标题： 梳状结构上的湍流扩散与反常扩散 显示英文标题

标题： Turbulence spreading and anomalous diffusion on combs

摘要： 本文提出了一种简单的模型来描述诸如混沌扩散或湍流溢出到稳定区域之类的过程。 在这个简单模型中，波在晶格上的非弹性共振相互作用是主要的传输方式。 结果显示，这种过程普遍导致波场的次扩散扩展。 这种扩展过程的分散性被发现仅取决于相互作用过程的类型（三波或四波），而不依赖于背后的特定不稳定性。 借助梳状几何结构的形式，推导出了场扩展的渐近输运方程。 结果可以概括为：渐近扩展遵循连续时间随机游走（CTRW），并且对应于用分数阶导数方程描述的动力学表述。 这些方程所涉及的分数指数通过梳状模型精确获得。 上述理论的一个特殊情况是当两个具有相反方向波矢的波耦合在一起形成零动量束缚态的情况。 这种情况被单独考虑，并与波状湍流自组织为带状流或阶梯状流动相关联。 总体而言，我们发现湍流扩展和阶梯状流动可以用相同的数学形式描述，使用非弹性波波相互作用的哈密顿量以及映射到梳状空间的程序。 理论上，梳状方法被视为一种替代更常见的准线性理论描述的方法。 讨论了本理论对聚变等离子体研究的一些影响，并给出了与现有观测和数值证据的比较。 显示英文摘要

摘要： This paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process is shown to result universally in a subdiffusive spreading of the wave field. The dispersion of this spreading process is found to depend exclusively on the type of the interaction process (three- or four-wave), but not on a particular instability behind. The asymptotic transport equations for field spreading are derived with the aid of a specific geometric construction in the form of a comb. The results can be summarized by stating that the asymptotic spreading pursues as a continuous-time random walk (CTRW) and corresponds to a kinetic description in terms of fractional-derivative equations. The fractional indexes pertaining to these equations are obtained exactly using the comb model. A special case of the above theory is a situation when two waves with oppositely directed wave vectors couple together to form a bound state with zero momentum. This situation is considered separately and associated with the self-organization of wave-like turbulence into banded flows or staircases. Overall, we find that turbulence spreading and staircasing could be described based on the same mathematical formalism, using the Hamiltonian of inelastic wave-wave interactions and a mapping procedure into the comb space. Theoretically, the comb approach is regarded as a substitute for a more common description based on quasilinear theory. Some implications of the present theory for the fusion plasma studies are discussed and a comparison with the available observational and numerical evidence is given.