The topology of fluid flow past a sequence of cylinders
type: Item
instance of: scholarly article
title: The topology of fluid flow past a sequence of cylinders
zbMATH Open document ID: 0940.37016
DOI: 10.1016/S0166-8641(98)00032-7
author: A. F. Sanjuan
author: James A. Yorke
author: C. Grebogi
author: Judy Kennedy
published in: Topology and its Applications
publication date: 2000-06-29T00:00:00Z
review text: This paper and an earlier, more physically oriented paper by the same authors [Chaos 7, No. 1, 125-138 (1997; Zbl 0967.76546)], treat a periodic differential equation in the plane. The differential equation models a fluid flow around a sequence of circular obstacles put with equidistant gaps along the \(x\)-axis. The flow is laminar some distance away from the \(x\)-axis. Based on numerical observations in this model, a number of properties for the period-map are assumed to hold. In particular, it is assumed that the period map possesses hyperbolic horseshoes in between consecutive obstacles. The unstable manifold of one such horseshoe is supposed to intersect the stable manifold of the horseshoe between the next obstacles. The structure of invariant sets and their unstable manifolds is described. Corresponding results are derived for systems with noise added. The set of points whose flow lines stay to the right of the starting point is proved to contain an indecomposable continuum.
reviewed by: Ale Jan Homburg
Mathematics Subject Classification ID: 37E35
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 76B99
zbMATH DE Number: 1317232
zbMATH Keywords: periodic differential equation in the plane
zbMATH Keywords: circular obstacles
zbMATH Keywords: unstable manifold
zbMATH Keywords: horseshoe
zbMATH Keywords: noise
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1317232