标题： 被动标量在光滑随机流中的分形等值线 显示英文标题

标题： Fractal iso-contours of passive scalar in smooth random flows

摘要： 我们考虑在泵浦、扩散和由具有拉格朗日混沌的平滑流场进行对流作用下的被动标量场。 我们提出了理论论证，表明标量统计特性不是共形不变的，并制定了新的有效半解析算法来模拟标量湍流。 然后我们进行了大量关于被动标量湍流的数值计算，重点研究节点线的统计特性。 显示轮廓在尺寸和周长上的分布既不依赖于流场实现，也不依赖于超过$r_d$的分辨率（扩散）尺度。 发现标量等值线在大于$r_d$的尺度上是分形/平滑的，在小于$L$的尺度上是平滑/分形的。 我们通过洛瓦尔映射的驱动函数来表征长等值线的弯曲统计特性，显示其行为类似于扩散，扩散率与分辨率无关，但最令人惊讶的是，它取决于速度场实现和标量演化的时刻。 显示英文摘要

摘要： We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new effective semi-analytic algorithm to model the scalar turbulence. We then carry massive numerics of passive scalar turbulence with the focus on the statistics of nodal lines. The distribution of contours over sizes and perimeters is shown to depend neither on the flow realization nor on the resolution (diffusion) scale $r_d$ for scales exceeding $r_d$. The scalar isolines are found fractal/smooth at the scales larger/smaller than the pumping scale $L$. We characterize the statistics of bending of a long isoline by the driving function of the L\"owner map, show that it behaves like diffusion with the diffusivity independent of resolution yet, most surprisingly, dependent on the velocity realization and the time of scalar evolution.