论文标题
自由核心营养及其与旋转模式的关系
Free Core Nutation and its relation to the Spin-Over Mode
论文作者
论文摘要
地球和其他行星向外部引力扭矩的旋转的时变响应很大程度上取决于它们的内部结构。特别是，已知在流体核心中称为自由核心营养的模式的存在，可以扩增近乎衰减的逆行频带中的强制营养（如行星参考框架中测量）。由于它们的形状和频率接近性，该模式有时等同于所谓的旋转模式，该模式表示稳定旋转的椭圆形流体核心的自由振荡。通过仔细研究具有刚性地幔和无粘性流体芯的自由旋转的两层行星模型，我们表明旋转模式频率与地幔上外部和内部扭矩的总和平衡，从而使其稳定旋转。核心壳边界的耗散的存在导致自由核心营养受到阻尼并稍微抵消其共振频率。我们表明，这种偏移量是地球的约1美元，可以解释为自由核心营养频率与旋转模式的近距离的结果，现在，该频率现在与营养转移函数的最小值相对应。我们还展示了这种接近度如何导致共振的质量略低于通常的公式。我们通过讨论这种机制对火星，月亮和地球的长期演变的可能含义来结束。
The time-varying response of the Earth's and other planets' rotation to external gravitational torques depends strongly on their internal structure. In particular, the existence of the mode known as the Free Core Nutation in the fluid core, is known to amplify the forced nutations in the near-diurnal retrograde frequency band (as measured in the planetary frame of reference). Due to their proximity in shape and frequency, this mode is sometimes equated with the so-called Spin-Over Mode which denotes the free oscillation of a steadily rotating ellipsoidal fluid core. Through a careful study of the freely rotating two-layer planetary model with a rigid mantle and an inviscid fluid core, we show that the Spin-Over Mode frequency corresponds to that where the sum of the external and internal torques on the mantle are balanced, causing it to rotate steadily. The presence of dissipation at the Core-Mantle Boundary causes the Free Core Nutation to become damped and slightly offset its resonance frequency. We show that this offset, which is $\approx-1$ day for the Earth, can be interpreted as the result of the proximity of the Free Core Nutation frequency to that of the Spin-Over Mode, which now corresponds to a minimum in the magnitude of the transfer function for nutations. We also show how this proximity leads to a slightly lower Quality factor for the resonance than that compute from the usual formula. We conclude by discussing possible implications of this mechanism for Mars, the Moon, and the long-term evolution of the Earth.
