Times of rise for turbulent forced plumes

The motion of turbulent forced plumes, issuing vertically from isolated sources into an otherwise stable environment, is examined using a Lagrangian approach. Previous Eulerian approaches have yielded only numerical solutions whereas the present approach yields partial analytic solutions from which times of rise, from the source to levels of zero buoyancy and zero momentum, are evaluated for fluid elements travelling with the mean speed of flow. Consideration of previous work describing the asymptotic behaviour of starting plumes shows that times of rise may also be found for the leading front of a starting plume rising in a neutral environment.