Height and stability of laminar plane fountains in a homogeneous fluid

Warm discharges in cold fresh water: 2. Numerical simulation of laminar line plumes

“…As the production of positively buoyant fluid from the source and the production of dense fluid by mixing are continuous processes, a continuous "flapping" and "bobbing" of the plume develops: the sideways deflection of detaching heads results in side-to-side flapping, and the exposure of the rising core of the plume after each head is detached leads to vertical bobbing. This behaviour has some similarities to that observed by Srinarayana et al [9] for a laminar plane fountain with Fr = 8 and a linear dependence of density on temperature; they also observed flapping from side to side as the top section of the fountain was repeatedly detached. A vertical bobbing behaviour has been previously observed by Turner [14] in a turbulent plume with reversing buoyancy, while a combination of flapping and bobbing has been seen by Vinoth and Panigrahi [21] in non-Boussinesq laminar fountains at higher Froude numbers.…”

“…Srinarayana et al [9] identified three regimes of Froude number dependence for the height of their fountains, reflecting qualitative differences in behaviour (e.g. between steady and unsteady flow) in different ranges of Fr.…”

“…These computations were for fixed Reynolds number Re = 200 and Prandtl number Pr = 7; subsequent computations in which these parameters were varied [8] indicated that z m /x 0 = a 0 + a 1 Fr Re −1/2 (and similarly for fountain width) as long as Re ≤ 200, but that fountain height and width became independent of Reynolds number at larger values of Re. When the range of Froude numbers was extended up to Fr = 10 and the symmetry constraint in the computational domain was removed, Srinarayana et al [9] found that the fountain remained steady and symmetric only up to Fr ≈ 2.25. At higher Froude numbers, lateral oscillations ("flapping") were found; these were periodic for Fr ≤ 4.0 but chaotic for Fr > 4.0.…”

Impinging plane fountains in a homogeneous fluid

“…Recently, Srinarayana et al [23] carried out a numerical investigation of laminar plane fountains in homogeneous fluid for 0:25 6 Fr 6 10:0; Re ¼ 100 and Pr ¼ 7. They categorised the flow into three regimes: steady and symmetric for 0: 25 [5] zm ¼ 2:75Fr Turner [6] zm ¼ 2:46Fr 2 K Fr K 30 Campbell and Turner [7] zm ¼ 2:07Fr 20 K Fr K 90 Baines et al [8] zm ¼ 2:46Fr 10 K Fr K 250 Mizushina et al [15] zm Kaye and Hunt [17] zm ¼…”

“…Further, it is ensured that the open boundaries are sufficiently far from the region of interest. The results are obtained using Gerris [37,23], an open source quad-tree based adaptive mesh solver which uses a fractional-step projection method. The total width of the computational domain is W ¼ 300X in , i.e., À150 6 x 6 þ150, and the height H is varied so that the fountain impinges on the ceiling.…”