Direct numerical simulations of hypersonic turbulent Couette flows are performed for top-wall Mach numbers of 6, 7 and 8, inspired by non-reactive high-enthalpy wind tunnel free-stream conditions, with the goal of analysing the physical processes driving the sub-filter-scale (SFS) stresses to inform development of large-eddy simulation techniques for hypersonic wall-bounded flows. Semi-local scaling laws collapse mean profiles and second-order turbulent statistics well, in spite of the strong wall-normal gradients of temperature and density. On the other hand, the SFS shear stresses exhibit an unexpected profile characterized by a region of pronounced shear stress deficit, which becomes more pronounced for higher Mach numbers. Instantaneous visualizations suggest that the SFS shear stress deficit is induced by the counter-gradient resolved momentum transport driven by residual velocity motions at the interface between high-density low-speed streaks being ejected away from the wall, and low-density high-speed ones replacing the displaced fluid, qualifying this as a compressibility effect. It is shown that the SFS shear stresses are primarily driven by second-order interactions between residual velocities, in spite of their triply nonlinear nature. This, in turn, motivated a statistical quadrant analysis revealing the presence of a SFS shear stress deficit, that is, SFS processes driving momentum transport of the resolved field towards the top wall. Additionally, higher-Reynolds-number simulations reveal that there is an upper limit of spatial filter widths to resolve large-scale structures, and such deficit is observable at any Reynolds number when a reasonable spatial filter is applied.

中文翻译：

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高超声速湍流库埃特流中的亚过滤尺度剪应力分析

受非反应性高焓风洞自由流条件的启发，对顶壁马赫数为 6、7 和 8 的高超声速湍流库埃特流进行了直接数值模拟，目的是分析驱动子流的物理过程。滤波器尺度（SFS）强调为高超声速壁界流大涡模拟技术的发展提供信息。尽管温度和密度的壁法向梯度很强，但半局部标度定律很好地瓦解了平均分布和二阶湍流统计。另一方面，SFS 剪应力表现出意想不到的轮廓，其特征是存在明显的剪应力不足区域，这在马赫数较高时变得更加明显。瞬时可视化表明，SFS 剪切应力不足是由从壁喷射的高密度低速条纹与低密度高速条纹之间的界面处的残余速度运动驱动的反梯度解析动量传输引起的替换排出的流体，将其视为压缩效应。结果表明，SFS 剪应力主要由残余速度之间的二阶相互作用驱动，尽管其具有三重非线性性质。这反过来又激发了统计象限分析，揭示了 SFS 剪切应力缺陷的存在，即 SFS 过程驱动解析场向顶壁的动量传输。此外，较高雷诺数模拟表明，解析大型结构的空间滤波器宽度存在上限，并且当应用合理的空间滤波器时，在任何雷诺数下都可以观察到这种缺陷。