Subcritical transition to turbulence in planar shear flows
Abstract
The twodimensional steady and time dependent properties of plane Poiseuille and plane Couette flows are analyzed using iterative techniques and full numerical simulation of the NavierStokes equations. It is shown that the finiteamplitude twodimensional states investigated are strongly unstable to very small threedimensional 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 threedimensional instability can be analyzed by a linear stability analysis of a twodimensional flow consisting of the basic parallel flow and a steady (or quasisteady) finiteamplitude twodimensional 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;
 NavierStokes Equation;
 Parallel Flow;
 Perturbation Theory;
 Planar Structures;
 Steady Flow;
 Three Dimensional Flow;
 Time Dependence;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer