Rise dynamics of unsteady laboratory jets with implications for volcanic plumes

- Common plume rise expressions are unsuitable for discrete volcanic eruptions.
- We present a new scaling law for plumes from short-lived and unsteady sources.
- Our expression accurately describes a range of laboratory and volcanic jets.
- Strongly-varying and transient source flux influences plume dynamics and hazards.

Geophysical observations of discrete volcanic eruptions suggest their eruption rates vary rapidly in time. To learn how such variations may impact the initial stages of plume rise, we conducted a laboratory study of neutrally-buoyant jets generated by unsteady source conditions analogous to the volcanic case. Turbulent jets were generated by quickly injecting a finite volume of water into a large volume of still water. The mass injection rates evolved over time with a Gaussian-like history, producing jets with peak Reynolds numbers ranging from 104 to 105, consistent with values estimated for small, discrete eruptions. Except during very early and late times, jet heights show a logarithmic dependence on time; this trend contrasts with the power law dependence for jets produced by steady-state or instantaneous discharge conditions. We show that this logarithmic dependence is the similarity form appropriate for impulsive releases from a time-varying source, and found characteristic length and time scales that consolidate the non-dimensional jet heights, as functions of non-dimensional times, from a range of experimental conditions onto a single trend. The rise of unsteady volcanic plume fronts from short-duration eruptions (Mori and Burton, 2009; Patrick, 2007) show the same trend as that observed in the laboratory. Variations in mass eruption rate strongly influence the initial phases of plume rise and may impact related processes such as mixing, entrainment and eruption column collapse. Consequently, source unsteadiness must be accounted for in physical plume models before they will reliably estimate trajectory, dilution, and stability for volcanic plumes from discrete eruptions.