标题： 一种多维脉动恒星包层的新框架 I：具有 SPHERLS 的静态 RR 导星包层中湍流对流的特性 显示英文标题

标题： A new framework of multidimensional pulsating stellar envelopes I.: Properties of turbulent convection in static RR Lyrae envelope models with SPHERLS

摘要： 上下文。 一维湍流对流处理在20世纪初直到2000年代初取得了巨大成功。 然而，最近观测数据的丰富性和精确性表明，这个问题远未解决。 应通过使用多维模型来开发一种现代方法。 目标。 我们建立了一个新的理论框架，用于比较一维和多维对流模型，通过映射对流区的二维结构并优化SPHERLS代码的建模参数。 方法。 我们为同一RR Lyrae恒星构建了一系列静态包层模型，但具有不同的水平尺寸和分辨率。 然后，我们使用一系列统计方法来量化对流涡旋的大小，映射能量级联，并描述对流区的不同结构部分。 这些包括积分长度尺度、傅里叶级数以及通过水平平均确定对流通量。 结果。 对流区的结构显著依赖于模型尺寸，在角尺寸小于$9^\circ$以下时尤为明显。 早期研究的水平分辨率足以描述大涡模拟方法中的granulation模式。 在准静态RR Lyrae恒星中，对流区由两个不同的动态不稳定区域组成，这两个区域连接松散。 大约一半的对流通量是由部分氢电离区中的电离能传输提供的。 结论。 本文中描述尺寸和分辨率参数的二维模型可用于与一维模型进行比较。 对流区的结构促使重新考虑一些近期用于径向恒星脉动代码中描述对流通量的方法，这将在另一篇论文中进行讨论。 显示英文摘要

摘要： Context. The one-dimensional treatment of turbulent convection had large successes until the early 2000s. However, the recent abundance and precision of observational data shows that this problem is far from solved. A modern approach should be developed by using multidimensional models. Aims. We established a new theoretical framework for comparison between one-dimensional and multidimensional convection models by mapping the two-dimensional structure of the convective zone and optimizing the modeling parameters of the SPHERLS code. Methods. We constructed a series of static envelope models for the same RR Lyrae stars, but with different horizontal sizes and resolutions. We then used a series of statistical methods to quantify the sizes of convective eddies, map the energy cascade, and describe the different structural parts of the convective zone. These include integral length scales, Fourier series, and the determination of the convective flux through horizontal averaging. Results. The structure of the convective zone depends significantly on the model size, below an angular size of $9^\circ$. The horizontal resolution of earlier studies is adequate to describe the granulation pattern in the large eddy simulation approach. In quasi-static RR Lyrae stars, the convective zone consists of two distinct dynamically unstable regions that are loosely connected. Approximately half of the convective flux is supplied by the transport of ionization energy in the partial hydrogen ionization zone. Conclusions. The 2D models presented in this work with the described size and resolution parameters can be used for comparison against 1D models. The structure of the convective zone urges reconsideration of some recent approaches to describe the convective flux currently used in radial stellar pulsation codes, which will be addressed in a separate paper.