New model for dispersion of volcanic ash and dust in the troposphere.

Abstract

Dispersion of volcanic ash and dust is traditionally modeled as advection and Gaussian diffusion. This is the tradition in treating smoke stack plumes. About 100 meters above earth, the velocity profile may disintegrate, diffusion coefficients become rather unpredictable and stratified flow occurs. The motivation of this paper is to improve the existing models for dispersion of dust plumes. The traditional models using Gaussian diffusion do consider vertical diffusion negligible, but include coefficients for horizontal diffusion large enough to explain the sideways dispersion, so clearly seen on satellite images. It is found that gravitational flattening caused by atmospheric density stratification may be the main cause of dispersion in dust plumes above the turbulent boundary layer. Additionally, this causes a dust plume in between two layers of small temperature difference to have a certain carrying capacity for dust load. The corresponding mass loading can be estimated from the temperature difference between the layers above and beneath the plume. Dust plumes having a mass load in excess of this carrying capacity will be forced to jettison the extra load. This may be seen as streak fallout from the plume. In the same time, the plume will be subjected to flattening to the sides, caused by density-controlled pressure gradients, in addition to any diffusion if there is any. The length scale of the plume width resulting from this flattening may be estimated from the temperature difference. This can explain the behavior of plumes like the plume from the Eyjafjallajökull 2010 in absence of diffusion. In the long run, diffusion and gravitational flattening will cause different developments of the plume width. Gravitational flattening and streak fallouts are important elements from plume physics not included in most plume models and are at work in a turbulence free environment. It is concluded that modelling dust plumes with diffusion and ordinary fallout only and can cause serious errors in the model; the simulated plumes will become too big. To avoid them, the new model should be included in dust models in the same manner as the turbulent diffusion, i.e. as a sub grid model. Then, the plume model only needs to include horizontal turbulent diffusion of the same order of magnitude as the vertical one.