The linear temporal stability of the fully developed pulsatile flow in a torus with high curvature is investigated using Floquet theory. The baseflow is computed via a Newton-Raphson iteration in frequency space to obtain basic states at supercritical Reynolds numbers in the steady case for two curvatures, $\delta =0.1$ and 0.3, exhibiting structurally different linear instabilities for the steady flow. The addition of a pulsatile component is found to be overall stabilizing over a wide range of pulsation amplitudes, in particular for high values of curvature. The pulsatile flows are found to be at most transiently stable with large intracyclic growth rate variations even at small pulsation amplitudes. While these growth rates are likely insufficient to trigger an abrupt transition at the parameters in this work, the trends indicate that this is indeed likely for higher pulsation amplitudes, similar to pulsatile flow in straight pipes. At the edge of the considered parameter range, subharmonic eigenvalue orbits in the local spectrum of the time-periodic operator, recently found in pulsating channel flow, have been confirmed also for pulsatile flow in toroidal pipes, underlining the generality of this phenomenon.

中文翻译：

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环形管道脉动流的流团稳定性分析

使用 Floquet 理论研究了高曲率环面中充分发展的脉动流的线性时间稳定性。基流通过频率空间中的牛顿-拉夫森迭代计算，以获得两个曲率稳定情况下超临界雷诺数的基本状态，$\delta =0.1$和0.3，表现出结构上不同的稳定流线性不稳定性。发现脉动分量的添加在较宽的脉动幅度范围内总体稳定，特别是对于高曲率值。发现脉动流至多是瞬时稳定的，即使在小的脉动幅度下也具有大的循环内增长率变化。虽然这些增长率可能不足以触发这项工作中参数的突然转变，但趋势表明，这确实可能适用于更高的脉动幅度，类似于直管中的脉动流。在所考虑的参数范围的边缘，最近在脉动通道流中发现的时间周期算子局部谱中的次谐波特征值轨道也已在环形管中的脉动流中得到证实，强调了这种现象的普遍性。