Weakly Nonlinear Analysis of a Localized Disturbance in Poiseuille Flow

In this article, we investigate, via a perturbation analysis, some important nonlinear features related to the process of transition to turbulence in a wall‐bounded flow subject to a spatially localized disturbance that is harmonic in time. We show that the perturbation expansion, truncated at secon...

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Bibliographic Details
Published in:Studies in applied mathematics (Cambridge) Vol. 105; no. 2; pp. 121 - 141
Main Authors: Ponziani, D., Casciola, C. M., Zirilli, F., Piva, R.
Format: Journal Article
Language:English
Published: Boston, USA and Oxford, UK Blackwell Publishers 01.08.2000
Blackwell
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Inviscid flows with vorticity
Laminar flows
Low-reynolds-number (creeping) flows
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Ordinary differential equations
Physics
Sciences and techniques of general use
Suction
Perturbation theory
Fluid dynamics
Partial differential equations
Eigenmode
Reynolds number
Digital simulation
Blowing
Equations of motion
Laplacian
Galerkin-Petrov method
Incompressible flow
Laminar flow
Poiseuille flow
Linearity
Vorticity
Boundary-value problems
Initial value problems
Interactions
Orr Sommerfeld equation
Navier-Stokes equations
ISSN:0022-2526, 1467-9590
Online Access:Get full text
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Summary:In this article, we investigate, via a perturbation analysis, some important nonlinear features related to the process of transition to turbulence in a wall‐bounded flow subject to a spatially localized disturbance that is harmonic in time. We show that the perturbation expansion, truncated at second order, is able to capture the generation of streamwise vorticity as a weakly nonlinear effect. The results of the perturbation approach are discussed in comparison with direct numerical simulation data for a sample case by extracting the contribution of the different orders. The main aim is to provide a tool to select the most effective nonlinear interactions to enlighten the essential features of the transitional process.
Bibliography:ark:/67375/WNG-D070GJV8-H
istex:AC8BD637A0800D8F22D3CF2F5A987FA933FD166D
ArticleID:SAPM145
ISSN:0022-2526
1467-9590
DOI:10.1111/1467-9590.00145