Fluid flows reveal a wealth of structures, such as vortices and barriers to transport. Usually, either an Eulerian or a Lagrangian frame of reference is employed in order to detect such features of the flow. However, the two frameworks detect structures that have different properties. Indeed, common Eulerian diagnostics (Hua-Klein and Okubo-Weiss criterion) employed in order to detect vortices do not always agree with Lagrangian diagnostics such as finite-time Lyapunov exponents. Besides, the former are Galilean-invariant whereas the latter is objective. However, both the Lagrangian and the Eulerian approaches to coherent structure detection must show some links under any inertial-frame. Compound channels flows have been accurately studied in the past, both from a Lagrangian and an Eulerian point of view. The features detected do not superimpose: Eulerian vortices do not coincide with barriers to transport. The missing link between the two approaches is here recovered thanks to a spectral analysis.

中文翻译：

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复合通道中有限时间李雅普诺夫指数的欧拉谱

流体流动揭示了丰富的结构，例如涡流和运输障碍。通常，使用欧拉或拉格朗日参考系来检测流的此类特征。但是，这两个框架检测具有不同属性的结构。实际上，用于检测涡流的常见欧拉诊断（Hua-Klein 和 Okubo-Weiss 判据）并不总是与拉格朗日诊断一致，例如有限时间李雅普诺夫指数。此外，前者是伽利略不变的，而后者是客观的。然而，拉格朗日和欧拉相干结构检测方法必须在任何惯性系下显示一些联系。过去曾从拉格朗日和欧拉的角度准确地研究了复合通道流。检测到的特征不叠加：欧拉涡旋与运输障碍不重合。由于光谱分析，这里恢复了两种方法之间缺失的链接。