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Density-driven unstable flows of miscible fluids in a Hele-Shaw cell

机译:密度驱动的Hele-Shaw池中混溶流体的不稳定流动

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Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are investigated by means of experimental measurements, as well as two- and three-dimensional numerical simulations. The experiments focus on the early stages of the instability growth, and they provide detailed information regarding the growth rates and most amplified wavenumbers as a function of the governing Rayleigh number Ra. They identify two clearly distinct parameter regimes: a low-Ra, 'Hele-Shaw' regime in which the dominant wavelength scales as Ra-1, and a high-Ra 'gap' regime in which the length scale of the instability is 5 +/- 1 times the gap width. The experiments are compared to a recent linear stability analysis based on the Brinkman equation. The analytical dispersion relationship for a step-like density profile reproduces the experimentally observed trend across the entire Ra range. Nonlinear simulations based on the two- and three-dimensional Stokes equations indicate that the high-Ra regime is characterized by an instability across the gap, wheras in the low-Ra regime a spanwise Hele-Shaw mode dominates. [References: 40]
机译:通过实验测量以及二维和三维数值模拟,研究了垂直Hele-Shaw池中混溶流体之间的密度驱动不稳定性。实验着重于不稳定性增长的早期阶段,它们提供了有关增长率和最大放大波数作为控制瑞利数Ra的函数的详细信息。他们确定了两个明显不同的参数状态:低Ra,“ Hele-Shaw”状态(其中主波长标度为Ra-1)和高Ra“间隙”状态,其中不稳定性的长度标度为5 + /-缝隙宽度的1倍。将实验与基于Brinkman方程的最新线性稳定性分析进行了比较。阶梯状密度分布的分析色散关系再现了整个Ra范围内实验观察到的趋势。基于二维和三维斯托克斯方程的非线性模拟表明,高Ra态的特征是整个间隙的不稳定性,而在低Ra态下,翼展方向上的Hele-Shaw模式占主导地位。 [参考:40]

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