The coalescence of adjacent turbulent plumes in a stratified and unstratified environment

• Published in: Environmental fluid mechanics (Dordrecht, Netherlands : 2001) Vol. 24; no. 5; pp. 923 - 951
• Main Authors: Piminchumo Sausa, Adolfo R., Li, Shuo, Kaye, Nigel B., Flynn, M. R.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2024; Springer Nature B.V
• Subjects: Benchmarks; Civil engineering; Classical Mechanics; Coalescence; Density stratification; Earth and Environmental Science; Earth Sciences; Entrainment; Environmental Physics; Evolution; Flow theory; Fluid flow; Fluid mechanics; Height; Hydrogeology; Hydrology/Water Resources; Interfaces; Investigations; Mechanical engineering; Oceanography; Original Article; Plumes; Potential flow; Self-similarity; Shape; Turbulent flow; Vertical distribution; Boussinesq plume; Stratification; Buoyancy; Plume merger
• ISSN: 1567-7419; 1573-1510
• DOI: 10.1007/s10652-023-09952-y

Plume merger has been the subject of a number of recent theoretical studies that employ turbulent plume theory (including Taylor’s entrainment hypothesis) with ambient fluid external to the plume described using potential flow theory. Notwithstanding this effort, important questions remain as to the rate at which a merged plume formed from two adjacent sources relaxes in the far-field. In this theoretical work, the process of relaxation is examined with respect to the shape of the plume perimeter (as compared against a circle) and the plume volume flux, Q ¯ (as compared against the volume flux predicted from self-similarity). Using these metrics, we find that merging plumes assume a nearly circular cross-sectional shape before Q ¯ realizes its corresponding self-similar value. The discrepancy is especially large when the ambient is stratified. Herein, we consider three different stratification scenarios: uniform ambient, linear stratification and two-layer stratification featuring a thick interface. In each case, the vertical evolution of the plume is modeled using as additional benchmarks the height of first contact between the merging plumes, the height of full merger and, where applicable, the height of neutral buoyancy. Our theoretical model thereby allows us to track the dynamical evolution of the plume and shows, for example, that a merging plume rising through a linearly stratified ambient will almost always spread laterally before completing the process of relaxation. Finally, we highlight some of the open mathematical challenges in extrapolating our two-source model to a situation involving three or more (colinear) sources. Article highlights The merger of adjacent plumes impacts plume growth by the entrainment of external ambient fluid. The process of plume merger can be tracked by measuring or calculating the plume shape and its variation with height. Plume merger is impacted by ambient density stratification; strong density variations may arrest merging.