Investigation of selfsimilar solutions describing flows in mixing layers
type: Item
instance of: scholarly article
title: Investigation of selfsimilar solutions describing flows in mixing layers
zbMATH Open document ID: 0632.76054
DOI: 10.1016/0021-8928(86)90125-5
author: V. N. Diesperov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: A complete investigation is made of the selfsimilar solutions of the boundary layer equation for the stream function with zero pressure gradient. They are a good description of the flow pattern in mixing layers since far from the separation point the latter is formed mainly under the effect of the boundary conditions and depends slightly on the initial conditions. The selfsimilar function \(\Phi\) (\(\zeta\) ;m) (\(\zeta\) is the selfsimilar variable, and m the selfsimilarity parameter) satisfies a well-known third-order nonlinear differential equation. It is successfully reduced to a first-order equation, which enables us to investigate the behaviour of all the integral curves of \(\Phi\) (\(\zeta\) ;m) and, in particular, the examination of the question of the existence and uniqueness of the solutions of the two- and three-point problems that occur in the theory of displacement layers. For \(m=1\) these are classical problems and the Blasius boundary layer problem and for \(m=2\) the Goldstein problem for the wake. The mixing layer encountered in the theory separations refers to the case \(m\in (1,2]\). The case \(m=\infty\) occurs in the theory of non-stationary separation. From the viewpoint of the behaviour of the integral curves, the cases \(m>1\) and \(0<m\leq 1\) differ substantially. For \(0<m\leq 1\) their pattern is reformed in such a manner that solutions describing the flows in mixing layers with reverse velocities do not occur.
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4029132
zbMATH Keywords: selfsimilar solutions
zbMATH Keywords: boundary layer equation
zbMATH Keywords: stream function with zero pressure gradient
zbMATH Keywords: mixing layers
zbMATH Keywords: separation point
zbMATH Keywords: initial conditions
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90125-5
OpenAlex ID: W2046854752
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description: scientific article; zbMATH DE number 4029132