Entrainment in two coalescing axisymmetric turbulent plumes

Abstract

A model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an 'effective' entrainment constant, α eff , as the value of α needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of α eff allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions.

Merging of two or more plumes arranged around a circle

“…The predicted merging height was somewhat greater than that observed in accompanying experiments, a result attributed in part to sensitivity of the model to the plume entrainment constant. Cenedese & Linden (2014) extended this model with the introduction of an intermediate region where the plumes overlap but are not yet fully merged. The model predictions compared favourably with measurements of the volume flux (inferred from interface movement) in two merging plumes obtained from 'filling-box' experiments, although these results are also sensitive to the entrainment constant, as will be discussed later.…”

Impact of Two Plumes’ Interaction on Submarine Melting of Tidewater Glaciers: A Laboratory Study

“…Hence, the virtual origin correction is the distance from the physical source that an imaginary pure plume, with zero momentum and volume fluxes but with the same buoyancy flux issuing from the virtual origin, has in order for the actual buoyancy, momentum, and volume fluxes of the plume to be the same at the physical source. The entrainment of warm bottom layer waters in the two merging plumes is reduced compared to that with two independent plumes (Cenedese and Linden 2014), and as a consequence the plume waters are colder and melting is reduced. As the two sources are located closer together, the two plumes interact for a larger portion of their vertical rise and consequently the melting is reduced for decreasing values of x 0 , as shown in Fig.…”

“…2). When the two sources of subglacial discharge are located closer together the two plumes will touch and merge at a distance from the ''virtual origin'' given by z T 5 0.35x 0 /a and z M 5 0.44x 0 /a, respectively (Cenedese and Linden 2014;Kaye and Linden 2004), where the distance from the virtual origin is z 5 (z 0 1 z V ), z 0 is the vertical distance from the source, and z V is the location of the virtual origin below the source (Hunt and Kaye 2001). The virtual origin correction is necessary because the plume's self-similar solutions of Morton et al (1956) are strictly valid only for a ''pure'' plume with zero momentum and volume fluxes.…”

“…Furthermore, using the self-similar solutions by Morton et al (1956) introduced by Cenedese and Linden (2014) for two interacting plumes, we calculated the amount of warm water entrained into the plume(s). A correction was also introduced to take into account that we are considering only half of a conical plume.…”

“…The laboratory results suggest a nonmonotonic dependence of the melt rate for small x 0 and an increase of melt rate with increasing x 0 for large x 0 . We explain this behavior using the plume's idealized self-similar solutions introduced by Morton et al (1956) and the entrainment into two interacting plumes introduced by Cenedese and Linden (2014).…”