The theory of isolated turbulent plumes given earlier is used to study a field of plumes. Each plume is immersed in the turbulent downdraft which comprises the return flow. The field of flow is specified by three parameters: the heat flux into the atmosphere at the surface, the depth of the convecting layer, and the intensity of turbulence at the surface (where turbulence is steadily generated by the wind) and where a plume element which leaves the surface returns there in a downdraft after a period of the order of 103 sec. The change in air properties during this period is of the essence of the problem. Since the process is driven by the changing density resulting from heating, the equations describing the field must be time-dependent in this essential respect. Wind is neglected, and the horizontal pressure gradient assumed to he the same at all heights.

The derived plume properties-size, temperature excess, upward velocity and turbulent intensity-are in agreement with observation. The formulation predicts a maximum possible depth for convection in the form of a field of plumes, depending on the magnitude of the heat flux and surface turbulence. As a result, it is suggested that the theory of a field of plumes could lead to a prediction of the onset of a different form of convection, such as on a larger scale, resulting from instabilities in the convecting layer as a whole.

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