Time‐dependent rotational stability of dynamic planets with elastic lithospheres
Time‐dependent rotational stability of dynamic planets with elastic lithospheres
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DOI：
10.1002/2013je004466
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发表时间：
2014-01
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影响因子：
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通讯作者：
N. Chan;J. Mitrovica;A. Daradich;J. Creveling;I. Matsuyama;S. Stanley
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作者：
N. Chan;J. Mitrovica;A. Daradich;J. Creveling;I. Matsuyama;S. Stanley
真极漂移（TPW）是旋转轴相对于固体的重新定向，由行星表面或内部的质量重新分布驱动，并通过行星粘弹性响应的两个方面来稳定：旋转凸起的延迟粘性重新调整和岩石圈中的弹性应力。后者继 Willemann (1984) 之后，被称为残余凸出稳定。在没有剩余核球的情况下，类地行星的自转据说本质上是不稳定的。已经开发出理论处理方法来处理这种情况下的最终（平衡）状态以及该状态的时间相关 TPW，包括假设惯性张量缓慢变化的非线性方法。此外，残余凸起稳定已被纳入平衡和线性化、时间相关的旋转稳定性处理中。我们扩展了 Ricard 等人的工作。 (1993) 推导了一种非线性、时间相关的 TPW 理论，该理论结合了残余凸起和旋转凸起的粘性重新调整的稳定性。我们使用应用于地球和火星模型的理想化表面载荷场景来说明该理论。我们证明，相对于忽略这种稳定的计算，包含残余凸起稳定会降低 TPW 的幅度和时间尺度。此外，考虑到目前对两颗行星地幔粘度的估计，我们的计算表明，响应时间尺度为 1 Myr 或更大的强迫而偏离旋转轴平衡方向对于地球来说很重要，但对于火星来说可以忽略不计。
True polar wander (TPW), a reorientation of the rotation axis relative to the solid body, is driven by mass redistribution on the surface or within the planet and is stabilized by two aspects of the planet's viscoelastic response: the delayed viscous readjustment of the rotational bulge and the elastic stresses in the lithosphere. The latter, following Willemann (1984), is known as remnant bulge stabilization. In the absence of a remnant bulge, the rotation of a terrestrial planet is said to be inherently unstable. Theoretical treatments have been developed to treat the final (equilibrium) state in this case and the time‐dependent TPW toward this state, including nonlinear approaches that assume slow changes in the inertia tensor. Moreover, remnant bulge stabilization has been incorporated into both equilibrium and linearized, time‐dependent treatments of rotational stability. We extend the work of Ricard et al. (1993) to derive a nonlinear, time‐dependent theory of TPW that incorporates stabilization by both the remnant bulge and viscous readjustment of the rotational bulge. We illustrate the theory using idealized surface loading scenarios applied to models of both Earth and Mars. We demonstrate that the inclusion of remnant bulge stabilization reduces both the amplitude and timescale of TPW relative to calculations in which this stabilization is omitted. Furthermore, given current estimates of mantle viscosity for both planets, our calculations indicate that departures from the equilibrium orientation of the rotation axis in response to forcings with timescale of 1 Myr or greater are significant for Earth but negligible for Mars.