MODELLING OF INTERACTIONS AND TRANSFERS IN PASSIVE WARM CLOUDS. PART I: MODEL DEVELOPMENT AND PRELIMINARY ANALYSIS

Roger N’Dri Djue (Côte d’Ivoire), Emile Danho (Côte d’Ivoire), Moustapha Karam Sangare (Côte d’Ivoire), Bakary Coulibaly (Côte d’Ivoire) and Kouassi Kouassi Serge Yanga (Côte d’Ivoire)

Received December 10, 2007

Abstract

The present paper deals with the modelling of the interactions and transfers processes occurring during passive warm clouds development. The model developed here, presents the cloud as a whole. From this point of view, the microphysical processes can be seen as an ensemble of particles that contribute collectively and in an integrated way to the macroscale dynamics and thermodynamics of the cloud. The mathematical model that governs these processes is reduced to an algebraic equation in which two matrices, one named the interaction matrix and the other one the transfer matrix play a key role. The matrix of transfer is globally governed by the entrainment rate. This fact allowed us to stress the importance of the entrainment phenomena in the modelling of convective clouds, and especially through the matrix of transfers modelling that points out the great influence of the entrainment on the flow. Thus, the surrounding environment can be a source or a sink for the water vapour and the droplets production according to the values of the different mixing ratios in the cloud compared to those in the surrounding environment of the cloud. This model can, finally, be presented as the survival of the classical gas dynamics in this polyphasic medium case. The classical problem of existence of discontinuity curves is pointed out and involves the sound speed, which is here modified to take into account the presence of the hydrometeors.

Keywords and phrases: clouds, droplets, microphysics, dynamics, thermodynamics, mixing ratio.