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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >On the instability of inviscid, rigidly rotating immiscible fluids in zero gravity
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On the instability of inviscid, rigidly rotating immiscible fluids in zero gravity

机译：关于零重力下无粘性，刚性旋转的不混溶流体的不稳定性

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摘要

The linear stability of an axisymmetric rotating two-fluid column in zero gravity is investigated. The inner core fluid of radius a and density p1 is surrounded by fluid of density p2 istself bounded by an outer impermeable cylinder of radius b. The surface tension coefficient at the immiscible interface is r. The parameters governing instability are the density ratio λ-p1/p2, the radius ratio k=b/a and the generalized Hocking parameter L_i=λ/p1a~3. While the necessary and sufficient condition for stability L2<(1-λ) is known, the preferred modes and wavenumbers at onset of instability have not been determined over the space of dimensionless parameters. Analytically and numerically determined maxmimum growth rates and corresponding preferred instability wavelengths for a rotating liquid column show that axisymmetric disturbances are most unstable for L1>0.1053 while planar disturbances determine instability when L1<0.10534. The rotating two-fluid system bounded by an outer cylinder with statically stable density ratios 0<λ<1 is unstable only to axisymmetric disturbances. Maximum growth rates and preferred wavelengths are computed as a function of λ and L_2 at radius ratios k=1.2 and k=5.0, respectively corresponding to relatively large and relatively small fluid cores. Complete results for the hollow-core vortex (λ=0) and a stationary two-fluid system (L2→∞) are also presented.
机译：研究了轴对称旋转两流体柱在零重力下的线性稳定性。半径为a且密度为p1的内芯流体被密度为p2的流体包围，该流体本身由半径为b的外部不可渗透圆柱体界定。不混溶界面处的表面张力系数为r。控制不稳定性的参数是密度比λ-p1/ p2，半径比k = b / a和广义霍金参数L_i =λ/ p1a〜3。尽管已知稳定性L2 <（1-λ）的必要和充分条件，但在无量纲参数的空间上尚未确定不稳定开始时的首选模式和波数。通过分析和数值确定的旋转液柱的最大增长率和相应的首选不稳定波长显示，当L1> 0.1053时，轴对称扰动最不稳定，而当L1 <0.10534时，平面扰动确定了不稳定。旋转的双流体系统以一个静态稳定的密度比0 <λ<1的外圆柱体为边界，仅对轴对称扰动不稳定。在半径比k = 1.2和k = 5.0时分别对应于相对较大和相对较小的流体核心，根据λ和L_2计算最大增长率和首选波长。还给出了空心涡旋（λ= 0）和平稳的双流体系统（L2→∞）的完整结果。

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