Nodal Analysis of Nonlinear Behavior of the Instability at a Fluid Interface

Mc, Renoult; Rosenblatt, Charles; Carlès, Pierre

doi:10.1103/physrevlett.114.114503

Cited by 3 publications

(1 citation statement)

References 17 publications

(18 reference statements)

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“…Specifically, Lewis & Taylor (1950) reported the first experimental study on RTI, and Meshkov (1969) conducted the earliest RMI experiment using thin nitrocellulose membranes, which have sparked continuous interests in the experimental studies of both RTI and RMI (see, e.g. Allred, Blount & Miller 1953;Jacobs & Sheeley 1996;Waddell, Niederhaus & Jacobs 2001;Wilkinson & Jacobs 2007;Renoult, Rosenblatt & Carles 2015). In the community of numerical simulation, Daly (1967) was among the first to carry out two-dimensional (2-D) simulations of RTI flow.…”

Section: Introductionmentioning

confidence: 99%

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

Liu,

Wu-Wang,

Zhang

et al. 2023

J. Fluid Mech.

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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.

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Section: Introductionmentioning

confidence: 99%

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

Liu,

Wu-Wang,

Zhang

et al. 2023

J. Fluid Mech.

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Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I

2017

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Weakly nonlinear instability of a Newtonian liquid jet

et al. 2018

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A weakly nonlinear stability analysis of an axisymmetric Newtonian liquid jet is presented. The calculation is based on a small-amplitude perturbation method and performed to second order in the perturbation parameter. The obtained solution includes terms derived from a polynomial approximation of a viscous contribution containing products of Bessel functions with different arguments. The use of such an approximation is not needed in the inviscid case and the planar case, since the equations of those problems can be solved in an exact form. The developed model depends on three dimensionless parameters: the initial perturbation amplitude, the perturbation wavenumber and the liquid Ohnesorge number, the latter being the dimensionless liquid viscosity. The influence of the approximate terms was shown to be relatively small for a large range of Ohnesorge numbers so that they can be ignored. This simplification provides a jet model as simple to use as the previous ones, but taking into account the liquid viscosity and the cylindrical geometry. The jet model is used to reveal the effect of both the wavenumber and the Ohnesorge number on the formation of satellite drops, which is known as a nonlinear effect. Results are found in good agreement with direct numerical simulations and forced liquid jet experiments for wavenumbers lower than a threshold value. Satellite drop formation is retarded with increasing Ohnesorge number and wavenumber, as expected by the damping and size effects of viscosity. The threshold number corresponds to the maximum wavenumber for which satellite drop formation is predicted before jet breakup, and for which volume conservation is satisfied within a certain amount. The volume conservation criterion is imposed to ensure that the conclusions inferred by our model are safe.

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Nodal Analysis of Nonlinear Behavior of the Instability at a Fluid Interface

Cited by 3 publications

References 17 publications

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

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

Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I

Weakly nonlinear instability of a Newtonian liquid jet

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