A theoretical study of the first transition for the non-linear Stokes problem in a horizontal annulus

作者：Ferrario Carlo; Passerini Arianna^*

来源：International Journal of Non-Linear Mechanics, 2016, 78: 1-8.

DOI：10.1016/j.ijnonlinmec.2015.08.005

• Steady convective flows
• Critical Rayleigh number

For any aspect ratio R-o/R-i of the cylinder radii, the non-linear stability of the steady 2D-solutions of the non-linear Stokes system, which is an approximation of the Oberbeck-Boussinesq system, is theoretically studied. The sufficient condition for the stability shows a critical Ra which is a function of the aspect ratio. It is the same of the associated homogeneous linear problem and it can be found by looking for the largest eigenvalue of a suitable symmetric operator. The critical Ra so defined proves to be uniformly bounded from below in the space of dimensionless parameters, while it is non-uniformly bounded from above for the aspect ratio going to infinity. A scheme to evaluate it as a function of the aspect ratio is given. The results do not depend on the Prandtl number Pr.

• 出版日期2016-1