Convection in stable and unstable fronts

Elliott, Drew; Vasquez, Desiderio A.

doi:10.1103/physreve.85.016207

Cited by 9 publications

(8 citation statements)

References 21 publications

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“…The speed of these branches was previously reported in Ref. 27, however, the scale in Fig. 3 of that reference is off by a factor of ffiffi ffi 2 p , therefore our new calculations should replace the previous results.…”

Section: A Steady Solutionssupporting

confidence: 71%

“…Assuming that j is non-zero, we introduce time and length scales defined by (3), we solve for each component of the stream function w n in terms of the Fourier coefficient of the front height H n , which leads to the fluid velocity at the front height. 27 Consequently, we arrive to an equation that involves only the front height h, and its Fourier coefficients…”

Section: Equations Of Motionmentioning

confidence: 99%

“…2, we show four different front profiles, with the front height function measured relative to the average front height. Without fluid motion at L ¼ 3.5, a nonaxisymmetric front develops due to the instability of the flat front for L > p. 27 This profile has a horizontal density gradient that leads to a single convective roll, which in turns modifies the front, resulting in the structure displayed in Fig. 2(a).…”

Section: A Steady Solutionsmentioning

confidence: 99%

“…26 Previous work by Elliott and Vasquez established the stability of flat fronts governed by the KS equation under density gradients. 27 However, this work did not analyzed the stability of more complex fronts arising in the KS equation. These fronts are not necessarily stable 28 requiring new computational techniques to obtain them and to analyze their stability under density gradients, which is what we present in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…If we continue to increase the magnitude of the Rayleigh number beyond Ra ¼ À0.769, we find only the flat front as a solution, without cellular structures, which is consistent with the linear stability analysis of the flat fronts. 27 …”

Section: Cellular Solutionsmentioning

confidence: 99%

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Rayleigh-Taylor instability of steady fronts described by the Kuramoto-Sivashinsky equation

Vilela

Vasquez

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study steady thin reaction fronts described by the Kuramoto-Sivashinsky equation that separates fluids of different densities. This system may lead to hydrodynamic instabilities as buoyancy forces interact with the propagating fronts in a two-dimensional slab. We use Darcy's law to describe the fluid motion in this geometry. Steady front profiles can be flat, axisymmetric, or nonaxisymmetric, depending on the slab width, the density gradient, and fluid viscosity. Unstable flat fronts can be stabilized having a density gradient with the less dense fluid on top of a denser fluid. We find the steady front solutions from the nonlinear equations executing a linear stability analysis to determine their stability. We show regions of bistability where stable nonaxisymmetric and axisymmetric fronts can coexist. We also consider the stability of steady solutions in large domains, which can be constructed by dividing the domain into smaller parts or cells. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4883500]Reaction fronts described by the Kuramoto-Sivashinsky (KS) equation can result in steady curved fronts as they propagate in two-dimensional domains. Transitions between these structures take place as the width of the domain is modified. We consider these fronts separating fluids of different densities, which may result in Rayleigh-Taylor (RT) instabilities as a less dense fluid is placed under a denser fluid. We find that convective fluid motion takes place changing the shape and speed of the fronts. In the case of curved fronts, convection always exists due to a horizontal density gradient, even if the less dense fluid is on top. We analyze the stability of the corresponding fronts with convection. We also consider fronts in extended domains generated from solutions in smaller domains or cells, finding that a favorable density gradient can provide a stability to an extended pattern.

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Section: A Steady Solutionssupporting

confidence: 71%

Section: Equations Of Motionmentioning

confidence: 99%

Section: A Steady Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Cellular Solutionsmentioning

confidence: 99%

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Rayleigh-Taylor instability of steady fronts described by the Kuramoto-Sivashinsky equation

Vilela

Vasquez

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Front instabilities in the presence of convection due to thermal and compositional gradients

Guzman,

Vasquez

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Reaction fronts separate fluids of different densities due to thermal and compositional gradients that may lead to convection. The stability of convectionless flat fronts propagating in the vertical direction depends not only on fluid properties but also in the dynamics of a front evolution equation. In this work, we analyze fronts described by the Kuramoto–Sivashinsky (KS) equation coupled to hydrodynamics. Without density gradients, the KS equation has a flat front solution that is unstable to perturbations of long wavelengths. Buoyancy enhances this instability if a fluid of lower density is underneath a denser fluid. In the reverse situation, with the denser fluid underneath, the front can be stabilized with appropriate thermal and compositional gradients. However, in this situation, a different instability develops for large enough thermal gradients. We also solve numerically the nonlinear KS equation coupled to the Navier–Stokes equations to analyze the front propagation in two-dimensional rectangular domains. As convection takes place, the reaction front curves, increasing its velocity.

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Complex network analysis of the gravity effect on premixed flames propagating in a Hele-Shaw cell

Nomi

Gotoda²,

Kandani³

et al. 2021

Phys. Rev. E

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Convection in stable and unstable fronts

Cited by 9 publications

References 21 publications

Rayleigh-Taylor instability of steady fronts described by the Kuramoto-Sivashinsky equation

Rayleigh-Taylor instability of steady fronts described by the Kuramoto-Sivashinsky equation

Front instabilities in the presence of convection due to thermal and compositional gradients

Complex network analysis of the gravity effect on premixed flames propagating in a Hele-Shaw cell

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