Downward axisymmetric plumes with their possible behaviours have just been studied numerically, with the assumption that density is a quadratic function of temperature. Results here are for different values of M0, where the value M0 = (5/2^5 )^(2/5) is termed critical forcing. Plumes with M0 value > (5/2^5 )^(2/5) are termed strongly forced plume. Within the interval 0 < M0 < (5/2^5 )^(2/5), two solutions are aimed: a warm weakly forced and cool weakly forced plume. Plume’s uniqueness are in accordance with their respective M0 values with the source offering some sort of forcing that is depended on the downward momentum. The warm weakly forced plume possess an unlimited temperature at its virtual source. At far
field where Q M0, M ∼ Q in (38) and from equation (35), both volume and momentum flux advances linearly with distance, such that the dimensionless velocity V approach unity as Y → ∞. The results also showed that both warm weakly forced and critically forced plumes come to rest with final volume flux at Q_f  ≤  1/2  with an infinite width. The temperature here decreases monotonically with increasing initial momentum flux. Our plumes are assumed to have come
from a virtual source condition, where giving interpretation as though they were from physical sources may be difficult. In terms of the study of plumes from physical sources, two types of such might be of practical importance: one of which is the power station warm discharge at a lake floor and a plume that descends from a surface gravity current. Those results in section 3.2 requires that it is important to prevent singularity at the virtual source (see Fig. 6) by making sure that the initial conditions suggest a physical source position at some point below the virtual source and this we have as a limitation. A more realistic model had been reached by George & Kay, 2017 for a fountain flow case, but need to be inverted in the case of a descending weakly forced plume. Lastly, with the entrainment model, it is expected that the plume will be fully turbulent. Thus, our results can be likened to the power station warm discharge which will definitely be fully turbulent with its large volume flux: these are basic conditions on the validity of these assumptions. The numerical results as presented here are very good as they present us with insight into downward plumes using (1).