Latitudinal libration driven flows in triaxial ellipsoids
Latitudinal libration driven flows in triaxial ellipsoids
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DOI：
10.1017/jfm.2015.130
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发表时间：
2015-04
影响因子：
3.7
通讯作者：
S. Vantieghem;D. Cébron;J. Noir
中科院分区：
文献类型：
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作者：
S. Vantieghem;D. Cébron;J. Noir
在了解潮汐变形的行星和卫星的液核动力学的激励下，我们提出了一项在刚性三轴椭球体内由纬度振动驱动的不可压缩流的研究。我们首先导出了在均匀涡度流动假设下无粘运动方程的层流解。如果振动频率与自旋过惯性模式的频率相匹配，则该解表现出共振。此外，我们通过引入低Ekman数极限下粘性Ekman层影响的简化模型扩展了我们的模型（Noir & c<e:1>， J.流体力学）。， vol. 737, 2013, pp. 412-439)。这种理论方法与Chan等人的结果是一致的。地球的星球。国际米兰。《流体力学与工程》，vol. 187, 2011, pp. 404-415)。球面几何，vol. 692, 2012, pp. 420-445)。我们的结果通过系统的三维数值模拟得到了验证。在论文的第二部分，我们首次给出了均匀涡度流的线性稳定性分析。为此，我们采用了不同的方法（Lifschitz & Hameiri, Phys）。《流体》，1991年第3卷，第2644页；格莱德泽和波诺马瑞夫，学术科学。苏联，伊兹夫。大气压。海洋。理论物理。，第13卷，1977年，第565-569页)，使我们能够推断出不稳定性增长率的上界和下界。分析表明，均匀涡度基流容易发生由参数共振机制引起的惯性不稳定性。一组直接数值模拟证实了这一点。将我们的结果应用到行星设置中，我们发现在月球、木卫一和水星的液体核心中既不存在自旋共振，也不存在惯性不稳定性。
Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a resonance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir & Cébron, J. Fluid Mech., vol. 737, 2013, pp. 412–439). This theoretical approach is consistent with the results of Chan et al. (Phys. Earth Planet. Inter., vol. 187, 2011, pp. 404–415) and Zhang et al. (J. Fluid Mech., vol. 692, 2012, pp. 420–445) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear stability analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz & Hameiri, Phys. Fluids A, vol. 3, 1991, p. 2644; Gledzer & Ponomarev, Acad. Sci., USSR, Izv., Atmos. Ocean. Phys., vol. 13, 1977, pp. 565–569) that allow us to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.