Abstract
A two-scale model of convective disturbances is developed in which the larger scale describes the disturbance as a whole and the smaller scale consists of convective turbulence. A novel formulation for the turbulence is developed in the context of a one-dimensional model for the disturbance scale flow. The convective turbulence scheme assumes that vertical mixing occurs when and only when an unstable lapse rate is present. The intensity of the mixing is explicitly computed via a linearized model for the turbulence, coupled with scaling arguments. The model is ultimately applied to moist convection over a heated island. Intense vertical mixing occurs near the top of the resulting cloud. This mixing has a strong effect on the mean cloud circulation, resulting in inflow top and bottom and outflow around the middle. This is in marked contrast to the ascending bubble structure that occurs when such mixing is suppressed. The results confirm the arguments of Fraser (1968).
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