Anomalous diffusion in fast cellular flows at intermediate time scales

• 成果类型: Article
• 署名作者: Iyer, Gautam; Novikov, Alexei
• 署名单位: Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0617-9
• 发表日期: 2016
• 页码: 707-740
• 关键词: periodic flows; random perturbations; hamiltonian flows; peclet numbers; shear flows; dispersion; transport

摘要

It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on intermediate time scales before diffusion sets in. Various heuristics suggest that an anomalous diffusive behaviour should be observed. We prove that the variance on intermediate time scales grows like . Hence, on these time scales the effective behaviour can not be purely diffusive, and is consistent with an anomalous diffusive behaviour.