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

瑞利-泰勒（RT）不稳定性发生在密度为pH的流体被密度较低的pL的流体加速或支撑以对抗重力时。它影响从惯性约束聚变到大雷诺数（Re）下的超新星爆炸等现象。richhtmyer - meshkov （RM）不稳定性发生在冲击遇到声阻抗的不连续时，例如在密度阶跃处。今天的三维数值模拟可以完全解决Re ~104的这些不稳定性，至少只要流动涉及简单的流体力学。然而，许多天体物理流具有非常大的雷诺数（> - 106），模拟不能很好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la型超新星的湍流火焰和星系团中agn吹空腔的演化。这种流动以自相似的方式演化，其涡长尺度与混合区域的宽度成正比。然后，需要亚网格或湍流模型来描述流动的演变。这是一个在天体物理学应用中经常被忽视的问题，但却是至关重要的。我们建议在自适应网格代码中实现和测试最先进的子网格模型，并将其应用于天体物理设置。在此提案框架内制定的代码将向社区公开。

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.