On the aspect ratio of Rayleigh-Benard convection cells

Numerical model calculations of isoviscous bottom-heated convection in a two-dimensional box with aspect ratio twelve are reported. The aim was to determine the preferred aspect ratio of convection cells. Time-dependent runs were started from two widely different initial conditions. At Rayleigh numbers in the range 10 to the 5th to 10 to the 6th about eight cells with a mean aspect ratio of 1.5 formed eventually in each case. Thus neither the preference for approximately square cells nor the stability of very elongated cells could be confirmed. The existence of large-scale convective structures in the earth's mantle must be due to deviations from the simple Rayleigh-Benard model of convection.