Abstract This paper presents numerical simulations of the natural laminar-turbulent transition in a flat plate boundary layer. Natural transition occurs in low disturbance environments and is triggered by the growth of boundary layer instabilities or disturbances. This contribution specifically aims at investigating the interaction of multiple disturbances and their effect on the transition mechanism. The numerical simulations employ a lattice Boltzmann method (LBM) in conjunction with a highly accurate cumulant collision operator and a shared memory multi-GPU framework. The numerical approach is validated by comparing the growth of single Tollmien-Schlichting (T-S) waves with results of the linear stability theory (LST) prior to transition. Moreover, a comprehensive comparison with available direct numerical simulation results (DNS) for the post transition and the fully turbulent regime confirms the validity of the employed numerical approach. Subsequently, the influence of disturbances on the transition process are investigated in detail and for different disturbance frequencies and amplitudes. Two types of natural transition scenarios (H- & K-type transition) are analyzed and the LBM results are compared to predictions of the classical eN-method. Both approaches are found to reproduce a similar frequency influence. Higher frequency T-S waves trigger an earlier transition until a critical frequency is reached, above which the boundary layer is stable. In addition, it is observed that in case of multiple interacting disturbances, the laminar-turbulent transition occurs earlier than predicted by simplified methods that eliminate the nonlinear interactions between disturbances. A spectral analysis of the velocity field then confirms that secondary disturbances are crucial for the resonance transition and can significantly accelerate the transition process. This paper offers a reproduction of the conventional LST map and furthermore the laminar-turbulent natural transition is comprehensively investigated using the LBM.

中文翻译：

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自然过渡平板边界层非线性相互作用的数值模拟

摘要 本文介绍了平板边界层中自然层流-湍流转变的数值模拟。自然过渡发生在低扰动环境中，由边界层不稳定性或扰动的增长触发。这一贡献专门旨在研究多重扰动的相互作用及其对过渡机制的影响。数值模拟采用格子 Boltzmann 方法 (LBM) 结合高精度累积碰撞算子和共享内存多 GPU 框架。通过比较单个 Tollmien-Schlichting (TS) 波的增长与过渡前线性稳定性理论 (LST) 的结果，验证了数值方法。而且，与过渡后和完全湍流状态的可用直接数值模拟结果 (DNS) 的综合比较证实了所采用数值方法的有效性。随后，详细研究了扰动对过渡过程的影响，并针对不同的扰动频率和幅度。分析了两种类型的自然过渡场景（H 型和 K 型过渡），并将 LBM 结果与经典 eN 方法的预测进行了比较。发现这两种方法都再现了类似的频率影响。更高频率的 TS 波触发更早的过渡，直到达到临界频率，高于该频率边界层是稳定的。此外，观察到在多个相互作用干扰的情况下，层流-湍流转变比通过消除扰动之间非线性相互作用的简化方法预测的要早。然后，速度场的频谱分析证实二次扰动对于共振转变至关重要，并且可以显着加速转变过程。本文提供了传统 LST 地图的再现，此外还使用 LBM 全面研究了层流-湍流自然过渡。