Low-Reynolds-number fountain behaviour

Abstract

Experimental evidence for previously unreported fountain behaviour is presented. It has been found that the first unstable mode of a three-dimensional round fountain is a laminar flapping motion that can grow to a circling or multimodal flapping motion. With increasing Froude and Reynolds numbers, fountain behaviour becomes more disorderly, exhibiting a laminar bobbing motion. The transition between steady behaviour, the initial flapping modes and the laminar bobbing flow can be approximately described by a function FrRe2/3=C. The transition to turbulence occurs at Re > 120, independent of Froude number, and the flow appears to be fully turbulent at Re≈2000. For Fr > 10 and Re≲120, sinuous shear-driven instabilities have been observed in the rising fluid column. For Re≳120 these instabilities cause the fountain to intermittently breakdown into turbulent jet-like flow. For Fr≲10 buoyancy forces begin to dominate the flow and pulsing behaviour is observed. A regime map of the fountain behaviour for 0.7≲Fr≲100 and 15≲Re≲1900 is presented and the underlying mechanisms for the observed behaviour are proposed. Movies are available with the online version of the paper.

Flow behaviour of negatively buoyant jets in immiscible ambient fluid

“…Values of Re in between, lead to a transitional regime where a part of the jet behaved as laminar and the other as turbulent. Another interesting classification is that proposed by Williamson et al (2008), who established the laminar-transitional threshold at Re = 240 and the transitional-turbulent at Re = 4000. Considering both Pearce (1966) and Williamson et al (2008) definitions, all Type I and II experiments would lay in the transitional regime whereas Type III would be transitional to turbulent.…”

“…Another interesting classification is that proposed by Williamson et al (2008), who established the laminar-transitional threshold at Re = 240 and the transitional-turbulent at Re = 4000. Considering both Pearce (1966) and Williamson et al (2008) definitions, all Type I and II experiments would lay in the transitional regime whereas Type III would be transitional to turbulent. Future studies need to investigate this aspect in detail and to try to define the limits for the laminar and turbulent regime for negatively buoyant jets in immiscible fluids since it can provide an important control on the mixing process of both fluids as suggested by Friedman et al (2006).…”

On the modelling of steady turbulent fountains

“…It is the reason why an extensive literature is devoted to that topic. The interested reader is referred to works by [14] and [17] for immiscible fountains, [22,33,35] for miscible laminar fountains, [18,38] for plane turbulent fountains and [1,2,6,8,9,16,25,34,37] for round turbulent fountains in both homogeneous and stratified ambients. Note that most of these studies have focused on the determination of fountain heights.…”

Interaction between a Vertical Turbulent Jet and a Thermocline

“…Instabilities are observed for fountains in a homogeneous fluid, and this oscillatory motion has become the object of research only recently (Friedman 2006;Friedman et al 2007;Williamson et al 2008;Burridge and Hunt 2013). The dynamics of a fountain in a homogeneous fluid is, analogously to the mean penetration height, fully controlled by the Froude and Reynolds numbers.…”