在弯曲流中探测横向射流拉格朗日输送的障碍及其破坏
Detecting barrier to cross-jet Lagrangian transport and its destruction in a meandering flow
摘要：
本文研究了二维弯曲层流不可压流运动学模型中被动标量的横向喷流输运，该模型被认为能产生混沌混合。我们开发了一种方法，用于检测障碍物的交叉射流运输相空间，这是一个物理空间，我们的模型。使用非扭曲映射理论的工具，我们构建了一个中心不变曲线，并计算其特性，可以很好地指示存在一个中心传输障碍，它的强度和拓扑结构。计算分形维数，长度和缠绕数的曲线在参数空间中，我们详细研究了它的几何形状的变化和破坏所造成的局部分岔和一个全球分岔称为重连接的共振分离。对于奇共振和偶共振，重连的情形是不同的。中心不变曲线与有理和无理（贵族）值的缠绕数安排成层次系列，这是描述的连分数。在参数空间中，中心输运势垒的破坏有两种方式：沿着缠绕数为有理值的共振分叉曲线运动时，以及沿着缠绕数为有理值的曲线运动时.
英文摘要：
Cross-jet transport of passive scalars in a kinematic model of the meandering laminar two-dimensional incompressible flow which is known to produce chaotic mixing is studied. We develop a method for detecting barriers to cross-jet transport in the phase space which is a physical space for our model. Using tools from theory of nontwist maps, we construct a central invariant curve and compute its characteristics that may serve good indicators of the existence of a central transport barrier, its strength, and topology. Computing fractal dimension, length, and winding number of that curve in the parameter space, we study in detail change of its geometry and its destruction that are caused by local bifurcations and a global bifurcation known as reconnection of separatrices of resonances. Scenarios of reconnection are different for odd and even resonances. The central invariant curves with rational and irrational (noble) values of winding numbers are arranged into hierarchical series which are described in terms of continued fractions. Destruction of central transport barrier is illustrated for two ways in the parameter space: when moving along resonant bifurcation curves with rational values of the winding number and along curves with noble (irrational) values.
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