Boundary layer stability on a rotating disk with corotation of the surrounding fluid
type: Item
instance of: scholarly article
title: Boundary layer stability on a rotating disk with corotation of the surrounding fluid
zbMATH Open document ID: 0793.76040
DOI: 10.1007/BF01051606
author: S. V. Pikhtov
author: E. M. Smirnov
published in: Fluid Dynamics
publication date: 1994-04-12T00:00:00Z
review text: The paper treats the linear stability problem for the flow in the boundary layer on a rotating disk in a corotating fluid (generalized Karman problem). For values of \(\sigma\) (the ratio of angular velocity of the fluid and the disk) between \(\sigma =0\) (Karman flow) and \(\sigma=\infty\) (Bödewadt flow), the problem is solved by the collocation method. For all \(\sigma\geq 0\) the lower critical Reynolds number is determined by A-type instability waves typical of Eckman layers. B-type instabilities, associated with the occurrence of an inflection point in the velocity profile, typically manifest themselves as an ordered system of spiral vortices. Even though the critical Reynolds number of the A-type instability is several times smaller than the critical Reynolds number of spiral vortices, it has never been observed in rotating disk boundary layers. The authors argue that the low amplification rate of the A-type waves is the reason.
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 536775
zbMATH Keywords: Karman flow
zbMATH Keywords: Bödewadt flow
zbMATH Keywords: B-type instability
zbMATH Keywords: linear stability
zbMATH Keywords: collocation method
zbMATH Keywords: A-type instability
zbMATH Keywords: inflection point
reviewed by: Werner Koch
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01051606
OpenAlex ID: W2067405564
description: scientific article; zbMATH DE number 536775