Turbulent convection is thought to act as an effective viscosity ($\nu_E$) in damping tidal flows in stars and giant planets. However, the efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency ($\omega$) exceeds the turnover frequency of the dominant convective eddies ($\omega_c$). We present the results of hydrodynamical simulations to study the interaction between tidal flows and convection in a small patch of a convection zone. These simulations build upon our prior work by simulating more turbulent convection in larger horizontal boxes, and here we explore a wider range of parameters. We obtain several new results: 1) $\nu_E$ is frequency-dependent, scaling as $\omega^{-0.5}$ when $\omega/\omega_c \lesssim 1$, and appears to attain its maximum constant value only for very small frequencies ($\omega/\omega_c \lesssim 10^{-2}$). This frequency-reduction for low frequency tidal forcing has never been observed previously. 2) The frequency-dependence of $\nu_E$ appears to follow the same scaling as the frequency spectrum of the energy (or Reynolds stress) for low and intermediate frequencies. 3) For high frequencies ($\omega/\omega_c\gtrsim 1-5$), $\nu_E\propto \omega^{-2}$. 4) The energetically-dominant convective modes always appear to contribute the most to $\nu_E$, rather than the resonant eddies in a Kolmogorov cascade. These results have important implications for tidal dissipation in convection zones of stars and planets, and indicate that the classical tidal theory of the equilibrium tide in stars and giant planets should be revisited. We briefly touch upon the implications for planetary orbital decay around evolving stars.

中文翻译：

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作用于平衡潮汐流的对流湍流粘度：有效粘度的新频率标度

湍流对流被认为是抑制恒星和巨行星潮汐流的有效粘度（$\nu_E$）。然而，这种机制的效率长期以来一直存在争议，特别是在快潮的情况下，当潮汐频率 ($\omega$) 超过主要对流涡旋的周转频率 ($\omega_c$) 时。我们展示了流体动力学模拟的结果，以研究一小块对流区中潮汐流和对流之间的相互作用。这些模拟建立在我们之前的工作基础上，通过在更大的水平盒子中模拟更多的湍流对流，在这里我们探索了更广泛的参数。我们获得了几个新结果：1) $\nu_E$ 是频率相关的，当 $\omega/\omega_c \lesssim 1$ 时缩放为 $\omega^{-0.5}$，并且似乎仅在非常小的频率 ($\omega/\omega_c \lesssim 10^{-2}$) 时才达到其最大常数值。以前从未观察到低频潮汐强迫的这种频率降低。2) $\nu_E$ 的频率相关性似乎遵循与低频和中频能量（或雷诺应力）频谱相同的标度。3）对于高频（$\omega/\omega_c\gtrsim 1-5$），$\nu_E\propto \omega^{-2}$。4) 能量占主导地位的对流模式似乎总是对 $\nu_E$ 贡献最大，而不是 Kolmogorov 级联中的共振涡流。这些结果对恒星和行星对流区的潮汐耗散具有重要意义，表明应该重新审视恒星和巨行星平衡潮汐的经典潮汐理论。