Stability of nonplane-parallel three-dimensional jet flows
type: Item
instance of: scholarly article
title: Stability of nonplane-parallel three-dimensional jet flows
zbMATH Open document ID: 0648.76029
DOI: 10.1007/BF01051912
author: S. Ya. Gertsenshtejn
author: A. Ya. Rudnitskij
author: A. N. Sukhorukov
published in: Fluid Dynamics
publication date: 1987-01-01T00:00:00Z
review text: The problem of the stability of nonplane-parallel flows is one of the most difficult and least studied problems in the theory of hydrodynamic stability. In contrast to the Heisenberg approximation, the basic state whose stability is investigaed depends on several variables, and the stability problem reduces to the solution of an eigenvalue problem for partial differential equations in which the coefficients depend on several variables. In the case of a periodic dependence of these coefficients on the time or the spatial coordinates, the analog of Floquet theory for the partial differential equations is constructed. With rare exceptions, the case of a nonperiodic dependence has usually been considered under the assumption of weak nonplane-parallelism, i.e., a fairly small deviation from the plane-parallel case has been assumed and the corresponding asymptotic expansions in the linear and nonlinear stability analyses considered. The present paper considers the case of an arbitrary dependence of the velocity profile of the basic flow on two spatial variables. The deviation from the plane-parallel case is not assumed to be small, and the corresponding eigenvalue problem for the partial differential equations is solved by means of direct methods.
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4059016
zbMATH Keywords: nonplane-parallel flows
zbMATH Keywords: hydrodynamic stability
zbMATH Keywords: Heisenberg approximation
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: Floquet theory
zbMATH Keywords: weak nonplane-parallelism
zbMATH Keywords: nonlinear stability
MaRDI profile type: Publication
cites work: Q4114881
cites work: Q5778182
cites work: Development of finite-amplitude two-dimensional and three-dimensional disturbances in jet flows
full work available at URL: https://doi.org/10.1007/bf01051912
OpenAlex ID: W2051095619
description: scientific article; zbMATH DE number 4059016