Considering the convection development scenario outlined in the previous section further, we can evaluate the convective velocities induced by the vertical and horizontal temperature differences, and compare their amplitudes.

The convective velocity induced by the vertical temperature difference

is obtained from ordinary boundary-layer theory:uThe velocity of convection beneath the plate

(10) is estimated by substituting foru'in (10) the value ofRain (8). In light of the comparison above with the numerical calculations, we divide equation (10) by to estimate the velocity amplitudes.Ra'Conversely, the velocity amplitude of the convection induced by the horizontal temperature difference

is determined by the dynamical balance of the equation of motion at steady state:u_{h}Differentiating (11) with respect to

(11) and using , we obtainzTemperature difference , is expressed as a function of the Rayleigh number using (5) and (9). The vertical scale of a convection cell is

(12) and the horizontal scale isL_{z}=1. Then we haveL_{x}We divide this equation by to evaluate the velocity amplitude, considering that the distributions of the temperature and stream function are approximately described by .

(13)