Analytical model of nonlinear evolution of single-mode Rayleigh–Taylor instability in cylindrical geometry

Zhao, Zhiye; Wang, Pei; Liu, Nansheng; Lu, Xi‐Yun

doi:10.1017/jfm.2020.526

Cited by 19 publications

(16 citation statements)

References 41 publications

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“…Velocity components in lower fluid 2 are obtained by differentiation of the series for 2 in (11), similarly to (12), and are obtained in the forms These velocity components ( 16) are substituted into the second kinematic condition at the interface, to give a result analogous to (13). The = 0 Fourier mode once again confirms Theorem 1, and the higher modes = 1, 2, … , N give analogous to the result (15) for the upper fluid.…”

Section: Proof We Wish To Show Thatmentioning

confidence: 79%

“…The second kinematic condition ( 17) is subtracted from the first condition (15), and the resulting expression is differentiated in time. After a little algebra, this yields The dynamic condition (18) is similarly differentiated in time and so gives an expression in the form ( 18)…”

Section: Proof We Wish To Show Thatmentioning

confidence: 99%

“…Furthermore, flows of this type are not just restricted to twodimensional planar geometry. They have been studied in cylindrical geometry by Forbes [14], corresponding to outflow from a line source, and recently by Zhao et al [15]. These flows also occur in spherical-type outflow from a point source, (see Forbes [16,17]), where they have possible application to the formation of one-sided jet flows in astrophysics, observed by Gómez et al [18].…”

Section: Introductionmentioning

confidence: 99%

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The Rayleigh–Taylor instability in a porous medium

2021

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The classical Rayleigh–Taylor instability occurs when a heavy fluid overlies a lighter one, and the two fluids are separated by a horizontal interface. The configuration is unstable, and a small perturbation to the interface grows with time. Here, we consider such an arrangement for planar flow, but in a porous medium governed by Darcy’s law. First, the fully saturated situation is considered, where the two horizontal fluids are separated by a sharp interface. A classical linearized theory is reviewed, and the nonlinear model is solved numerically. It is shown that the solution is ultimately limited in time by the formation of a curvature singularity at the interface. A partially saturated Boussinesq theory is then presented, and its linearized approximation predicts a stable interface that merely diffuses. Nonlinear Boussinesq theory, however, allows the growth of drips and bubbles at the interface. These structures develop with no apparent overturning at their heads, unlike the corresponding flow for two free fluids.

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Section: Proof We Wish To Show Thatmentioning

confidence: 79%

Section: Proof We Wish To Show Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Rayleigh–Taylor instability in a porous medium

2021

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“…These models have been confirmed by a series of experiments (Ding et al 2017;Luo et al 2018bLuo et al , 2019. Theoretical analyses were extended in recent studies to predict the growth of perturbations in the case of multiple shocks (Flaig et al 2018), nonlinear stages (Goncharov & Li 2005;Zhao et al 2020;Dimonte 2021), or late-time turbulent mixing (Mikaelian 1990(Mikaelian , 2005Rafei et al 2019;El Rafei & Thornber 2020). Besides, numerical simulations have been carried out to investigate the convergent RM instability.…”

Section: Introductionmentioning

confidence: 80%

“…2018), nonlinear stages (Goncharov & Li 2005; Zhao et al. 2020; Dimonte 2021), or late-time turbulent mixing (Mikaelian 1990, 2005; Rafei et al. 2019; El Rafei & Thornber 2020).…”

Section: Introductionmentioning

confidence: 99%

Evaluating the stretching/compression effect of Richtmyer–Meshkov instability in convergent geometries

Zhang

et al. 2022

J. Fluid Mech.

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Richtmyer–Meshkov (RM) instability in convergent geometries (such as cylinders and spheres) plays a fundamental role in natural phenomena and engineering applications, e.g. supernova explosion and inertial confinement fusion. Convergent geometry refers to a system in which the interface converges and the fluids are compressed correspondingly. By applying a decomposition formula, the stretching or compression (S(C)) effect is separated from the perturbation growth as one of the main contributions, which is defined as the averaged velocity difference between two ends of the mixing zone. Starting from linear theories, the S(C) effect in planar, cylindrical and spherical geometries is derived as a function of geometrical convergence ratio, compression ratio and mixing width. Specifically, geometrical convergence stretches the mixing zone, while fluid compression compresses the mixing zone. Moreover, the contribution of geometrical convergence in the spherical geometry is more important than that in the cylindrical geometry. A series of cylindrical cases with high convergence ratio is simulated, and the growth of perturbations is compared with that of the corresponding planar cases. As a result, the theoretical results of the S(C) effect agree well with the numerical results. Furthermore, results show that the S(C) effect is a significant feature in convergent geometries. Therefore, the S(C) effect is an important part of the Bell–Plesset effect. The present work on the S(C) effect is important for further modelling of the mixing width of convergent RM instabilities.

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