Experimental and numerical results cannot yet settle whether, between horizontal coaxial cylinders, if the curvature is large, the first transition for convection is an exchange of stability or rather an Hopf bifurcation. We directly show that if the curvature tends to infinity, no periodic linear perturbation exists when the Rayleigh number is equal to the critical one for nonlinear stability.

中文翻译：

---

关于水平环空对流的 Hopf 分岔的开始

实验和数值结果还不能确定，在水平同轴圆柱体之间，如果曲率很大，对流的第一个转变是稳定性的交换还是霍普夫分岔。我们直接证明，如果曲率趋于无穷大，当瑞利数等于非线性稳定性的临界数时，不存在周期性线性扰动。