The formation and evolution of convective H2O clouds in the deep Jovian troposphere are investigated using an axisymmetric model with parameterized microphysics to calculate the vertical and radial wind components and the liquid and ice contents in the clouds. A constant upwelling velocity from within the deep atmosphere was assumed, and the model was initiated with a slightly superadiabatic lapse rate below the lifting condensation level (LCL), which was located at 5160 mbar. The abundance of water in Jupiter's atmosphere was assumed to be solar, and several relative humidity profiles were evaluated. The initial temperature profile above the LCL was assumed to be dry-adiabatic. The role of condensate mass-loading in the dynamic evolution of the cloud was considered. Results show that for plausible values of superadiabatic deviations and upwelling velocities, the Jovian water clouds are 25 km deep and extend up to the 3-bar pressure level. These cumulus clouds contain 2.5-5 g/m3 of liquid water and ice, with updrafts at the axis reaching 30 m/sec and a cloud top temperature of 235 K. Clouds could retain their vertical structure for long periods of time. According to the model the water clouds reach the ammonia condensation level only when the temperature and relative humidity profiles are coupled in such a way that instability (or at least neutrality) to moist convection is ensured over a large depth of the troposphere. Under intermediate conditions, at which the upper layers were assumed to be stable, clouds were 40-50 km deep with updrafts of 60-70 m/sec, but did not reach the ammonia cloud deck. Thus, they were probably not connected to the observed equatorial "plumes".