Gravity currents down a slope in deceleration phase

Modified thermal theory with both entrainment and detrainment is proposed and the analytical solutions are derived in this study. We find that the data in [Beghin, P., Hopfinger, E.J., Britter, R.E., 1981. Gravitational convection from instantaneous sources on inclined boundaries. J. Fluid Mech. 107, 407-422] support the idea that both entrainment and detrainment occur in the deceleration phase of thermal motion. Our modified model gives a better description of the data as compared with the model in [Beghin, P., Hopfinger, E.J., Britter, R.E., 1981. Gravitational convection from instantaneous sources on inclined boundaries. J. Fluid Mech. 107, 407-422] in which detrainment was neglected. While entrainment slows down thermal motion, the effect of detrainment is twofold. On one hand, the thermal gradually loses the driving force as the buoyancy is lost through detrainment. On the other hand, detrainment takes redundant fluid off the thermal so that the thermal can move faster. As a result, detrainment mitigates the deceleration that a thermal experiences during the deceleration phase.