Michael Karp

Michael Karp




Wind Tunnel Complex 405

Transition to turbulence in wall-bounded shear Flows

Personal page:  http://mkarptx.github.io

Transition to turbulence in wall-bounded shear Flows

Albeit great advancement, transition to turbulence continues to be an intriguing subject, challenging many researchers worldwide. For many basic flows, the linear stability theory (LST) fails to predict the critical Reynolds number, where the flow becomes unstable to small disturbances. For example, plane Couette and pipe flows are linearly stable whereas in experiments transition is observed for Reynolds numbers as low as 350 for Couette flow and 2,000 for pipe flow. This has led to extensive theoretical, numerical and experimental work, in quest for a model that can predict transition. In particular, the promising scenario of transient growth, which proposed a mechanism where a combination of linearly stable modes can grow initially before its final decay due to viscous effects, trigger nonlinear interactions and transition. In addition, it has been observed that the late stages of transition in such flows are governed by several key coherent structures: counter-rotating vortex pairs, streaks and hairpins.

The present proposal is aimed to understand the transition processes in flows which are linearly stable to infinitesimal disturbances. The initial stage concentrated on the evolution of localized disturbances in homogenous shear flows and demonstrated that the key coherent structures mentioned above can be produced by such disturbances. For this purpose an analytical based method has been developed [‎1] and preliminary results were published in [‎2]. The research was then extended to include periodic (in space) disturbances in order to follow the formation of packets of hairpin vortices, which seem to precede the final breakdown to turbulence. The results of the model were compared successfully with direct numerical simulation (DNS) of transition in Couette flow and with experimental flow visualization in pipe flow [‎3].

In the rest of the research we plan to employ our knowledge regarding the formation of key coherent structures during the transition process to characterize and study the underlying mechanisms of transition to turbulence in Couette flow. Recently, we have discovered a simple analytical model which can predict analytically the linear transient growth scenario. The combination of our knowledge about the formation of the key coherent structures and the simple analytical model for transient growth will enable us to follow deeply into the late stages of the transition process using linear and nonlinear analytical tools, to be verified by DNS results.


  1. Cohen, J., Shukhman, I.G., Karp, M., and Philip, J., 2010 “An analytical-based method for studying the nonlinear evolution of localized vortices in planar homogenous shear flows”, J. Comput. Phys. 229, 7765-7773.
  2. Karp, M., Cohen, J. and Shukhman, I. “The evolution of localized Gaussian vortices in planar homogenous shear flows”. The 52nd Israel Annual Conference on Aerospace Sciences, Tel-Aviv and Haifa, Israel, Feb 29 – Mar 1, 2012.
  3. Cohen, J., Karp, M. and Mehta, V., 2014 “A minimal flow-elements model for the generation of packets of hairpin vortices in shear flows”. J. Fluid Mech. 747, 30–43.