Buoyant plume rise described by a Lagrangian turbulence model

A Lagrangian turbulence model is presented, which describes buoyant turbulence fully consistent with Eulerian budget equations as motion of fluid particles and change of their temperatures. This model is applied to the description of buoyant plume rise. Due to the simulation the turbulent mixing processes between the plume and ambient fluid in dependence on varying ambient conditions, the plume rise model presented here offers different advantages in comparison to existing models: the different plume rise phases are calculated consistently and the full plume statistics is obtained. The model predictions are compared to consequences of the similarity theory, results of large-eddy simulations and lidar measurements of the plume height and width in the atmosphere. For different flows with varying shear and stratification, we find in all these comparisons a good agreement between our computations and measurements, simulations and theoretical predictions. In particular, it is shown that the similarity theory appears as a special case of the theory presented here. The simplicity and the low computational costs of our model make it well-suited for routine applications.