AI 中文总结
该研究通过数值模拟揭示了不可混溶瑞利-泰勒湍流中表面张力对界面动力学、能量级联及气泡液滴演化的控制规律，为相关大涡模拟提供了物理框架。
AI 中文摘要
我们采用具有不同表面张力系数σ的数值模拟，研究不可混溶瑞利-泰勒湍流中的界面动力学与多尺度能量传递。研究表明，表面张力控制特征长度尺度、界面面积以及全局能量和拟能收支。该流动表现出与表面张力相关的自相似演化，最大动能按σ^(1/2)比例缩放，流动持续时间按σ^(-1/4)比例缩放。逐尺度收支分析显示，表面张力在大尺度移除动能，同时在小尺度注入动能，交叉发生在欣泽（Hinze）尺度附近。我们进一步重构并验证了表面张力功率与界面拉伸之间的局部运动学关系（至保守输运项）：f^σ·u = -σS|∇c| + Transport，其中f^σ为表面张力力，u为速度，c为重物体积分数，S为界面拉伸率。该关系将动能传递与标量方差级联关联，表明向界面的能量传递由局部应变控制。对单个气泡和液滴的统计显示，其具有直径约为3个毛细尺度的垂直细长丝状物，呈现线性体积-面积关系；它们的垂直速度与等效直径的平方根成比例，符合阻力-浮力平衡。这些发现，特别是表面张力功率与解析界面拉伸之间的直接联系，为开发不可混溶湍流大涡模拟的亚格子闭合模型提供了严谨的物理框架。
英文摘要
We investigate interfacial dynamics and multiscale energy transfer in immiscible Rayleigh-Taylor turbulence using numerical simulations with varying surface tension coefficients $σ$. Capillarity is shown to control characteristic length scales, interfacial area, and global energy and enstrophy budgets. The flow exhibits self-similar evolution with respect to surface tension, with the maximum kinetic energy scaling as $σ^{1/2}$ and the flow duration as $σ^{-1/4}$. A scale-by-scale budget shows that surface tension removes kinetic energy at large scales while injecting it at small scales, with the crossover occurring near the Hinze scale. We further recast and verify a local kinematic relationship between surface-tension power and interface stretching, up to conservative transport, $ \boldsymbol{f}^σ\cdot\boldsymbol{u} = - σ\mathcal{S}~|\nabla c| + \mathrm{Transport}$, where $\boldsymbol{f}^σ$ is the surface-tension force, $\boldsymbol{u}$ the velocity, $c$ the heavy-fluid volume fraction, and $\mathcal{S}$ the interface stretch rate. This relation links kinetic-energy transfer to the scalar-variance cascade and shows that energy transfer to the interface is governed by local strain. Statistics of individual bubbles and droplets reveal vertically elongated filaments with diameters of about three capillary scales, yielding a linear volume-area relation. Their vertical velocities scale with the square root of equivalent diameter, consistent with drag-buoyancy balance. These findings, particularly the direct link between surface tension power and resolved interface stretching, provide a rigorous physical framework for developing subgrid-scale closures for large eddy simulation of immiscible turbulent flows.
