A new analytical scaling for turbulent wind-bent plumes: Comparison of scaling laws with analog experiments and a new database of eruptive conditions for predicting the height of volcanic plumes

Various scaling relationships relate the height of volcanic plumes to eruptive source conditions, atmospheric density stratification, turbulent entrainment, and wind stresses. However, observational, analog, and numerical studies used to test these scalings capture only a narrow range of natural eruptive conditions. In particular, existing analytical scalings are not appropriate for the wind stress conditions typical of the majority of volcanic eruptions. Accordingly, we develop a new analytical scaling for the height of buoyant plumes rising in density-stratified uniform crossflows. We compare this scaling to existing analytical scalings (Morton et al. 1956; Hewett et al. 1971) as well as “functional” scalings (i.e., parameterizations expressed as a function of the Morton et al. (1956) scaling and a regime parameter related to wind stress, Degruyter and Bonadonna (2012), Woodhouse et al. (2013), Carazzo et al. (2014)) using the extensive experimental dataset from Carazzo et al. (2014) along with natural events from a new database including 94 eruptive phases. Our proposed scaling best predicts the height of experimental plumes, which enables us to constrain the ratio of the wind to radial entrainment coefficients. For natural eruptions, the Woodhouse et al. (2013) and Carazzo et al. (2014) scalings, which account explicitly for wind gradient, best predicts plume heights. We show that accounting for atmospheric stratification and wind improves empirical relationships between mass eruption rates and plume heights. For tested scalings, analyze of residual heights for natural eruption supports the hypothesis that volcanic plumes rise higher in a wetter atmosphere. Finally, for analog plumes rising under moderate to high wind stresses, we show that plume shapes evolve over the plume height, violating the self-similarity assumption on which all scalings and integral model results rely. We discuss consequences for relaxing the self-similarity hypothesis as well as potential improvements for standard integral plume models, in turn.