用二维流体动力学模拟检验动态剪切混合的一维公式
Testing a one-dimensional prescription of dynamical shear mixing with a two-dimensional hydrodynamic simulation
摘要：
混合过程的处理仍然是一维恒星演化模型的主要不确定性之一。这主要是由于需要在流体静力学代码中参数化和近似流体动力学方面。特别是，旋转恒星中的流体动力学不稳定性的影响，例如，动力学剪切不稳定性，逃避一致的描述。我们打算通过比较一维模型和相同初始条件下的第一原理流体力学模拟来研究流体静力学恒星演化模型中动力学剪切的扩散近似的准确性。我们选择了一个用恒星演化代码GENEC计算的初始模型，该模型正好处于动力学剪切不稳定性的开始，但没有显示出任何其他不稳定性（例如，对流）。这被映射到流体动力学代码SLH，以在赤道平面上进行2D模拟。我们比较了两个代码中得到的配置文件，并计算一个有效的扩散系数的水力模拟。在线性理论预测的区域中，在二维模拟中剪切不稳定性发展为在一维模型中变得不稳定。角速度和化学成分在不稳定区域中重新分布，从而产生新的不稳定区域。最终，2D模拟稳定在一个对称的稳定状态，这是理查森稳定的任何地方，而不稳定性保持在1D模型由于目前的限制，在1D代码更长的时间。通过比较平均原子质量的初始和最终分布，提取空间分辨扩散系数。所提出的模拟给出了第一个洞察剪切不稳定性在一个真实的恒星环境中的流体动力学，甚至允许我们直接提取一个有效的扩散系数。我们看到了临界Richardson数为0.25的证据，因为高于此值的区域在模拟过程中保持稳定。
英文摘要：
The treatment of mixing processes is still one of the major uncertainties in 1D stellar evolution models. This is mostly due to the need to parametrize and approximate aspects of hydrodynamics in hydrostatic codes. In particular, the effect of hydrodynamic instabilities in rotating stars, for example, dynamical shear instability, evades consistent description. We intend to study the accuracy of the diffusion approximation to dynamical shear in hydrostatic stellar evolution models by comparing 1D models to a first-principle hydrodynamics simulation starting from the same initial conditions. We chose an initial model calculated with the stellar evolution code GENEC that is just at the onset of a dynamical shear instability but does not show any other instabilities (e.g., convection). This was mapped to the hydrodynamics code SLH to perform a 2D simulation in the equatorial plane. We compare the resulting profiles in the two codes and compute an effective diffusion coefficient for the hydro simulation. Shear instabilities develop in the 2D simulation in the regions predicted by linear theory to become unstable in the 1D model. Angular velocity and chemical composition is redistributed in the unstable region, thereby creating new unstable regions. Eventually the 2D simulation settles in a symmetric, steady state, which is Richardson stable everywhere, whereas the instability remains for longer in the 1D model due to current limitations in the 1D code. A spatially resolved diffusion coefficient is extracted by comparing the initial and final profiles of mean atomic mass. The presented simulation gives a first insight on hydrodynamics of shear instabilities in a real stellar environment and even allows us to directly extract an effective diffusion coefficient. We see evidence for a critical Richardson number of 0.25 as regions above this value remain stable for the course of the simulation.
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