Cumulus Convection in Shear Flow—Three-Dimensional Numerical Experiments

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Abstract
A three-dimensional model of deep, moist convection is described. The model is fully compressible and utilizes a “time-splitting” method of integration in order to make the model economically feasible. This study represents an extension of the numerical experiments reported by Cotton (1975). In that work the profiles of the ratio of average cloud water content to the moist-adiabatic water content (Q̄c/QA) predicted by a one-dimensional Lagrangian (1DL) and a one-dimensional time-dependent (1DTD) model are compared with case study observed data and the average Q̄c/QA profiles reported by Warner (1970a). In this work, data predicted by a three-dimensional (3D) cloud simulation in a stagnant environment and a 3D cloud simulation in the observed shear flow are compared with observed data and the earlier model calculations. The results of this study demonstrated that all the cloud simulations in an initially stagnant environment, including the 1DL, 1DTD and 3D models, predicted profiles of Q̄c/QA which exhibited very high magnitudes near the top of the rising cloud. The predicted magnitudes of Q̄c/QA near the top of the rising cloud exceeded the observed magnitude by as much as a factor of 3. In contrast, the 3D simulation in the observed shear flow predicted profiles of Q̄c/QA and magnitudes of peak Q̄c/QA which were in good agreement with observations. What is most surprising is that the improved prediction of cloud liquid water content was not at the expense of the prediction of cloud-top height. Instead the cloud-top heights predicted in both the no-motion and shear-flow simulations were identical and equal to the observed cloud-top height. This is in contrast to the earlier 1DL and 1DTD model numerical experiments reported by Cotton using the same sounding. In those calculations, predicted cloud-top height varied considerably (over several kilometers) with different entrainment rates and eddy exchange coefficients. As a further benefit, the prediction of cloud-scale averaged vertical velocity in the shear-flow simulation was also better than that predicted in the no-motion simulation. It is thus concluded that the interaction of a cumulus cloud with an environment characterized by vertical shear of the horizontal wind is a major control on the prediction of cloud internal properties. Associated with the improved prediction of Q̄c/QA, the 3D simulation in shear flow also exhibited major changes in the structure of the cloud circulation. A particularly interesting feature was the formation of rotating cloud elements in several portions of the main cloud element.

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