The effect of source Reynolds number on the rise height of a fountain

Abstract

The focus of this paper is to establish the effect of source Reynolds number, Re0, on the mean rise heights of Boussinesq miscible fountains and thereby the range of Re0 for which rise heights are independent of Re0. We present results from experiments on aqueous-saline fountains spanning source Reynolds numbers of 15 ≤ Re0 ≤ 4000 and source Froude numbers of 0.3 ≤ Fr0 ≤ 40. We provide threshold values for the source Reynolds number, i.e., values above which fountain rise height may be regarded as independent of Re0. For Reynolds numbers immediately beneath these threshold values, the fountain rise height increases as Re0 decreases—in agreement with Lin and Armfield [“The Reynolds and Prandtl number dependence of weak fountains,” Comput. Mech. 31, 379–389 (2003)]. At even lower Re0, we show that the rise heights reach a maximum and that further decreases in Re0 decrease the rise height attained—in agreement with Phillipe et al., [“Penetration of a negatively buoyant jet in a miscible liquid,” Phys. Fluids 17, 053601 (2005)]. As such, we resolve an apparent inconsistency within the existing fountain literature.