A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

被引:2
|
作者
Bongarzone, Alessandro [1 ]
Jouron, Baptiste [1 ]
Viola, Francesco [2 ]
Gallaire, Francois [1 ]
机构
[1] Ecole Polytech Fed Lausanne, Lab Fluid Mech & Instabil, CH-1015 Lausanne, Switzerland
[2] Gran Sasso Sci Inst, Viale F Crispi 7, I-67100 Laquila, Italy
基金
瑞士国家科学基金会;
关键词
parametric instability; Hele-Shaw flows; Faraday waves; GRAVITY-CAPILLARY WAVES; CONTACT-LINE; ADAPTIVE SOLVER; SURFACE-TENSION; INSTABILITY; HYSTERESIS; STABILITY; EQUATIONS; DYNAMICS; FRICTION;
D O I
10.1017/jfm.2023.986
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Existing theoretical analyses of Faraday waves in Hele-Shaw cells rely on the Darcy approximation and assume a parabolic flow profile in the narrow direction. However, Darcy's model is known to be inaccurate when convective or unsteady inertial effects are important. In this work, we propose a gap-averaged Floquet theory accounting for inertial effects induced by the unsteady terms in the Navier-Stokes equations, a scenario that corresponds to a pulsatile flow where the fluid motion reduces to a two-dimensional oscillating Poiseuille flow, similarly to the Womersley flow in arteries. When gap-averaging the linearised Navier-Stokes equation, this results in a modified damping coefficient, which is a function of the ratio between the Stokes boundary layer thickness and the cell's gap, and whose complex value depends on the frequency of the wave response specific to each unstable parametric region. We first revisit the standard case of horizontally infinite rectangular Hele-Shaw cells by also accounting for a dynamic contact angle model. A comparison with existing experiments shows the predictive improvement brought by the present theory and points out how the standard gap-averaged model often underestimates the Faraday threshold. The analysis is then extended to the less conventional case of thin annuli. A series of dedicated experiments for this configuration highlights how Darcy's thin-gap approximation overlooks a frequency detuning that is essential to correctly predict the locations of the Faraday tongues in the frequency-amplitude parameter plane. These findings are well rationalised and captured by the present model.
引用
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页数:35
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