What is the entrainment coefficient of a pure turbulent line plume?

Despite its pivotal role in the classic theory of turbulent line plumes, there has been no consensus on the value of the entrainment coefficient alpha suitable for a pure plume. Reported measurements vary by 100 %, from alpha = 0.1 to alpha = 0.2, hindering the predictive capabilities of plume theory. Following our theoretical developments, measurements of plume entrainment using a new approach and a rigorous assessment of reported values for alpha, we conclude that alpha = 0.11 +/- 15 % should be adopted as the consensus value. Our theoretical framework demonstrates how alpha is determined from underlying plume measurements, and places an emphasis on the link between measurement uncertainty and uncertainty in alpha. This framework inspired our experimental design, intentionally conceived to precisely determine alpha. From measurements of the plume scalar width and the entrainment velocity outside the plume, we determine that alpha = 0.108 +/- 2 % (95 % confidence interval). Complementing our experiments is an evaluation of the historical data which, after we explain why some reported values of alpha are erroneous, supports the range 0.095 less than or similar to alpha less than or similar to 0.13. The proposed consensus value thus represents both our precisely determined value and the variation in the published data. The significance of a consensus value for alpha can be summarised as follows: (i) it enhances confidence in the application of plume theory to practical situations and (ii) it permits more detailed comparison of entrainment between pure line plumes and related turbulent flows, including forced and lazy line plumes and wall plumes.

Automated summary

There has been no consensus on the value of the entrainment coefficient alpha for a pure plume. However, after theoretical developments, measurements, and evaluation, it is concluded that alpha = 0.11 +/- 15% should be adopted as the consensus value. This consensus value enhances the application of plume theory and allows for detailed comparison with other turbulent flows.