Numerical solutions of the conservation equation of mass, momentum, and energy in two spatial dimensions and time have been carried out for two shallow convective envelopes (we consider only regions below the photosphere). Cells of a preferred width form and have growth rates larger than cells of other widths. Nonlinear effects substantially alter the velocity distribution (and hence every other quantity) from that of the linear calculations and introduce a pronounced asymmetry between upward and downward moving elements. Matter is found to flow from the top of the convection zone to the bottom, even when the depth of the convection zone is several pressure scale heights. (AIP)