Linear and Nonlinear Unstable 3D Waves for Boundary Layers in Differentially Heated Enclosures

1996 ◽  
pp. 55-64
Author(s):  
R. A. W. M. Henkes ◽  
P. Le Quéré
Keyword(s):  
Boundary Layers ◽  
Linear And Nonlinear ◽  
3D Waves

An alternative approach to linear and nonlinear stability calculations at finite Reynolds numbers

1984 ◽  
Vol 146 ◽  
pp. 313-330 ◽  
Author(s):  
F. T. Smith ◽  
D. Papageorgiou ◽  
J. W. Elliott
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Nonlinear Stability ◽  
Numerical Technique ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Interactive Approach ◽  
Boundary Layer Method ◽  
Linear And Nonlinear

An extended version of the interactive boundary-layer approach which has been used widely in steady-flow calculations is applied here to the linear and nonlinear stability properties of channel flows and boundary layers in the moderate-to-large Reynolds-number regime. This is the regime of most practical concern. First, for linear stability the agreement found between the interactive approach and Orr-Sommerfeld results remains fairly close even at Reynolds numbers as low as about$\frac{1}{10}$of the critical value for plane Poiseuille flow, or$\frac{1}{5}$for Blasius flow. Secondly, nonlinear unsteady calculations and comparisons with full solutions obtained by enlarging the same method are also presented. Overall the work suggests that, at the finite Reynolds numbers where real interest lies, the dominant physical processes of instability in channel flow and boundary layers are of boundary-layer form, with interaction, and it suggests also an alternative numerical technique for determining those processes. This alternative technique uses the interactive boundary-layer method as the central means for obtaining full unsteady Navier-Stokes solutions.

scholarly journals A Survey of Some Topics Related to Differential Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Denise Huet
Keyword(s):  
Applied Sciences ◽  
Differential Equations ◽  
Boundary Layers ◽  
Singular Perturbations ◽  
Spectral Properties ◽  
Differential Operators ◽  
Inertial Manifolds ◽  
Alphabetical Order ◽  
Linear And Nonlinear ◽  
Young Researchers

This paper is the result of investigations suggested by recent publications and completes the work of Huet, 2010. The topics, which are dealt with, concern some spaces of functions and properties of solutions of linear and nonlinear, stationary and evolution differential equations, namely, existence, spectral properties, resonances, singular perturbations, boundary layers, and inertial manifolds. They are presented in the alphabetical order. The aim of this document and of Huet, 2010, is to be a useful reference for (young) researchers in mathematics and applied sciences.

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