Set-Up for Modelling

A dry material for modelling snow avalanches with an aerosol cloud was selected experimentally by testing different dry-powder materials such as sand, cement, coal and dental powders, salt, meal, semolina, poppy corn, and so on. As a result, it was found that the mixture of ferromagnetic sawdust and aluminium dust (in a relation 20:1–10:1) is the best material. This mixture forms a remarkable aerosol cloud. The average size of particles was of order 0.1 mm for ferromagnetic sawdust and 0.01 mm for aluminium dust. The angle of friction for the mixture was equal to 35–38°. It was possible to control the cohesion of the mixture to the slope with electromagnets.

The set-up for the physical modelling was two wooden plates assembled on a table. The angle of slope can be varied. The aluminium chute of triangular cross-section is attached along the transit zone. The electromagnets were fixed beneath the lateral sides of the chute. The mixture of ferromagnetic sawdust and aluminium dust with a volume up to 2 cm³ was poured into the chute above the electromagnets and the electricity was switched off. The avalanche motion and the deposition of dense and aerosol components were observed with photo-, cine- and video-cameras.

Mechanism of Powder Cloud Generation

The first series of experiments is concerned with the generation mechanism of the aerosol-avalanche cloud. Typical cine-gram of the origin and the propagation of the model cloud is shown in Figure 1.

Fig. 1.

The cinegram of the generation and propagation of the aerosol component in a model avalanche (side view, light section; interval between frames is 0.5 s, distance between lines is 10 cm).

When an avalanche sharply decelerates, sometimes the powder-snow cloud separates from the dense-flowing layer. This has been considered by Reference GrigoryanGrigoryan (1974), Reference Grigoryan, Urumbayev and Nekrasov.Grigoryan and others (1982) and Shukhanov (1982). A huge semi-circular vortex over the dense component of an avalanche propagates in the direction of the avalanche motion (Reference Yakimov and Shurova.Yakimov and Shurova, 1968). The laboratory experiments have shown that another origin mechanism of an avalanche cloud is possible. This origin mechanism is due to compression of the model material and creation of vortices from aerosol jets. This process is similar to the hydraulic jump of fluid flow when a stormy flow (Fr > 1) changes to a calm one (Fr < 1). The flow velocity sharply decreases and the flow depth increases. In such processes, the separation of partieles according to the free-fall velocity takes place. The heavy solid phase generates the avalanche deposit. On the other hand, the powder component including air and aluminium dust is thrown away with the short-term jets, and the aerosol cloud propagating ahead is generated, as shown in Figure 2. The front of the aerosol cloud generation moves upstream.

Fig. 2.

Generation of the aerosol component for model avalanche (side view; light section, five-fold enlargement, direction of the motion from right to left).

The structure of the model aerosol cloud is characterized by the combinations of spiral arc- and ring-type vortices generated with aerosol jets. The existence time of the vortices is comparable with the time of the cloud generation but sometimes it is much higher, achieving 3 seconds and more. During this period, the vortices pass along a distance up to 10–20 cm, and create the divergent stripes of aluminium particles.

Destructive Action of the Powder Cloud

The destructive action of the powder cloud was investigated in the second series of experiments (Reference Bozhinskiy and SukhanovBozhinskiy and Sukhanov, 1995). For convenience, the deceleration zone was covered with a glass under which the black cloth was put. Thus, one can make accurate photo-images of the model process beneath side-slide illumination: dense and powder components of the model avalanche at the deposit zone. The sizes of the powder clouds at the spread zone are of the order of several decimeters. The velocities of the cloud are about 3–5 cm s⁻¹. Thus the pressure is of order 10⁻³ Pa, if the cloud density is close to the air’s one. The locations of isobars for such small values of pressure have been determined using the very light markers installed across the model-avalanche path (Fig. 3a).

Fig. 3.

Locations of markers before (a) and after (b) passing of the aerosol cloud for the model avalanche; V = 1 cm³; α = 55°.

Dandelion “parachutes” were used as markers. The diameter of the dandelion’s crown and height were of order 10–12 mm. These markers correspond to trees in Nature, because the coefficient of geometric similarity of the model and real avalanche path is of order 10³. One can create a whole forest using such markers. It allows us to investigate the location of the isobars under different conditions. The destructive zone due to avalanche action was determined by the location of the markers after avalanche passing (Fig. 3b). The dependency of the size of this zone in the model avalanche volume is given in Figure 4.

