Subgrid modelling of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in astrophysical contexts

瑞利-泰勒（RT）不稳定性发生在当密度为pH的流体被较低密度为pL的流体加速或支撑以抵抗重力时。它影响着从惯性约束聚变到超新星爆炸的大雷诺数（Re）范围内的现象。当激波遇到声阻抗的不连续性（如密度阶跃）时，就会发生里希特迈尔-梅什科夫（RM）不稳定性。目前的三维数值模拟可以完全解决Re ~104时的不稳定性问题，至少在涉及简单流体力学的情况下是这样。然而，许多天体物理流动具有非常大的雷诺数（> 106），并且模拟不能正确地解决流体动力学不稳定性。在许多情况下，不稳定性变成非线性并产生湍流。这种流动的例子包括Ia型超新星中的湍流火焰和星系团中活动星系核吹出的空腔的演化。这样的流动演化自相似的涡流长度规模的混合区域的宽度成比例地增长。然后，亚网格或湍流模型是必要的，以描述流动的演变。这是一个在天体物理学应用中经常被忽视的问题，但却至关重要。我们建议实施和测试一个国家的最先进的子网格模型到一个自适应网格代码，并将其应用到天体物理设置。在本建议框架内制定的守则将向社会公布。

The Rayleigh-Taylor (RT) instability occurs when a fluid of density pH is accelerated or supported against gravity by a fluid of lower density pL. It affects phenomena from inertial confinement fusion to supernova explosions in the regime of large Reynolds number (Re). The Richtmyer-Meshkov (RM) instability occurs when a shock encounters a discontinuity in acoustic impedance such as at a density step. Today s three-dimensional numerical simulations can fully resolve these instabilities for Re ~104, at least as long as the flow involves simple hydrodynamics. However, many astrophysical flows have very large Reynolds numbers (> 106) and the simulations cannot properly resolve the hydrodynamical instabilities. In many cases, the instabilities become nonlinear and produce turbulence. Examples for such flows include the turbulent flames in type la Supernovae and the evolution of AGN-blown cavities in galaxy clusters. Such flows evolve self-similarly with an eddy length scale that grows in proportion to the width of the mixing region. Then, subgrid or turbulence models are necessary to describe the evolution of the flow. This is an issue that is routinely neglected in astrophysical applications but, yet, crucially important. We propose to implement and test a state-of-the-art subgrid model into an adaptive-mesh code and apply it to astrophysical settings. The code developed in the framework of this proposal will be made public to the community.