延迟时间对混沌平流反应标量空间结构的作用
The role of a delay time on the spatial structure of chaotically advected reactive scalars
摘要：
反应标量场的定态空间结构，混沌平流的二维大尺度流，检查的情况下，反应方程包含延迟项。先前的理论研究表明，在没有延迟项和扩散可以忽略的情况下（大的Péclet数），涌现的空间结构是非线性的，其特征在于具有单一标度区域的Hölder指数，该指数取决于反应过程的收敛速率和由平均拉伸速率测量的搅拌强度。在延迟项的存在下，我们表明，对于足够小的尺度，所有的相互作用领域应该共享相同的空间结构，在没有延迟项。根据搅拌的强度和延迟时间的大小，延迟系统特有的两个另外的缩放机制可能出现在中间长度尺度。给出了划分小尺度区和中尺度区的跃迁长度标度表达式，解释了标量场的标度行为。两种类型的反应模型，都是基于延迟微分方程，耦合到一个二维混沌平流的数值计算的理论结果进行说明。第一个对应于一个单一的反应标量和第二个非线性生物模型，包括营养物质，浮游植物和浮游动物。在无延迟的情况下，生物物种之间的非对称耦合的存在导致非通用的缩放行为。
英文摘要：
The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations have shown that, in the absence of delay terms and in a regime where diffusion can be neglected (large Péclet number), the emergent spatial structures are filamental and characterized by a single scaling regime with a Hölder exponent that depends on the rate of convergence of the reactive processes and the strength of the stirring measured by the average stretching rate. In the presence of delay terms, we show that for sufficiently small scales all interacting fields should share the same spatial structure, as found in the absence of delay terms. Depending on the strength of the stirring and the magnitude of the delay time, two further scaling regimes that are unique to the delay system may appear at intermediate length scales. An expression for the transition length scale dividing small-scale and intermediate-scale regimes is obtained and the scaling behavior of the scalar field is explained. The theoretical results are illustrated by numerical calculations for two types of reaction models, both based on delay differential equations, coupled to a two-dimensional chaotic advection flow. The first corresponds to a single reactive scalar and the second to a nonlinear biological model that includes nutrients, phytoplankton and zooplankton. As in the no-delay case, the presence of asymmetrical couplings among the biological species results in a non-generic scaling behavior.
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。
