Vertical Round Buoyant Jets and Fountains in a Linearly, Density-Stratified Fluid

Abstract

Turbulent round buoyant jets and fountains issuing vertically into a linearly density-stratified calm ambient have been investigated in a series of laboratory experiments. The terminal (steady-state) height of rise and the mean elevation of subsequent horizontal spreading have been measured in positively buoyant jets (at source level), including pure momentum jets and plumes, as well in momentum-driven negatively buoyant jets (fountains). The results from experiments confirmed the asymptotic analysis that was based on dimensional arguments. The normalized terminal height and spreading elevation with respect to the elevation of injection of momentum-driven (positively) buoyant jets and fountains attained the same asymptotic values. The numerical results from the solution of entrainment equations, using an improved entrainment coefficient function, confirmed the results related to buoyancy dominant flows (plumes), while their predictions in momentum-driven flows were quite low if compared to measurements.

On the Computational Modeling of Inclined Brine Discharges

“…The previous model will be also implemented using a different entrainment formula. Papanicolaou and Stamoulis [41] presented a new formula for the entrainment coefficient which was analytically derived from the equations of motion for the vertical buoyant jet assuming top-hat distributions for velocity and apparent acceleration of gravity. Following the same work but for Gaussian distributions, the following equation is obtained for the local entrainment coefficient (see Appendix A)…”

“…where z is the elevation above the source; α is the local entrainment coefficient; µ, m and β are the local specific (per unit mass) mass, momentum and buoyancy fluxes, respectively; and λ = b c /b is the ratio of the 1/e widths of tracer concentration (or apparent gravity) and velocity distributions. Following the procedure presented by Papanicolaou and Stamoulis [41] we can integrate the momentum equation by substituting m 1/2 = µ/(zC p ), C p being the constant jet width parameter proposed by List and Imberger [42] and evaluated by Papanicolaou and List [40], in the rhs obtaining…”

Semi-collapse of turbulent fountains in stratified media and the mechanisms to control their dynamics

“…However, the spreading behaviour of the fountain was not considered in this investigation. Papanicolau et al [18] conducted an experimental study on the collapse and spreading of turbulent fountains and performed a comparison with those obtained in [8]. As various authors have pointed out [19][20][21], to assume a constant entrainment coefficient is an approximation due to its dependence on the turbulence intensity, and, as a consequence, it can vary with the rise of the fountain.…”