Subcritical transition to turbulence in planar shear flows
Abstract
The two-dimensional steady and time dependent properties of plane Poiseuille and plane Couette flows are analyzed using iterative techniques and full numerical simulation of the Navier-Stokes equations. It is shown that the finite-amplitude two-dimensional states investigated are strongly unstable to very small three-dimensional perturbations. It is also shown, through full numerical simulation, that this explosive secondary instability can explain the subcritical transitions that occur in real flows. Finally, it is shown that the three-dimensional instability can be analyzed by a linear stability analysis of a two-dimensional flow consisting of the basic parallel flow and a steady (or quasi-steady) finite-amplitude two-dimensional cellular motion.
- Publication:
-
Transition and Turbulence
- Pub Date:
- 1981
- Bibcode:
- 1981trtu.proc..127O
- Keywords:
-
- Computational Fluid Dynamics;
- Couette Flow;
- Laminar Flow;
- Shear Flow;
- Subcritical Flow;
- Transition Flow;
- Flow Stability;
- Iterative Solution;
- Linear Equations;
- Navier-Stokes Equation;
- Parallel Flow;
- Perturbation Theory;
- Planar Structures;
- Steady Flow;
- Three Dimensional Flow;
- Time Dependence;
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer