A study of bifurcation of Kolmogorov flows with an emphasis on the singular limit
type: Item
instance of: scholarly article
title: A study of bifurcation of Kolmogorov flows with an emphasis on the singular limit
zbMATH Open document ID: 0905.76022
author: Hisashi Okamoto
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/225272
full work available at URL: Okamoto.MAN.html
review text: We consider a family of stationary Navier-Stokes flows on two-dimensional flat tori. The flow is driven by an external force which is of the form (\(\sin y\), \(0\)). Varying the Reynolds number and the aspect ratio of the torus, we numerically compute bifurcating solutions by a path-continuation method. Folds and cusps are obtained in the range where the Reynolds number is \(<100\). Some solutions are computed up until the Reynolds number becomes 10,000. Asymptotic properties as the Reynolds number tends to infinity are discussed. Also given is an analysis as the aspect ratio of the torus tends to zero.
Mathematics Subject Classification ID: 76M45
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1184389
zbMATH Keywords: internal layer
zbMATH Keywords: inviscid limit
zbMATH Keywords: folds
zbMATH Keywords: asymptotic properties
zbMATH Keywords: two-dimensional flat tori
zbMATH Keywords: path-continuation method
zbMATH Keywords: cusps
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184389