Sensitivity of buoyant plume heights to ambient atmospheric conditions: Implications for volcanic eruption columns

A theoretical model is developed to investigate the sensitivity of buoyant atmospheric plumes to a wide range of ambient atmospheric conditions, including the temperature gradient, the latitude of the source, and the season. The formulation highlights the compressibility of an ideal gas, internal consistency between the governing equations for the conservation of momentum and energy, and the explicit use of the equation of state. Specific results are presented for water vapor plumes and implications are developed for multicomponent (water vapor, silicate particles, and condensates) volcanic plumes, If plume cooling is due solely to adiabatic expansion and the entrainment and mixing of ambient air, then the atmospheric temperature gradient is shown to be a dominant influence on plume height. Changes in the atmospheric gradient of 10 K/km cause the height of a low-level plume to differ by a factor of 2. We estimate the magnitude of this effect on volcanic plumes by considering water vapor erupted with equivalent heat fluxes. The sensitivity of plumes to ambient conditions is a result of the small density difference driving buoyancy. The plume density, in turn, is strongly controlled by the thermal energy of the system. Sensitivities associated with the thermal energy balance in the eruption column are also investigated. A modest thermal loss (1-2%/km) from the column by a process other than entrainment can result in a plume height significantly lower than one that cools by entrainment alone. Additional cooling of this magnitude could be caused by a variety of combinations of phenomena, including radiative heat loss and, possibly, the conversion of heat energy into turbulent rotational energy. For particle-laden plumes, there is the possibility of additional heat loss through the fallout of solids from the eruption column. To understand the details of the thermal energy balance in a plume, measurements must be made of the bulk plume temperature profile under known atmospheric conditions.