Fig. 4.

Average sizes L of the destructive zone for a model cloud us its volume V, α = 45°; ◊ is length S, • is width B, □ is width B_g of forest “gates”.

Comparison of Model and Real Avalanche Data

The numerical characteristics of the model avalanche obtained in the study can be compared using the scale coefficients (3) with actual snow avalanches. The “home” avalanche accompanied by a huge powder cloud was released by mortar on 23 March 1988 in the vicinity of the Elbrus station of Moscow University. The cine survey of the cloud motion and the photo-theodolite survey of the deposit-zone surface before and after the avalanche passing were made. Then, using the stereophotogrammetric processing of the values of the leading-avalanche front and the powder cloud were determined. Also, the map of the thickness for the avalanche deposit was constructed (Reference Firstov, Sukhanov, Pergament and RadionovskiyFirstov and others, 1991). The volume of the avalanche was 1.1 × 10⁴ m³, the vertical drop was 1000 m, and the average angles in the transit and deceleration zones were 36° and 10°. The initial angle of the avalanche deceleration zone was 24°. Thus, the slope angle for the model must be increased by Δγ = 14° as γ_m = 38°. They were assumed as α_tr,m = 50° and α_dec,m = 24°. The coefficient λ of the geometric similarity of the model and the real avalanche path was 2.2 × 10³. Then we can use Equations (3) to calculate the model-avalanche parameters, corresponding to the “natural” ones. We have the scales: for volumes λ³ = 1.06 × 10¹⁰, for time intervals and rates of the process λ^½ = 47. The altitude of the starting point for the model avalanche has to be H_m = λ⁻¹ (sin α_m sin⁻¹ α_n) H_n = 0.59 m, because the model slope angle was changed by Δα. The scaled results from the model avalanche correspond well with the field data (see Table 1).

Table 1.

Comparison of data from, the model and the “home” avalanches.

Next, a three-dimensional scale model of the “home” avalanche path was constructed (scale 1:2500) (Fig. 5).

Fig. 5.

Three-dimensional model of the “home” avalanche path.

A topographic map with the 10 m contours, between 2300 and 3300 m, was used. The model was built of plywood leaves, in accordance with the location of contours. The thickness of plywood leaves was equal to 4 mm which corresponds to 10 m of altitude difference. Using this model set-up the next series of experiments was carried out using a line river sand as a model material. The model characteristics recalculated to “Nature”, with a scale of coefficients to similarity (3), were in good agreement with the parameters of the “home” avalanche.

From Figure 6, one can see that the qualitative velocity changes for the leading front are generally the same for both avalanches. The discrepancies of absolute values of velocities on the same path intervals do not exceed their local fluctuations. The deceleration of the model and “home” avalanches also begins at the same zones in the vicinity of 2340 m. At this level, the slope angle, for the real slope, changes from 27° to 20°, passing through the value of the friction angle for snow which is equal to 24°. The leading fronts of deposit for the model and “home” avalanches practically agreed and the volumes and locations of deposits are the same. It should be noticed that deposits of the model material are almost independent of the initial distribution of the material in the starting zone and at the height of the starting point. Probably, this effect is due to the deep (15 m), narrow (12 m) and winding rock channel which restricts the velocity of the avalanche. A powder cloud was also observed in these experiments. Sizes, velocities and run-out distances of this cloud are similar to the analogous data of clouds generated by aluminium dust. However, the density of this cloud is very-low. Visible deposits of the aerosol are weak. Probably, in this case, the model cloud has been formed from fine dust-loamy particles involved in the dry sand. The artificial addition of aluminium dust to the sand allows us to use the same powder cloud as in the first experiments.

Fig. 6.

Measured velocity of leading front for “home” avalanche (◊) and model velocity recalculated to “Nature” (•) vs horizontal distance of retardation zone.

On the whole, physical modelling of avalanches, using the three-dimensional model set-up, gives results which are close to the results of modelling when the simplest model set-up was used. However, modelling on three-dimensional models of actual avalanche paths is preferable, because it is possible to achieve space distributions of the avalanches and to estimate the destructive action of the avalanches.