Landau Equation and Mean Flow Distortion in Nonlinear Stability Theory of Parallel Free Flows
Abstract
Weakly nonlinear stability theory of parallel flows is known to encounter a difficulty when it is applied to free shear layers, that is, the mean flow distortion induced by the disturbance does not satisfy the boundary conditions. A new formulation of the nonlinear stability theory of general parallel free flows is proposed by considering an initial value problem of a disturbance and taking a fasttimedependence of the induced flows into account. In this formulation, a nonsecular condition for the thirdorderterm gives the Landau equation and the difficulty concerning the mean flow distortion does not arise.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 August 1986
 DOI:
 10.1143/JPSJ.55.2641
 Bibcode:
 1986JPSJ...55.2641Y
 Keywords:

 Flow Distortion;
 Flow Stability;
 Free Flow;
 Parallel Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Flow Equations;
 LandauGinzburg Equations;
 Nonlinear Equations;
 Time Dependence;
 Fluid Mechanics and Heat Transfer