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Stability in a plane channel flow with viscosity stratification

Date: 
Friday 12th September 2008 - 10:40 to 11:00
Venue: 
INI Seminar Room 1
Session Chair: 
T Mullin
Abstract: 
We discuss the stability of a channel flow with viscosity stratification. Three mechanisms of route to transition, namely linear, transient and secondary instability growths are investigated here. How does a viscosity-stratification alter the stability behaviour of these mechanisms in a channel flow? A temperature dependent viscosity is used obtain the viscosity gradients. It is concluded that all three routes to transition has different stability characteristics for any given kind of stratification. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Rayleigh-Benard and Poiseuille modes for Grashof numbers upto $\sim 25000$, which merge thereafter. We conclude that a knowledge of transition mechanism and type of stratification is necessary for viscosity variation to be exploited as an effective flow control mechanism.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons