On the size and shape of condensing steam jets and plumes

Abstract

Droplet-laden cloud dynamics emerge from coupled phase transitions and turbulent mixing. Combining experiments and mean-field theory, we establish scaling laws for steam-injected clouds in unsaturated air seeded with condensation nuclei. Depending on whether the cloud is confined to the initial momentum-dominated zone of the jet or extends into the buoyancy-dominated plume, two asymptotic regimes arise. In the momentum regime, cloud dimensions scale with the injector radius. In the buoyancy regime, size follows a \(\dot{m}^{2/5}\) scaling, where \(\dot{m}\) is the injected steam mass flow rate. Assuming inter-droplet air remains humidity-saturated, our mean-field analysis predicts cloud persistence governed by enthalpy and humidity mixing. These findings bridge microphysical processes and macroscale dynamics, offering a quantitative framework for atmospheric cloud evolution.