标题： 流体流动中粘度的变化 显示英文标题

标题： Viscosity variation in fluid flows across scale

摘要： 广泛范围的自然和工程流体流动表现出空间或时间的粘度变化，尺度从微生物运动到行星地幔对流。这些变化引入了在恒定粘度流动中不存在的定性新物理机制。本综述调查了这些现象在不同尺度上的表现。在低雷诺数（斯托克斯）流动中，粘度梯度将平移和旋转耦合，使粒子对均匀作用力产生新的响应机制——微生物可能利用这些机制。在剪切流动中，粘度变化改变基础流动轮廓并破坏对称性，从而修改稳定性及过渡动力学。在高雷诺数情况下，分层从根本上改变了控制能量产生的奇异摄动结构，增强或抑制经典不稳定性并引入新的不稳定性。粘度变化还影响非正规增长和非线性相互作用，这些是导致湍流过渡的动力。尽管层流和充分发展的湍流已被广泛研究，但在变粘度流动中过渡过程仍知之甚少。在湍流区域，粘度变化影响射流、壁面约束流动和混合层。在地球物理尺度上，在气候模型中引入涡旋粘度分层可能提高预测精度，而在地球地幔中，粘度差异驱动大尺度对流和地质演化。颗粒载流体在各种情况下都很常见，可以通过不均匀加载产生有效粘度分层。在整个过程中，我们强调粘度变化定性改变流动行为的情况，并指出开放性问题。本综述旨在引导研究生和研究人员关注可行的跨学科问题。 显示英文摘要

摘要： A wide range of natural and engineered fluid flows exhibit spatial or temporal viscosity variations, spanning scales from microbial locomotion to planetary mantle convection. These variations introduce qualitatively new physical mechanisms absent in constant-viscosity flows. This review surveys such phenomena across scales. In low Reynolds number (Stokes) flows, viscosity gradients couple translation and rotation, enabling novel particle responses to uniform forcing-- mechanisms that microorganisms may exploit. In shear flows, viscosity variation alters base flow profiles and breaks symmetries, modifying stability and transition dynamics. At high Reynolds numbers, stratification fundamentally changes the singular perturbation structure governing energy production, enhancing or suppressing canonical instabilities and introducing new ones. Viscosity variation also affects nonnormal growth and nonlinear interactions that drive transition to turbulence. While laminar and fully developed turbulence have been extensively studied, transitional processes remain poorly understood in variable-viscosity flows. In turbulent regimes, viscosity variation impacts jets, wall-bounded flows, and mixing layers. At geophysical scales, incorporating eddy viscosity stratification in climate models may improve predictions, while in Earth's mantle, viscosity contrasts drive large-scale convection and geological evolution. Particle-laden flows, common across contexts, can generate effective viscosity stratification through inhomogeneous loading. Throughout, we highlight cases where viscosity variation alters flow behavior qualitatively, and point to open questions. This review aims to guide graduate students and researchers toward tractable, cross-disciplinary problems.