In this paper, vortex-dynamical perspectives were adopted to interpret the recently reported observation that the total viscous dissipation of off-center droplet bouncing varies nonmonotonically with the impact parameter [C. He, X. Xia, and P. Zhang, “Non-monotonic viscous dissipation of bouncing droplets undergoing off-center collision,” Phys. Fluids 31, 052004 (2019)]. The particular interest of this study is on analyzing the velocity and vorticity vector fields and their correlations, such as helicity and enstrophy. The helicity analysis identifies a strong interaction between the “ring-shaped” vortices and the “line-shaped” shear layers in the non-axisymmetric droplet internal flow. A general relation between the total enstrophy and the total viscous dissipation rate for an unsteady free-surface flow was theoretically derived and numerically verified. It shows that the equality between the total enstrophy and the total viscous dissipation rate holds for a single-phase flow confined by stationary boundaries but is not satisfied for a gas–liquid two-phase flow due to the interfacial movement. Both the total enstrophy and a defined “half-domain” helicity show the nonmonotonic variation with the impact parameter, implying their interrelation with the nonmonotonic viscous dissipation.

中文翻译：

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偏心液滴弹跳非单调粘性耗散的涡旋动力学意义

在本文中，采用涡流动力学的观点来解释最近报道的观察结果，即偏心液滴弹跳的总粘性耗散随冲击参数的变化而非单调变化。他，X。Xia和P. Zhang，“偏离中心碰撞的弹跳液滴的非单调粘性耗散”，物理。流体31，052004（2019）]。这项研究的特别兴趣在于分析速度和涡度矢量场及其相关性，例如螺旋度和涡旋。螺旋分析确定了非轴对称液滴内部流动中“环形”涡旋和“线形”剪切层之间的强相互作用。理论上推导并数值验证了非稳态自由表面流的总涡旋和总粘性耗散率之间的一般关系。结果表明，总涡流和总粘滞耗散率之间的相等对固定边界限制的单相流成立，但由于界面运动对气液两相流不满足。