Journal ArticleDOI
Non-linear theory of unstable plane Poiseuille flow
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In this paper, a theoretical study of plane Poiseuille flow is made using the full non-linear Navier-Stokes equations, using a Fourier decomposition in the streamwise spatial variable and a Galerkin expansion in the lateral variable.Abstract:
A theoretical study of plane Poiseuille flow is made using the full non-linear Navier-Stokes equations. The mathematical technique employed is to use a Fourier decomposition in the streamwise spatial variable, a Galerkin expansion in the lateral variable and numerical integration with respect to time. By retaining the non-linear terms, the limit cycle oscillations of an unstable (in a linear sense) flow are obtained. A brief investigation of the possibility of instability due to large (non-linear) disturbances is also made. The results are negative for the cases examined. Comparisons with results previously obtained by others from linear theory illustrate the accuracy and efficacy of the method.read more
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Nonlinear cellular motions in Poiseuille channel flow
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Journal ArticleDOI
Hydrodynamic stability in plane Poiseuille flow with finite amplitude disturbances
W. D. George,J. D. Hellums +1 more
TL;DR: In this paper, a general method for studying two-dimensional problems in hydrodynamic stability is presented and applied to the classical problem of predicting instability in plane Poiseuille flow.
Book ChapterDOI
The Effects of Compliant Walls on Transition and Turbulence
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References
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Journal ArticleDOI
On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow
TL;DR: In this paper, the authors considered the nature of a non-linear, two-dimensional solution of the Navier-Stokes equations when the rate of amplification of the disturbance, at a given wave-number and Reynolds number, is sufficiently small.
Journal ArticleDOI
On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow
TL;DR: In this paper, a re-formulation of the Poiseuille flow problem is presented, which readily yields the complete solution for Couette flow, but this solution is only a formal one for the present because the conditions imposed in deriving the solution may not be valid for couette flow; this flow is believed to be stable to infinitesimal disturbances of the type considered.
Journal ArticleDOI
The stability of plane poiseuille flow
TL;DR: In this article, the fourth-order differential equation is replaced by a difference system of the same order with a truncation error involving the eighth derivative, so that the error is sufficiently small with a reasonably large interval.
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