arXiv 2007.133922020-07astro-ph.SRastro-ph.EPphysics.flu-dyn

缓慢旋转的完全对流恒星或行星中潮汐耗散的效率

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Jérémie Vidal, Adrian J. Barker

备注：: 14 pages, 17 figures, 1 table, published 6 August 2020 in MNRAS
DOI：: 10.1093/mnras/staa2239

摘要：

湍流对流被认为是一种有效的粘性阻尼平衡潮汐流，驱动自旋和轨道演化的封闭对流双星系统。与混合长度预测相比，当潮汐频率$|ω_t|$超过占主导地位的对流涡旋的周转频率$ω_{cν}$时，这种粘度应该减少，但这种减少的效率一直存在争议。我们重新审视这一长期存在的争议，使用一个理想化的全球模型的直接数值模拟。我们模拟了在一个完整的球体中的热对流，并在外部强迫的平衡潮汐流，测量有效粘度$ν_E$作用于潮汐流时，$|ω_t|/ω_{cν} \gtrsim 1$。我们表明，$ν_E$的频率降低与（未扰动）对流的频谱。对于低于湍流叶栅（$|ω_t|/ω_{cν} \sim 1-5$）中的中频，频谱显示出反常的$1/ω^α$幂律，该幂律导致频率降低$ν_E \propto 1/|ω_t|^α$，其中$α< 1$取决于模型参数。然后，我们得到了$|ν_E| \propto 1/|ω_t|^δ$与$δ> 1$的较高频率，和$δ=2$的Kolmogorov湍流叶栅。一般的$|ν_E| \propto 1/|ω_t|^{2}$抑制下发现较高的频率内的对流耗散范围（但与负值）。我们的研究结果表明，更好地了解对流的频谱是必要的，以准确地预测的效率潮汐耗散在恒星和行星中产生这种机制。

英文摘要：

Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency $|ω_t|$ exceeds the turnover frequency $ω_{cν}$ of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equilibrium tidal flow, to measure the effective viscosity $ν_E$ acting on the tidal flow when $|ω_t|/ω_{cν} \gtrsim 1$. We demonstrate that the frequency reduction of $ν_E$ is correlated with the frequency spectrum of the (unperturbed) convection. For intermediate frequencies below those in the turbulent cascade ($|ω_t|/ω_{cν} \sim 1-5$), the frequency spectrum displays an anomalous $1/ω^α$ power law that is responsible for the frequency-reduction $ν_E \propto 1/|ω_t|^α$, where $α< 1$ depends on the model parameters. We then get $|ν_E| \propto 1/|ω_t|^δ$ with $δ> 1$ for higher frequencies, and $δ=2$ is obtained for a Kolmogorov turbulent cascade. A generic $|ν_E| \propto 1/|ω_t|^{2}$ suppression is next found for higher frequencies within the dissipation range of the convection (but with negative values). Our results indicate that a better knowledge of the frequency spectrum of convection is necessary to accurately predict the efficiency of tidal dissipation in stars and planets resulting from this mechanism.

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