The rise heights of low- and high-Froude-number turbulent axisymmetric fountains

Abstract

AbstractWe present the results of an experimental investigation across a broad range of source Froude numbers,$0. 4\leq {\mathit{Fr}}_{0} \leq 45$, into the dynamics, morphology and rise heights of Boussinesq turbulent axisymmetric fountains in quiescent uniform environments. Typically, these fountains are thought to rise to an initial height,${z}_{i} $, before settling back and fluctuating about a lesser (quasi-) steady height,${z}_{ss} $. Our measurements show that this is not always the case and the ratio of the fountain’s initial rise height to steady rise height,$\lambda = {z}_{i} / {z}_{ss} $, varies widely,$0. 5\lesssim \lambda \lesssim 2$, across the range of${\mathit{Fr}}_{0} $investigated. As a result of near-ideal start-up conditions provided by the experimental set-up we were consistently able to form a vortex at the fountain’s front. This enabled new insights into two features of the initial rise of turbulent fountains. Firstly, for$1. 0\lesssim {\mathit{Fr}}_{0} \lesssim 1. 7$the initial rise height islessthan the steady rise height. Secondly, for${\mathit{Fr}}_{0} \gtrsim 5. 5$, the vortex formed at the fountain’s front pinches off, separates from the main body and rises high above the fountain; there is thus a third rise height to consider, namely, the maximum vortex rise height,${z}_{v} $. From our observations we propose classifying turbulent axisymmetric fountains into five regimes (as opposed to the current three regimes) and present detailed descriptions of the flow in each. Finally, based on an analysis of the rise height fluctuations and the width of fountains in (quasi-) steady state we provide further insight into the physical cause of height fluctuations.