On Mixing by Trade-Wind Cumuli

Mixing processes associated with tropical marine boundary-layer cumuli are examined with a one-dimensional, steady-state model of the cloud and inversion layers which explicitly differentiates between cloud-scale and subcloud-scale motions. Physically, the clouds are modelled as an ensemble average of well-mixed turbulent bursts into an otherwise quiescent, subsiding environment. The cloud-base vertical velocity distribution is found from a new closure based on a simplified vertical momentum budget. The clouds are described by two free parameters; fractional area and a detrainment time scale. Faster detrainment rates are shown to be associated with undiluted clouds, in the sense that the cloud entrainment rate becomes zero. For this case, the cloud-scale `fluxes dominate the boundary-layer mixing. Conversely, slower detrainment and large entrainment imply a diluted cloud, with the boundary-layer mixing dominated by the subcloud-scale turbulence. Simple qualitative arguments show that the vertically averaged temperature perturbation of the clouds is small and that increases in cloud-base moist static energy fluxes lead to enhancement of the cloud-top entrainment instability and vertical mixing associated with increasingly larger scales.