Current state-of-the-art models of the solar convection zone consist of solutions to the Navier-Stokes equations in rotating, 3D spherical shells. Such models are highly sensitive to the choice of boundary conditions. Here, we present two suites of simulations differing only in their outer thermal boundary condition, which is either one of fixed-entropy or fixed-entropy-gradient. We find that the resulting differential rotation is markedly different between the two sets. The fixed-entropy-gradient simulations have strong differential rotation contrast and isocontours tilted along radial lines (in good agreement with the Sun's interior rotation revealed by helioseismology), whereas the fixed-entropy simulations have weaker contrast and contours tilted in the opposite sense. We examine in detail the force balances in our models and find that the poleward transport of heat by Busse columns drives a thermal wind responsible for the different rotation profiles. We conclude that the Sun's strong differential rotation along radial lines may result from the solar emissivity being invariant with latitude (which is similar to the fixed-entropy-gradient condition in our models) and the poleward transport of heat by Busse columns. In future work on convection in the solar context, we strongly advise modelers to use a fixed-gradient outer boundary condition.

中文翻译：

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重新审视太阳沿径向线的强微分自转

当前最先进的太阳对流区模型包括旋转 3D 球壳中纳维-斯托克斯方程的解。这种模型对边界条件的选择高度敏感。在这里，我们展示了两组模拟，它们的不同之处仅在于它们的外部热边界条件，即固定熵或固定熵梯度之一。我们发现两组之间产生的差动旋转明显不同。固定熵梯度模拟具有很强的微分旋转对比度和沿径向线倾斜的等值线（与日震学揭示的太阳内部旋转非常吻合），而固定熵模拟具有较弱的对比度和相反方向倾斜的轮廓。我们详细检查了模型中的力平衡，并发现 Busse 柱向两极的热量传输驱动了导致不同旋转剖面的热风。我们得出结论，太阳沿径向线的强烈微分旋转可能是由于太阳辐射率随纬度不变（类似于我们模型中的固定熵梯度条件）和布斯柱向极地传输热量。在未来关于太阳环境中对流的工作中，我们强烈建议建模者使用固定梯度外边界条件。沿径向线的强烈差异旋转可能是由于太阳辐射率随纬度不变（类似于我们模型中的固定熵梯度条件）和布斯柱向极地传输热量。在未来关于太阳环境中对流的工作中，我们强烈建议建模者使用固定梯度外边界条件。沿径向线的强烈差异旋转可能是由于太阳辐射率随纬度不变（类似于我们模型中的固定熵梯度条件）和布斯柱向极地传输热量。在未来关于太阳环境中对流的工作中，我们强烈建议建模者使用固定梯度外边界条件。