Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media

Bouchgl, Jamila; Aniss, Saı̈d

doi:10.1142/s1758825121500885

Cited by 2 publications

(2 citation statements)

References 33 publications

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“…Recently, and on the experimental side, Li et al [14] investigated an extreme case of two coupled Faraday waves of three layers in a covered Hele-Shaw cell with periodic vertical vibration. More recently, the works by Bouchgl et al [12] and that by Lyubimova et al [13] were extended to a fully saturated porous media [15]. Bouchgl and Aniss [15] showed that the Darcy number has a destabilizing effect on the parametric instability and on the Kelvin-Helmholtz instability.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, the works by Bouchgl et al [12] and that by Lyubimova et al [13] were extended to a fully saturated porous media [15]. Bouchgl and Aniss [15] showed that the Darcy number has a destabilizing effect on the parametric instability and on the Kelvin-Helmholtz instability. Furthermore, the decrease in permeability significantly increases the stability threshold of the parametric instability, which is displaced to the short-wave regions.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Horizontal Quasi-Periodic Oscillation on the Interfacial Instability of Two Superimposed Viscous Fluid Layers in a Vertical Hele-Shaw Cell

Assoul

Jaouahiry

Bouchgl³

et al. 2023

Fluids

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We investigate the effect of horizontal quasi-periodic oscillation on the stability of two superimposed immiscible fluid layers confined in a horizontal Hele-Shaw cell. To approximate real oscillations, a quasi-periodic oscillation with two incommensurate frequencies is considered. Thus, the linear stability analysis leads to a quasi-periodic oscillator, with damping, which describes the evolution of the amplitude of the interface. Two types of quasi-periodic instabilities occur: the low-wavenumber Kelvin-Helmholtz instability and the large-wavenumber resonances. We mainly show that, for equal amplitudes of the superimposed accelerations, and for a low irrational frequency ratio, there is competition between several resonance modes allowing a very large selection of the wavenumber from lower to higher values. This is a way to control the sizes of the waves. Furthermore, increasing the frequency ratio has a stabilizing effect for both types of instability whose thresholds are found to correspond to quasi-periodic solutions using the frequency spectrum. For a ratio of the two superimposed displacement amplitudes equal to unity and less than unity, the number of resonances and competition between their modes also become significant for the intermediate values of the ratio of frequencies. The effects of other physical and geometrical parameters, such as the damping coefficient, density ratio, and heights of the two fluid layers, are also examined.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Horizontal Quasi-Periodic Oscillation on the Interfacial Instability of Two Superimposed Viscous Fluid Layers in a Vertical Hele-Shaw Cell

Assoul

Jaouahiry

Bouchgl³

et al. 2023

Fluids

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A Fast Time-Discontinuous Peridynamic Method for Stress Wave Propagation Problems in Saturated Porous Media

Zheng,

Liu,

Qiu

et al. 2024

Int. J. Appl. Mechanics

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When employing numerical methods to simulate the behavior of saturated porous media under impact load, the Gibbs phenomenon often occurs, significantly compromising the accuracy of numerical calculations. To improve the accuracy of numerical solutions, this study introduces a fast time-discontinuous peridynamic (TDPD) method for simulating the propagation of fluid pressure and solid stress waves within saturated porous media. In this method, the classical u–p and u–U models are reformulated from spatial differential equations into integral equations to facilitate the simulation of fracture problems. Subsequently, the basic field variables are independently interpolated in the temporal domain, with the introduction of jump terms representing the discontinuities of variables between adjacent time steps. Then an integral weak form in the temporal domain of the spatially discrete governing equations is constructed and the basic formula of the TDPD is derived. Additionally, an efficient approximation method that directly uses the internal force to calculate its time derivative is further proposed. These characteristics ensure that the TDPD can effectively and efficiently capture the inherent sharp gradient features of wave propagation in solid phase and fluid while controlling spurious numerical oscillations. Several representative numerical examples demonstrate that the TDPD can obtain more accurate results compared with conventional peridynamic solution schemes. Moreover, the TDPD can also be viewed as a novel time integration technique, holding substantial potential for high-precision numerical solutions of hyperbolic equations in diverse physical contexts.

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Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media

Cited by 2 publications

References 33 publications

Effect of Horizontal Quasi-Periodic Oscillation on the Interfacial Instability of Two Superimposed Viscous Fluid Layers in a Vertical Hele-Shaw Cell

Effect of Horizontal Quasi-Periodic Oscillation on the Interfacial Instability of Two Superimposed Viscous Fluid Layers in a Vertical Hele-Shaw Cell

A Fast Time-Discontinuous Peridynamic Method for Stress Wave Propagation Problems in Saturated Porous Media

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