Subcritical transition to turbulence in planar shear flowsThe 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.
Document ID
19820028910
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Orszag, S. A. (Massachusetts Inst. of Tech. Cambridge, MA, United States)