轴对称几何中Beltrami流的统计力学：平衡和分叉
Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations
摘要：
我们刻画了轴对称Euler-Beltrami流的几何平衡态。它们具有呈现一个或多个细胞的连贯结构的形式。我们找到相关的控制参数，并推导出相应的状态方程。我们证明了对于给定的控制参数值，如在2D湍流中，几个平衡态共存[Chavanis和Sommeria，J. Fluid Mech.314，267（1996）]。我们探讨这些平衡态的稳定性，并表明，所有的状态是鞍点熵，原则上，可以通过一个更大的波数扰动不稳定，导致在最小的可用规模的结构。因此，这种机制让人想起3D Richardson能量级联，其尺度越来越小。因此，我们的系统是真正的2D湍流（相干结构）和3D湍流（能量级联）之间的中间。我们进一步探讨数值的鲁棒性的平衡态相对于随机扰动使用松弛算法在正则和微正则系综。我们表明，鞍点熵可以是非常强大的，因此发挥作用的动态。我们的证据的鲁棒性的解决方案中的典型和微正则系综的差异。提出了两种不同平衡（具有一个或两个单元）之间的分叉方案，并结合冯卡门实验中最近观察到的湍流分叉进行了讨论[Ravelet等人，物理修订信函93，164501（2004）]。
英文摘要：
We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding equations of state. We prove the coexistence of several equilibrium states for a given value of the control parameter like in 2D turbulence [Chavanis and Sommeria, J. Fluid Mech. 314, 267 (1996)]. We explore the stability of these equilibrium states and show that all states are saddle points of entropy and can, in principle, be destabilized by a perturbation with a larger wavenumber, resulting in a structure at the smallest available scale. This mechanism is therefore reminiscent of the 3D Richardson energy cascade towards smaller and smaller scales. Therefore, our system is truly intermediate between 2D turbulence (coherent structures) and 3D turbulence (energy cascade). We further explore numerically the robustness of the equilibrium states with respect to random perturbations using a relaxation algorithm in both canonical and microcanonical ensembles. We show that saddle points of entropy can be very robust and therefore play a role in the dynamics. We evidence differences in the robustness of the solutions in the canonical and microcanonical ensembles. A scenario of bifurcation between two different equilibria (with one or two cells) is proposed and discussed in connection with a recent observation of a turbulent bifurcation in a von Karman experiment [Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
