聚合物流体膜中非平衡涡旋晶体的熔化：弹性与流体turbulence
Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence
摘要：
我们进行了一个直接的数值模拟（DNS）的强制，不可压缩的二维纳维-斯托克斯方程耦合的FENE-P方程的聚合物构象张量。该强制使得在没有聚合物的情况下并且在低雷诺数$\mbox{Re}$下，膜达到稳定状态，该稳定状态是涡旋和反涡旋的正方形晶格。我们发现，当我们增加韦森伯格数$\mbox{Wi}$，一系列的非平衡相变转换这个晶格，首先空间扭曲，但时间稳定，晶体，然后到一个序列的晶体振荡的时间，周期性的，在低$\mbox{Wi}$，和准周期性的，稍大的$\mbox{Wi}$。最后，系统变得无序，表现出时空混沌和弹性湍流。然后，我们得到该系统的非平衡相图，在$\mbox{Wi} - Ω$平面，其中$Ω\propto {\mbox{Re}}$，并表明（a）之间的边界的结晶相和湍流相具有复杂的，分形型字符和（b）Okubo-Weiss参数$Λ$为我们提供了一个自然的措施，在这个图中的相位和过渡的特点。
英文摘要：
We perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers $\mbox{Re}$, the film attains a steady state that is a square lattice of vortices and anti-vortices. We find that, as we increase the Weissenberg number $\mbox{Wi}$, a sequence of nonequilibrium phase transitions transforms this lattice, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low $\mbox{Wi}$, and quasiperiodically, for slightly larger $\mbox{Wi}$. Finally, the system becomes disordered and displays spatiotemporal chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the $\mbox{Wi} - Ω$ plane, where $Ω\propto {\mbox{Re}}$, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter $Λ$ provides us with a natural measure for characterizing the phases and transitions in this diagram.
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