发表机构
Universitat Politècnica de Catalunya; Centre de Recerca Matemàtica; Leuphana Universität Lüneburg（加泰罗尼亚理工大学; 数学研究中心; 吕讷堡莱普纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过拉格朗日分析二维环形瑞利-贝纳德对流，提出新诊断方法，建立FTLE与羽流对应关系，并利用滑动窗口方法关联热通量，提出UBL厚度判据。
AI 中文摘要
为了深入了解由对流不稳定性产生的全局、长寿命相干流动结构如何自组织，我们从拉格朗日视角研究了这些不稳定性。我们考虑一个从内部均匀加热并受径向重力作用的二维环形流体层，并提出了几种新的拉格朗日诊断方法来表征其对流不稳定性。特别地，我们在广泛的无量纲参数范围内对流场进行了全面的拉格朗日分析，建立了对流羽流与有限时间李雅普诺夫指数（FTLE）场局部极大值曲线之间的启发式对应关系。此外，我们表征了对流卷内与流动非零曲率相关的相干涡旋运动。通过引入滑动窗口方法处理我们的有限时间运动学测量，我们展示了其与通过努塞尔数量化的径向热通量之间的直接关系，并识别出在两者上都留下痕迹的相关动力学转变。最后，我们提出了一种基于径向FTLE剖面确定粘性边界层（UBL）厚度的形式化判据，并与经典欧拉方法进行了验证。
英文摘要
Convective instabilities are studied from a Lagrangian perspective in order to gain new insights into how the resulting global, long-lived coherent flow structures organize themselves. We consider a 2D annular fluid layer uniformly heated from the inside and subject to radial gravity and propose several new Lagrangian diagnostics for characterizing its convective instabilities. In particular, we perform a comprehensive Lagrangian analysis of the flow field across a wide range of dimensionless parameters, establishing a heuristic correspondence between convective plumes and curves of local maxima of Finite-Time Lyapunov Exponent (FTLE) fields. Moreover, we characterize coherent swirling motions inside convective rolls, which are associated to the non-zero curvature of the flow. By introducing a sliding window method for our finite-time kinematic measures, we demonstrate a direct relationship with radial heat flux quantified by means of the Nusselt number and identify relevant dynamical transitions that leave a trace on both. Finally, we propose a formal criterion for determining viscous boundary layer (UBL) thickness by virtue of radial FTLE profiles and validated against a classical Eulerian method.
Comments24 pages, 11 figures and 1 table
