Equilibrium Shapes and Their Stability for Liquid Films in Fast Flows

Likhit, Ganedi,; Oza, Anand U.; Shelley, Michael; Ristroph, Leif

doi:10.1103/physrevlett.121.094501

Cited by 9 publications

(2 citation statements)

References 32 publications

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“…To alleviate the issues that arise with a direct discretization of the boundary position, we instead use the θ-L method to discretize the boundary by the arclength s and tangent angle θ(s, t). This method is well-developed and has been used extensively for the study of 2D free-boundary problems in fluid dynamics [23,24,25,29,30]. We provide a brief overview of the method here.…”

Section: θ-L Methods For Boundary Evolutionmentioning

confidence: 99%

A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method

Mac Huang,

Shelley,

Stein

2020

Preprint

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The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan problem, which describes how the motion of a phase-separating interface depends on local concentration gradients, coupled to a fluid flow. Simulating these problems is challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field in an ever-changing domain. Moreover, density differences created in the fluid domain induce self-generated convecting flows that further complicate the numerical study of dissolution processes. In this contribution, we present a numerical method for the simulation of the Stefan problem coupled to a fluid flow. The scheme uses the Immersed Boundary Smooth Extension method to solve the bulk advection-diffusion and fluid equations in the complex, evolving geometry, coupled to a θ-L scheme that provides stable evolution of the boundary. We demonstrate 3 rd -order temporal and pointwise spatial convergence of the scheme for the classical Stefan problem, and 2 nd -order temporal and pointwise spatial convergence when coupled to flow. Examples of dissolution of solids that result in high-Rayleigh number convection are numerically studied, and qualitatively reproduce the complex morphologies observed in recent experiments.

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Section: θ-L Methods For Boundary Evolutionmentioning

confidence: 99%

A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method

Mac Huang,

Shelley,

Stein

2020

Preprint

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show abstract

“…The purpose of the present manuscript is to provide a more comprehensive treatment of the combined experimental and theoretical efforts of Bolles et al (2019) [5] and [29,30]. We present a variety of new findings that have resulted from a synergetic interaction between theory and experiments -a cooperative strategy with a proven record of success [6,38,14]. That outline of the paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

Anomalous waves triggered by abrupt depth changes: laboratory experiments and truncated KdV statistical mechanics

Moore¹,

Bolles²,

Majda³

et al. 2020

Preprint

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Recent laboratory experiments of Bolles et al. (2019) demonstrate that an abrupt change in bottom topography can trigger anomalous statistics in randomized surface waves. Motivated by these observations, Majda et al. (2019) developed a theoretical framework, based on deterministic and statistical analysis of the truncated Kortewegde Vries (TKdV) system, that successfully captures key qualitative features of the experiments, including the robust emergence of anomalous statistics and heightened skewness in the outgoing wavefield. Here, we extend these parallel experimental and modeling efforts with several new findings that have resulted from a synergetic interaction between the two. By precisely relating model parameters to physical ones, we calibrate the model inverse temperature to the specific conditions present in the experiments, thereby permitting a quantitative comparison. We find theoretically predicted distributions of surface displacement to match the experimental measurements with surprising detail. Prompted by the presence of surface slope in the TKdV Hamiltonian, we present new experimental measurements on surface slope statistics and compare them to model predictions. Analysis of some deterministic trajectories of TKdV elucidates the experimental length and time scales required for the statistical transition to a skewed state. Finally, the theory predicts a peculiar relationship between the outgoing displacement skewness and the change in slope variance, specifically how their ratio depends on the wave amplitude and depth ratio. New experimental measurements confirm this prediction in spectacular fashion.

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Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics

et al. 2020

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Equilibrium Shapes and Their Stability for Liquid Films in Fast Flows

Cited by 9 publications

References 32 publications

A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method

A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method

Anomalous waves triggered by abrupt depth changes: laboratory experiments and truncated KdV statistical mechanics

Anomalous Waves Triggered by Abrupt Depth Changes: Laboratory Experiments and Truncated KdV Statistical Mechanics

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