Stability of a radially bounded rotating fluid heated from below

The stability of a bounded rotating cylinder of fluid heated from below is treated mathematically under the assumptions of stationary onset and axisymmetry. Critical Rayleigh numbers are computed by Galerkin's method as a function of the Taylor number and cylinder aspect ratio for Taylor numbers,10⁶. The constraining effect of the side walls is shown to decrease with either increasing or increasing radius/height ratios. For>10⁶, most cylinders, excluding extremely tall ones, will appear infinite in horizontal extent as far as stability characteristics are concerned. The form of the motion at onset is discussed in relation to previous work.