The Energy Stability Limit for Flow in a Curved Channel

1976 ◽  
Vol 43 (4) ◽  
pp. 548-550 ◽  
Author(s):  
D. F. Jankowski ◽  
D. I. Takeuchi
Keyword(s):  
Poiseuille Flow ◽  
Stability Limit ◽  
Energy Stability ◽  
Instability Mechanism ◽  
Plane Poiseuille Flow ◽  
Energy Limit ◽  
Curved Channel ◽  
Linear Limit ◽  
The Difference ◽  
Flow Case

The energy stability limit is calculated for flow in a curved channel due to a pressure gradient acting around the channel. The energy limit is found among transverse disturbances and is of the same order for all channel radius ratios. The difference between the previously available linear limit and the energy limit increases dramatically as the instability mechanism changes, with radius ratio, from centrifugal force to viscosity in the limiting plane Poiseuille flow case.

Energy stability limit for rotation-modified plane Poiseuille flow

1977 ◽  
Vol 20 (12) ◽  
pp. 2149 ◽  
Author(s):  
Daniel F. Jankowski ◽  
David R. Squire
Keyword(s):  
Poiseuille Flow ◽  
Stability Limit ◽  
Energy Stability ◽  
Plane Poiseuille Flow

Subcritical convective instability Part 2. Spherical shells

1966 ◽  
Vol 26 (4) ◽  
pp. 769-777 ◽  
Author(s):  
Daniel D. Joseph ◽  
Shlomo Carmi
Keyword(s):  
Spatial Variation ◽  
Linear Theory ◽  
Internal Heat ◽  
Stability Limit ◽  
Critical Value ◽  
Energy Limit ◽  
Spherical Shells ◽  
Gravity Fields ◽  
The Difference ◽  
The Many

In this paper we consider the effect of internal heat generation and a spatial variation of the gravity field on the onset of thermal convection in spherical shells. If the temperature gradient and gravity fields have the same spatial variation, then initially quiet fluids are subcritically stable. For these flows the effect of inertially non-linear disturbances is not destabilizing if the Rayleigh number is below the critical value set by linear theory plus ‘exchange of stabilities’. For subcritically-stable flows a principle of exchange of stabilities is not necessary; a stronger statement of stability for the same stability limit can be made. For the many cases calculated here in which subcritical instabilities can exist, the difference between the linear and energy limits is small and can be contracted only toward the energy limit by an improved linear theory.

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