A Numerical Study of Atmospheric Convective Scaling

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Abstract
The phenomenon of selective scaling in shallow atmospheric convection is examined with the use of a two-dimensional, fine-resolution numerical model with a large domain aspect ratio. No extra model physics (such as latent heat release, eddy anisotropy, large-scale sinking motion, or radiative-entrainment effects) is incorporated in order to show that the preferred convective mode can be determined through the action of the nonlinear terms. The governing equations have the same form as that for Benard-Rayleigh convection, with the Rayleigh number being varied over approximately three orders of magnitude times supercritical. The scale of the convection in the steady state solutions is found to increase with Rayleigh number. At the largest Rayleigh numbers considered, the scale increases with time from initial modes with aspect ratio of roughly unity, to modes with aspect ratio larger by nearly one order of magnitude. The results, supported by radar and aircraft observations of boundary layer clear-air convection and mesoscale cellular convection, corroborate the evidence to suggest a mesoscale organization of small-scale convective elements into a system with a broad horizontal scale. Such a process may be attributable to the nonlinearity inherent in the shallow convection problem as demonstrated in these model simulations.

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