标题： 扭结和非扭结流场的拉伸行为 显示英文标题

标题： Stretching Behavior of Knotted and Unknotted Flow Fields

摘要： 涡旋拉伸是许多复杂流动的共同特征，包括湍流。孤立涡旋环的实验和模拟表明，这种行为也可以在相对简单的系统中观察到，并似乎依赖于涡旋拓扑结构。在这里，我们模拟了在环面上涡旋冻结流动场中物质线的输运。我们发现，打结配置会导致指数拉伸行为，这与由未打结组成的集合所观察到的行为定性不同。这种拉伸可以通过形成弯折来解释，即物质线中的尖锐弯曲，可用于预测拉伸率。通过计算流动场的有限时间李雅普诺夫指数来验证这种行为，这些指数表明指数拉伸是由涡旋线之间的弯折形成区域介导的。这项工作不仅建立了拓扑结构与拉伸行为之间的明确联系，还为打结流动中物质线的指数增长提供了一个直观的机制。 显示英文摘要

摘要： Vortex stretching is a common feature of many complex flows, including turbulence. Experiments and simulations of isolated vortex knots demonstrate that this behavior can also be seen in relatively simple systems, and appears to be dependent on vortex topology. Here we simulate the advection of material lines in the frozen flow fields of vortices on the surface of a torus. We find that knotted configurations lead to exponential stretching behavior which is qualitatively different than that observed by collections of unknots. This stretching can be explained by the formation of bights, sharp bends in the material lines which can be used to predict the stretching rate. This behavior is confirmed by computing the finite time Lyapunov exponents of the flow fields, which demonstrate the exponential stretching is mediated by bight forming regions between the vortex lines. This work both establishes a clear connection between topology and stretching behavior, as well as providing an intuitive mechanism for exponential growth of material lines in knotted flows.