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 occur. It is suggested that gravitational flattening may be the main cause of dispersion in dust plumes above the turbulent boundary layer. A dust plume in between two layers of small temperature difference has a certain carrying capacity of dust. The corresponding mass loading can be estimated from the temperature difference between the layers above and beneath the plume. Such dust plumes will be forced to jettison a load they may have in excess of this carrying capacity; this may be seen as streak fallout from the plume. In the same time, the plume will be subjected to gravitational flattening to the sides, in addition to any diffusion if there is any. The plume width resulting from the flattening may be estimated from the temperature difference. This can explain the behavior of plumes like the plume from the Eyjafjallaj?kull 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. It is concluded that modelling dust plumes with diffusion and ordinary fallout only; 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.
Highlights
The scope of this article is the science of the advection and dispersion of buoyant plumes and the physics governing their migration and the modeling of dust plumes
Smoke plumes are almost all in the PBL (Planetary Boundary Layer) where the diffusion is governed by the Gaussian air pollutant dispersion [1] equation and the mixing force is the shear turbulence created by the vertical gradient of the horizontal wind velocity profile close to the surface as originally proposed by the early theories on the structure of turbulence, accessible in textbooks on Fluid Dynamics
Streak fallouts are very common in the start of the neutrally buoyant flight of volcanic plumes, they can be seen in almost any picture of such a plume, see e.g. Figure 3
Summary
The scope of this article is the science of the advection and dispersion of buoyant plumes and the physics governing their migration and the modeling of dust plumes. It is suggested that gravitational flattening of dust clouds is responsible for the dispersion rather than diffusion, and the gravitational flow of non-buoyant parts out of the cloud—streak fallout—is what controls the mass flux in dust plumes in the long run, rather than ordinary fallout or what is blown up in the air at the source This is further explained, and a new formula developed for the maximum carrying capacity of a neutrally buoyant plume. The major disruption of air transport in Europe during the Eyjafjallajökull volcanic eruption in 2010, caused a huge economic loss to the world, US$ 4 - 6 billion according to various estimates, mostly incurred by private firms If this figure is taken at face value, this eruption is the costliest in history. It must be considered that the aviation authorities used maps of simulated ash clouds, not direct observations
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