Richardson and Reynolds number effects on the near field of buoyant plumes: temporal variability and puffing

Using numerical simulations, we investigate the near-field temporal variability of axisymmetric helium plumes as a function of inlet-based Richardson (Ri(0)) and Reynolds (Re-0) numbers. Previous studies have shown that Ri(0) plays a leading-order role in determining the frequency at which large-scale vortices are produced (commonly called the 'puffing' frequency). By contrast, Re-0 dictates the strength of localized gradients, which are important during the transition from laminar to turbulent flow. The simulations presented here span a range of Ri(0) and Re-0, and use adaptive mesh refinement to achieve high spatial resolutions. We find that as Re-0 increases for a given Ri(0), the puffing motion undergoes a transition at a critical Re-0, marking the onset of chaotic dynamics. Moreover, the critical Re-0 decreases as Ri(0) increases. When the puffing instability is non-chaotic, time series of different variables are well-correlated, exhibiting only modest changes in the dynamics (including period doubling and flapping). Once the flow becomes chaotic, denser ambient fluid penetrates the core of the plume, similar to penetrating 'spikes' formed by Rayleigh-Taylor instabilities, leading to only moderately correlated flow variables. These changes result in a non-trivial dependence of the puffing frequency on Re-0. Specifically, at sufficiently low Re-0, the puffing frequency falls below the prediction from Wimer et al. (J. Fluid Mech., vol. 895, 2020). As Re-0 increases beyond the critical Re-0, the puffing frequency increases and then drops back down to the predicted scaling. The dependence of the puffing frequency on Re-0 provides a possible explanation for previously observed changes in the scaling of the puffing frequency for high Ri(0).