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arXiv 1005.2397astro-ph.SRastro-ph.EP
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旋转物体中的动力潮汐：完全对流或正压恒星和行星中惯性波的数值研究

Dynamic tides in rotating objects: a numerical investigation of inertial waves in fully convective or barotropic stars and planets

J. C. B. Papaloizou, P. B. Ivanov

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to be published in MNRAS, resolution of several figures is reduced to comply with the size requirements
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摘要：

我们进行直接的数值模拟潮汐遇到一个旋转的行星上的高度偏心或抛物线轨道上的中心恒星制定为一个初始值问题。这种方法使我们能够扩展Ivanov和Papaloizou以前的工作，考虑固体核心的行星模型，并避免作出滞弹性近似。我们得到的无芯模型，使全球惯性模式被识别的潮汐响应的功率谱。他们的频率被发现是在良好的协议与那些使用WKBJ方法或滞弹性频谱的方法在以前的工作中采用的小行星旋转速率。我们还发现，在较高的旋转速率的情况下，行星角速度的正常模式的频率的依赖性，可以在很大程度上理解通过应用一阶微扰理论的滞弹性模式。我们计算的能量和角动量交换的潮汐相遇的结果，并为无芯模型再次找到良好的协议，使用任一滞弹性谱方法得到的结果。具有固体核心的模型显示出在临界纬度处的剪切层发射的证据，并且在遭遇之后可能有波吸引子，但是只要核心半径与总半径的比率小于50%，在遭遇期间交换的总能量与无核心情况没有显著差异，当该比率小于总半径的25%时，几乎没有任何差异。我们给出了这个结果的物理和数学解释。最后，我们能够验证滞弹性近似在这里提出的工作和我们之前的工作中的使用，这些工作导致了对高偏心轨道行星循环率的估计。

英文摘要：

We perform direct numerical simulations of the tidal encounter of a rotating planet on a highly eccentric or parabolic orbit about a central star formulated as an initial value problem. This approach enables us to extend previous work of Ivanov & Papaloizou to consider planet models with solid cores and to avoid making an anelastic approximation. We obtain a power spectrum of the tidal response of coreless models which enables global inertial modes to be identified. Their frequencies are found to be in good agreement with those obtained using either a WKBJ approach or the anelastic spectral approach adopted in previous work for small planet rotation rates. We also find that the dependence of the normal mode frequencies on the planet angular velocity in case of higher rotation rates can for the most part be understood by applying first order perturbation theory to the anelastic modes. We calculate the energy and angular momentum exchanged as a result of the tidal encounter and for coreless models again find good agreement with results obtained using either the anelastic spectral method. Models with a solid core showed evidence of the emission of shear layers at critical latitudes and possibly wave attractors after the encounter but the total energy exchanged during the encounter did not differ dramatically from the coreless case as long as the ratio of the core radius to the total radius was less than 50%, there being hardly any difference at all when this ratio was less than 25% of the total radius. We give a physical and mathematical interpretation of this result. Finally we are able to validate the use of the anelastic approximation for both the work presented here and our previous work which led to estimates of circularisation rates for planets in highly eccentric orbits.

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