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arXiv 1907.01263physics.flu-dynphysics.geo-ph
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旋转球壳中热组分对流的起始

The onset of thermo-compositional convection in rotating spherical shells

Luis Silva, James F. Mather, Radostin D. Simitev

摘要:

在旋转球壳中,由热浮力和成分浮力驱动的双扩散对流可以表现出与单扩散系统不同的大量行为。为了了解热扩散系数和成分分子扩散系数的差异如何决定热成分对流的动力学,我们数值研究了双扩散设置中对流不稳定性的线性发作。我们构建了一个替代的等效配方的无量纲方程的线性化双扩散问题是由一个有效的瑞利数,$\text{Ra}$,测量的幅度相结合的浮力驱动,和第二个参数,$α$,测量混合的热和成分的贡献。这个公式是有用的,因为它允许几个极限情况下的分析,并揭示在参数空间中的动力学相似性,这是不明显的,否则。我们分析了在这个$\text{Ra}-α$空间中的临界曲线的结构,解释了在$α$中的渐近行为,惯性和扩散制度之间的过渡,以及大规模(快速漂移)和小规模(缓慢漂移)对流之间的过渡。我们进行这种分析的各种扩散率,旋转速率和壳的长宽比显示在何处和何时发生新的对流模式。

英文摘要:

Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviours often distinct from that of the single diffusive system. In order to understand how the differences in thermal and compositional molecular diffusivities determine the dynamics of thermo-compositional convection we investigate numerically the linear onset of convective instability in a double-diffusive setup. We construct an alternative equivalent formulation of the non-dimensional equations where the linearised double-diffusive problem is described by an effective Rayleigh number, $\text{Ra}$, measuring the amplitude of the combined buoyancy driving, and a second parameter, $α$, measuring the mixing of the thermal and compositional contributions. This formulation is useful in that it allows for the analysis of several limiting cases and reveals dynamical similarities in the parameters space which are not obvious otherwise. We analyse the structure of the critical curves in this $\text{Ra}-α$ space, explaining asymptotic behaviours in $α$, transitions between inertial and diffusive regimes, and transitions between large scale (fast drift) and small scale (slow drift) convection. We perform this analysis for a variety of diffusivities, rotation rates and shell aspect ratios showing where and when new modes of convection take place.

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