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多孔介质中流体不稳定界面的分枝现象

THE BIFURCATION OF UNSTABLE INTERFACE BETWEEN FLUIDS IN POROUS MEDIUM

  • 摘要: 本文通过理论分析和数值实验发现多孔介质中流体不稳定界面的分枝主要取决于无量纲参数C_1和S的值。对C_1取值范围内任一给定的值,存在S的一个临界值S_1,使当1S_1时,平面界面受小扰动后就有可能发展成分枝。S_1随C_1的减小而增大。存在C_1的一个临界值C_1~*,对取值范围内任一给定的C_1>C_1~*,还存在S的另外两个临界值S_2和S_3,使当S_2C_1~*情形,当S_1s_3时,或在C_1>C_1~*情形当S>S_1时,界面是否会发展成分枝则还与扰动形式有关。此外,本文还通过任意界面的线化稳定性分析和频谱分析得到了界面发生分枝的必要条件。

     

    Abstract: In the paper it is found by a theoretical analysis and numerical experiments that the bifurcation of unstable interface between fluids in porous medium can be determined essentially by the values of dimensionless parameters C1 and 5. For any given C1 there is a critical value S1 of 5 such that when 1 < 5 < S1 the flat interface perturbed by any small disturbance will develop to a long finger without bifurcation. There is a critical value C1* of C1 such that for any given C1 > C1* there are two distinct crit...

     

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