High-resolution direct numerical simulations (DNS) were carried out to investigate the nonlinear breakdown process of a three-dimensional wave packet initiated by a short-duration pulse in a flared cone boundary layer at Mach 6 and zero angle of attack. For these simulations the cone geometry of the flared cone experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was considered. The computational domain covered a large extent of the cone in the azimuthal direction to allow for a wide range of azimuthal wavenumbers ( $k_{c}$ ) and to include shallow instability waves with small azimuthal wavenumbers. The simulation results indicated that the wave packet development was dominated by axisymmetric and shallow (small $k_{c}$ ) second-mode waves for a large downstream extent. Towards the downstream end of the computational domain a rapid broadening of the disturbance amplitude spectra was observed, which is an indication that the wave packet reached the strongly nonlinear stages. The disturbance spectra of the nonlinear regime, and the downstream amplitude development of the dominant disturbance wave components, provided conclusive evidence that the so-called fundamental breakdown was the dominant nonlinear mechanism. Furthermore, contours of the time-averaged Stanton number exhibited ‘hot’ streaks within the wave packet on the surface of the cone. Hot streaks have also been observed in the Purdue flared cone experiments using temperature sensitive paint (TSP) and in numerical investigations using DNS. The azimuthal streak spacing obtained from the wave packet simulation agrees well with that observed in the Purdue quiet tunnel experiments.

中文翻译：

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喇叭形锥体上 6 马赫边界层中的三维波包

进行高分辨率直接数值模拟 (DNS) 以研究由短持续脉冲在 6 马赫和零攻角的喇叭形锥形边界层中引发的三维波包的非线性击穿过程。对于这些模拟，考虑了在普渡大学的波音/AFOSR 马赫 6 安静隧道 (BAM6QT) 中进行的喇叭形锥体实验的锥体几何形状。计算域覆盖了方位角方向上的大部分锥体，以允许大范围的方位角波数 ($k_{c}$) 并包括具有小方位角波数的浅不稳定波。模拟结果表明，波包发展以轴对称和浅（小 $k_{c}$ ）第二模式波为主，下游范围大。在计算域的下游端，观察到扰动幅度谱的快速展宽，这表明波包达到了强非线性阶段。非线性状态的扰动谱以及主要扰动波分量的下游振幅发展提供了确凿的证据，证明所谓的基本击穿是主要的非线性机制。此外，时间平均斯坦顿数的轮廓在锥体表面的波包内表现出“热”条纹。在使用温敏涂料 (TSP) 的普渡喇叭形锥体实验和使用 DNS 的数值研究中也观察到了热条纹。