Tracking stages of transition in Couette flow analytically

Michael Karp
Timnat Prize Seminar, work towards Ph.D. degree under the supervision of Prof. Y. Cohen
Department of Aerospace Engineering
Technion – Israel Institute of Technology

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. A possible explanation for this phenomenon may be the transient growth mechanism where a combination of linearly stable modes can grow initially before its final decay due to viscous effects. During the initial growth nonlinear interactions may become significant and transition may occur.

In this talk a simple analytical model (consisting of only four modes) capable of predicting analytically the linear transient growth scenario. The analytical approximation allows performing a secondary linear stability analysis of the modified base flow consisting of the Couette flow and a transient growth disturbance. The predictions of the secondary stability analysis are verified by obtaining transition in a direct numerical simulation (DNS) initiated with the analytical expressions. The relatively small number of modes in the analytical approximation enables us to follow most of the process analytically.

The talk will be given in Hebrew

Wed, 05-11-2014, 16:30 (Gathering at 16:00)

Classroom 165, ground floor, Library, Aerospace Eng.

Light refreshments will be served before the lecture

Tracking stages of transition in Couette flow analytically