Instability of Plane Poiseuille Flow Caused by a Nonlinear, Nonperiodic and ThreeDimensional Disturbance
Abstract
By means of the Fourier transform, an amplitude expansion and a wavenumber expansion, the NavierStokes equation is reduced to a weakly nonlinear equation for the slowly varying complex amplitude of an envelope of a quasimonochromatic and weakly threedimensional disturbance. The reduced equation for the amplitude discloses severe condition of justification of the nonlinear Schrödinger type equation. The weak threedimensionality of disturbance as well as the weak nonperiodicity has significant effects on the instability of plane Poiseuille flow.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 February 1978
 DOI:
 10.1143/JPSJ.44.667
 Bibcode:
 1978JPSJ...44..667I
 Keywords:

 Flow Stability;
 Fourier Transformation;
 Laminar Flow;
 NavierStokes Equation;
 Two Dimensional Flow;
 Amplitude Modulation;
 Incompressible Flow;
 Nonlinear Equations;
 Parallel Flow;
 Schroedinger Equation;
 Wave Equations;
 Fluid Mechanics and Heat Transfer