Onset of convective time dependence in cylindrical containers

Abstract

Thermal measurements probe time dependence in a convecting helium layer with cylindrical geometry and aspect ratios $\Gamma \equiv \frac{\mathrm{radius}}{\mathrm{height}}$ in the range $2.4<\mathrm{}\Gamma <22\mathrm{}$. For all $\Gamma$, there is a first transition at a Rayleigh number $R_1>R_c$ where convection begins at $R_c$. Time dependence occurs for $R>\mathrm{}{R}_1$ when $\Gamma \gtrsim 4$. The character of the transition at $R_1$ is identified over the full range of $\Gamma$. As $\Gamma$ becomes large $\frac{R_1}{R_c}\to 1.09$, a value which is difficult to reconcile with predictions for the expected skewed varicose instability.