Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Linear Stability of Spiral Poiseuille Flow with a Radial Temperature Gradient: Centrifugal Buoyancy Effects



David Cotrell, Geoffrey B. McFadden


Instability of steady circular Couette flow with radial heating across a vertically oriented annulus with inner cylinder rotating and outer cylinder stationary is investigated using linear stability analysis. The convection regime base flow is developed for infinite aspect ratio and constant fluid properties where buoyancy is included through the Boussinesq approximation. Critical stability boundaries are calculated for this presumed base flow. Stability of mixed convection is tested with respect to both toroidal and helical disturbances of uniform wavenumber. The numerical investigation is primarily restricted to radius ratio (? = r1/r2) = 0.6 at Prandtl number 100. Critical stability boundaries in Taylor-Grashof number space are presented for two values of the stratification parameter ? (4 and 13). The results follow the development of critical stability from Taylor cells at small Grashof number up to a maximum Grashof number used in this calculation of 80000 and 20000 for g = 13 and 4, respectively. Results show that increasing the stratification parameter stabilize the isothermal Taylor vortices followed by a destabilization effect at higher azimuthal mode number (n > 0). The results also show that for ? = 4 (close to conduction regime), two modes are obtained: one is axisymmetric, and the other is non-axisymmetric. However, for the completely convection regime (boundary-layer type) six asymmetric modes are obtained. Finally, disturbance wavelength, phase speed, and spiral inclination angle are presented as a function of the critical Grashof number for the stratification parameters mentioned earlier.
Physics of Fluids


centrifugal buoyancy effects, linear stability, radial temperature gradient, spiral Poiseuille flow, Taylor Couette flow


Cotrell, D. and McFadden, G. (2005), Linear Stability of Spiral Poiseuille Flow with a Radial Temperature Gradient: Centrifugal Buoyancy Effects, Physics of Fluids (Accessed July 12, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created December 1, 2005, Updated February 19, 2017