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 fast-time-dependence of the induced flows into account. In this formulation, a non-secular condition for the third-order-term 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;
- Landau-Ginzburg Equations;
- Nonlinear Equations;
- Time Dependence;
- Fluid Mechanics and Heat Transfer