Evolution of Turbulence from the Rayleigh-Bénard Instability

Abstract

Measurements of heat transport through horizontal layers of fluid heated from below are reported for three aspect ratios $\Gamma (\Gamma =\frac{D}{2d}, D=\mathrm{diameter}, d=\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{cells})$.They show that for $\Gamma =57\mathrm{}$ the fluid flow is turbulent, in the sense that it has an a nonperiodic time dependence, for numbers $R>\mathrm{}{R}_t$ with $R_t\cong R_c \left(R_c\right)$ is the critical $R$ for onset of fluid flow). For $\Gamma =4.72\mathrm{}$, we find $R_t\cong 2R_c$. For $\Gamma =2.08\mathrm{}$, a quasiperiodic state exists for $R_p<~R<~R_t$, with $R_p\cong 10R_c$ and $R_t\cong 11R_c$.