Journal of Fluid Mechanics

Papers

Relevance of local parallel theory to the linear stability of laminar separation bubbles

Sourabh S. Diwana1 and O. N. Ramesha2 c1

a1 Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India

a2 Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India

Abstract

Laminar separation bubbles are thought to be highly non-parallel, and hence global stability studies start from this premise. However, experimentalists have always realized that the flow is more parallel than is commonly believed, for pressure-gradient-induced bubbles, and this is why linear parallel stability theory has been successful in describing their early stages of transition. The present experimental/numerical study re-examines this important issue and finds that the base flow in such a separation bubble becomes nearly parallel due to a strong-interaction process between the separated boundary layer and the outer potential flow. The so-called dead-air region or the region of constant pressure is a simple consequence of this strong interaction. We use triple-deck theory to qualitatively explain these features. Next, the implications of global analysis for the linear stability of separation bubbles are considered. In particular we show that in the initial portion of the bubble, where the flow is nearly parallel, local stability analysis is sufficient to capture the essential physics. It appears that the real utility of the global analysis is perhaps in the rear portion of the bubble, where the flow is highly non-parallel, and where the secondary/nonlinear instability stages are likely to dominate the dynamics.

(Received November 07 2011)

(Reviewed January 04 2012)

(Accepted February 01 2012)

(Online publication April 05 2012)

Key Words:

  • boundary layer separation;
  • boundary layer stability;
  • transition to turbulence

Correspondence:

c1 Email address for correspondence: onr@aero.iisc.ernet.in

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