论文标题
缓慢旋转完全对流的星星或行星的潮汐消散效率
Efficiency of tidal dissipation in slowly rotating fully convective stars or planets
论文作者
论文摘要
湍流对流被认为是阻尼平衡潮流，在密切对流二元系统中驱动自旋和轨道进化的有效粘度。与混合长度预测相比，当潮汐频率$ |ω_t| $超过主流对流涡流的周转频率$ω_{cν} $时，应降低这种粘度，但是这种降低的效率已质疑。我们使用理想化的全球模型的直接数值模拟进行了长期存在的争议。 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 $|ω_t|/ω_{cν} \gtrsim 1$.我们证明，$ν_e$的频率降低与（不受干扰）对流的频率频谱相关。 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.然后，我们得到$ |ν_e| \ propto 1/|ω_t|^δ$带有$δ> 1 $，用于更高的频率，$δ= 2 $是为Kolmogorov湍流级联而获得的。通用$ |ν_e| \ Propto 1/|ω_t|^{2} $抑制是在对流的耗散范围内的较高频率（但为负值）。我们的结果表明，必须更好地了解对流的频谱，以准确预测这种机制导致的恒星和行星中潮汐耗散的效率。
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.
