Pulsatile channel and pipe flows constitute a fundamental flow configuration with significant bearing on many applications in the engineering and medical sciences. Rotating machinery, hydraulic pumps or cardiovascular systems are dominated by time-periodic flows, and their stability characteristics play an important role in their efficient and proper operation. While previous work has mainly concentrated on the modal, harmonic response to an oscillatory or pulsatile base flow, this study employs a direct–adjoint optimisation technique to assess short-term instabilities, identify transient energy-amplification mechanisms and determine their prevalence within a wide parameter space. At low pulsation amplitudes, the transient dynamics is found to be similar to that resulting from the equivalent steady parabolic flow profile, and the oscillating flow component appears to have only a weak effect. After a critical pulsation amplitude is surpassed, linear transient growth is shown to increase exponentially with the pulsation amplitude and to occur mainly during the slow part of the pulsation cycle. In this latter regime, a detailed analysis of the energy transfer mechanisms demonstrates that the huge linear transient growth factors are the result of an optimal combination of Orr mechanism and intracyclic normal-mode growth during half a pulsation cycle. Two-dimensional sinuous perturbations are favoured in channel flow, while pipe flow is dominated by helical perturbations. An extensive parameter study is presented that tracks these flow features across variations in the pulsation amplitude, Reynolds and Womersley numbers, perturbation wavenumbers and imposed time horizon.

中文翻译：

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脉动通道和管道流中的最佳能量增长

脉动通道和管道流动构成了一种基本的流动配置，对工程和医学科学中的许多应用具有重要意义。旋转机械、液压泵或心血管系统以时间周期流动为主，其稳定性特性对其高效和正常运行起着重要作用。虽然以前的工作主要集中在对振荡或脉动基流的模态谐波响应，但本研究采用直接伴随优化技术来评估短期不稳定性，识别瞬态能量放大机制并确定它们在宽参数内的普遍性空间。在低脉动幅度下，发现瞬态动力学类似于等效稳定抛物线流剖面产生的瞬态动力学，振荡流分量似乎只有微弱的影响。在超过临界脉动幅度后，线性瞬态增长显示出随脉动幅度呈指数增加，并且主要发生在脉动周期的缓慢部分。在后一种情况下，对能量转移机制的详细分析表明，巨大的线性瞬态增长因子是半个脉动周期内 Orr 机制和循环内正常模式增长的最佳组合的结果。二维曲折扰动在通道流动中是有利的，而管道流动主要是螺旋扰动。提出了一项广泛的参数研究，该研究在脉动幅度、雷诺数和沃默斯利数的变化中跟踪这些流动特征，