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

被引:0
作者
Assoul, Mouh [1 ]
El Jaouahiry, Abdelouahab [1 ]
Bouchgl, Jamila [2 ]
Echchadli, Mourad [1 ]
Aniss, Said [1 ]
机构
[1] Univ Hassan II Casablanca, Fac Sci Ain Chock, Lab Mech, Casablanca 20100, Morocco
[2] Higher Inst Marine Fisheries, Agadir 80000, Morocco
关键词
Hele-Shaw cell; quasiperiodic oscillation; Kelvin-Helmholtz and parametric instabilities; DYNAMIC STABILIZATION; VISCOSITY; STABILITY; FLOW;
D O I
10.3390/fluids8060164
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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.
引用
收藏
页数:20
相关论文
共 22 条
[1]   Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media [J].
Bouchgl, J. ;
Aniss, S. .
INTERNATIONAL JOURNAL OF APPLIED MECHANICS, 2021, 13 (08)
[2]   Interfacial instability of two superimposed immiscible viscous fluids in a vertical Hele-Shaw cell under horizontal periodic oscillations [J].
Bouchgl, Jamila ;
Aniss, Said ;
Souhar, Mohamed .
PHYSICAL REVIEW E, 2013, 88 (02)
[3]   Effect of quasi-periodic gravitational modulation on the convective instability in Hele-Shaw cell [J].
Boulal, T. ;
Aniss, S. ;
Belhaq, M. ;
Azouani, A. .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2008, 43 (09) :852-857
[4]   Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer [J].
Boulal, Taoufik ;
Aniss, Said ;
Belhaq, Mohamed ;
Rand, Richard .
PHYSICAL REVIEW E, 2007, 76 (05)
[5]   Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant [J].
El Jaouahiry, Abdelouahab ;
Aniss, Said .
PHYSICS OF FLUIDS, 2020, 32 (03)
[6]   Shear instability of two-fluid parallel flow in a Hele-Shaw cell [J].
Gondret, P ;
Rabaud, M .
PHYSICS OF FLUIDS, 1997, 9 (11) :3267-3274
[7]   Interface dynamics of immiscible fluids under circularly polarized vibration (Experiment) [J].
Ivanova A.A. ;
Kozlov V.G. ;
Tashkinov S.I. .
Fluid Dynamics, 2001, 36 (6) :871-879
[8]   Oscillatory transverse instability of interfacial waves in horizontally oscillating flows [J].
Jalikop, Shreyas V. ;
Juel, Anne .
PHYSICS OF FLUIDS, 2012, 24 (04)
[9]   STABILITY OF AN UNSTEADY KELVIN-HELMHOLTZ FLOW [J].
KELLY, RE .
JOURNAL OF FLUID MECHANICS, 1965, 22 :547-&
[10]   Stability of plane-parallel vibrational flow in a two-layer system [J].
Khenner, MV ;
Lyubimov, DV ;
Belozerova, TS ;
Roux, B .
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 1999, 18 (06) :1085-1101