curvature.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A decoupled mechanism of interface growth in single-mode hydrodynamic instabilities

Liu,

Wu-Wang,

Zhang

et al. 2023

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

Interfacial instabilities driven by co-directional rarefaction and shock waves

Gao,

Guo,

Zhai

et al. 2024

J. Fluid Mech.

View full text Add to dashboard Cite

We report the first experiments on hydrodynamic instabilities of a single-mode light/heavy interface driven by co-directional rarefaction and shock waves. The experiments are conducted in a specially designed rarefaction-shock tube that enables the decoupling of interfacial instabilities caused by these co-directional waves. After the impacts of rarefaction and shock waves, the interface evolution transitions into Richtmyer–Meshkov unstable states from Rayleigh–Taylor (RT) stable states, which is different from the finding in the previous case with counter-directional rarefaction and shock waves. A scaling method is proposed, which effectively collapses the RT stable perturbation growths. An analytical theory for predicting the time-dependent acceleration and density induced by rarefaction waves is established. Based on the analytical theory, the model proposed by Mikaelian (Phys. Fluids, vol. 21, 2009, p. 024103) is revised to provide a good description of the dimensionless RT stable behaviour. Before the shock arrival, the unequal interface velocities, caused by rarefaction-induced uneven vorticity, result in a V-shape-like interface. The linear growth rate of the amplitude is insensitive to the pre-shock interface shape, and can be well predicted by the linear superposition of growth rates induced by rarefaction and shock waves. The nonlinear growth rate is higher than that of a pure single-mode case, which can be predicted by the nonlinear models (Sadot et al., Phys. Rev. Lett., vol. 80, 1998, pp. 1654–1657; Dimonte & Ramaprabhu, Phys. Fluids, vol. 22, 2010, p. 014104).

show abstract

Lagrangian investigation of the interface dynamics in single-mode Rayleigh–Taylor instability

Zhao,

Xiao,

Aluie

et al. 2023

Physics of Fluids

View full text Add to dashboard Cite

We apply Lagrangian particle tracking to the two-dimensional single-mode Rayleigh–Taylor (RT) instability to study the dynamical evolution of fluid interface. At the onset of the nonlinear RT stage, we select three ensembles of tracer particles located at the bubble tip, at the spike tip, and inside the spiral of the mushroom structure, which cover most of the interfacial region as the instability develops. Conditional statistics performed on the three sets of particles and over different RT evolution stages, such as the trajectory curvature, velocity, and acceleration, reveals the temporal and spatial flow patterns characterizing the single-mode RT growth. The probability density functions of tracer particle velocity and trajectory curvature exhibit scalings compatible with local flow topology, such as the swirling motion of the spiral particles. Large-scale anisotropy of RT interfacial flows, measured by the ratio of horizontal to vertical kinetic energy, also varies for different particle ensembles arising from the differing evolution patterns of the particle acceleration. In addition, we provide direct evidence to connect the RT bubble re-acceleration to its interaction with the transported fluid from the spike side, due to the shear driven Kelvin–Helmholtz instability. Furthermore, we reveal that the secondary RT instability inside the spiral, which destabilizes the spiraling motion and induces complex flow structures, is generated by the centrifugal acceleration.

show abstract

A unified theoretical model for spatiotemporal development of Rayleigh–Taylor and Richtmyer–Meshkov fingers

Cited by 6 publications

References 54 publications

A decoupled mechanism of interface growth in single-mode hydrodynamic instabilities

A decoupled mechanism of interface growth in single-mode hydrodynamic instabilities

Interfacial instabilities driven by co-directional rarefaction and shock waves

Lagrangian investigation of the interface dynamics in single-mode Rayleigh–Taylor instability

Contact Info

Product

Resources

About