Related Experiment Video
Updated: Jun 26, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Linear and nonlinear instabilities in rotating cylindrical Rayleigh-Bénard convection
Ligang Li1, Xinhao Liao, Kit H Chan
1Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China.
Abstract:
Linear and nonlinear convection in a rotating annular cylinder, under experimental boundary conditions, heated from below and rotating about a vertical axis are investigated. In addition to the usual physical parameters such as the Rayleigh and Taylor number, an important geometric parameter, the ratio of the inner to outer radius, enters into the problem. For intermediate ratios, linear stability analysis reveals that there exist two countertraveling convective waves which are nonlinearly significant: a retrograde wave located near the outer sidewall and a prograde wave adjacent to the inner sidewall. Several interesting phenomena of nonlinear convection are found: (i) tempospatially modulated countertraveling waves caused by an instability of the Eckhaus-Benjamin-Feir type, (ii) destructive countertraveling waves in which the existence or disappearance of the prograde wave is determined by its relative phase to the retrograde wave, and (iii) a saddle-node-type bifurcation in which the prograde wave takes an infinite amount of time to pass over the retrograde wave.
Related Concept Videos
Irrotational Flow
Steady, Laminar Flow in Circular Tubes
Steady, Laminar Flow Between Parallel Plates
Relating Angular And Linear Quantities - II
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Navier–Stokes Equations

