Turbulent Convection at Very High Rayleigh Numbers and the Weakly Nonlinear Theory

To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version complete Boussinesq equations containing only one horizontal wavenumber. In light later observations robust large-scale circulation sweeping through convecting enclosures at high Rayleigh numbers, it is perhaps not an implausible point view from which to reexamine high-Rayleigh-number data. Here we compare past experimental data on convective heat transport numbers with predictions Herring’s model and, in fact, find excellent agreement. The has unknown parameter compared two free parameters present lowest-order least-squares power-law fit. We discuss why underlying simplistic physical picture, meant work slightly critical value few thousand, consistent when single revised, over some eleven decades number—stretching about million 1017.