Preferred horizontal scale for thermal convection

Linear stability theory for Rayleigh-Benard convection shows that for a specified Rayleigh number, greater than some critical value, only a finite range of horizontal wave numbers support convective instability in a horizontal layer of fluid heated from below. However, it is not possible to predict the preferred horizontal scale of established motions from this approach although it is clear from observations, particularly of the solar surface, that a preferred cell size does prevail. In an endeavour to establish a preferred horizontal scale appropriate non-linear model equations have been integrated forward in time, initially incorporating a discrete band of wave numbers equally spaced across the range that supports convection, for a specific Rayleigh number.