Mountains crests

At a higher scale, we may consider deposit problems around mountain crests. We have studied a litterature case, the Schwarzhorngrat from [F¨ohn et Meister 1983]

in eastern Switzerland, and a more practical case in La Marlennaz (Valais, swiss Alps), where defence works are currently built.

Schwarzhorngrat

Although other crest cases exist in litterature, analysing a situation after long period often appear to be very irregular (many different conditions have ruled the system, different winds, snow falls with no wind, freezing of the upper deposit layer. . . ). From these points of view, the 1981 Schwarhorngrat study (recorded by [F¨ohn et Meister 1983]) offers three advantages:

1. the prevailing wind blows perpendiculary to the crest;

2. the deposit growth have been monotonuous during the recoding period, as displayed in figure 3.27;

3. measurments along three different profiles of the same crest (with steep, medium and gentle slopes) have been recorded, thus showing three deposits under the same input conditions.

For these reasons, we have choosen this case study. Our model parameters were calibrated on the middle slope profile, and ran with the same condition on the two other ones. Compared to the fence deposit parameters, the threshold number of frozen particle to solidfy a site,θf rz, has increased from 10² up to 10⁴, thus increasing the “actual size” of a lattice cell. From the fluid point of view,

Figure 3.28: numerical results over three profiles at different positions along the Schwarzgrat crest, on the left, compared to field recorded measurments by [F¨ohnet Meister 1983] after the two first months of winter 80-81 on the right.

Our model was calibrated on the middle slope profile, and ran with the same parameters on the two other ones. Space scale is given by the computer resources availability (i.e. the smallest possible cell size, but limited by both memory and time), but time scale is more difficult to approximate a priori: therefore, the simulation shall be stopped when the total amount of deposited snow reaches the experimental reference one. Anyway, as displayed in figure 3.27, the deposit in this case grows monotonuously, developing a basic pattern; it is this pattern to be recovered by the numerical model. To this respect, the results shown are in good agreement with reality.

Csmago has been decreased to its lowest value possible without a numerical blow up (Csmago was different for the three profiles, as it can be tuned lower when the profile is smoother).

The results of the numerical model over the three crests are confronted to outdoor observations in figure 3.28 with a very good agreement.

La Marlennaz

A more challenging situation occurs in the Marlennaz case, as no deposit records exist. However, in this site situated in the swiss Alps near the Verbier ski resort, different defense works are tested in real conditions by the Canton du Valais (service des forˆets et du paysage). When nothing is done, a cornice grows at the crest level and later trigger avalanches that may cause serious damages to habitations, as it has already happened in the past.

To retain the mantle of snow, avalanche barriers have traditionnaly been built on the whole avalanche release slope, for more than one century. However, another approach (at least a complementary one) can be undertaken by trying to fight

Figure 3.29: two different types of defense works, aimed at modifying the wind pattern and therefore the snow deposit at the crest location. Foreground, a slanted screen accelerates the wind parallel to the leeward slope and prevent the deposit. In the middle distance, the wind-veering will higher the wind turbulence leewards and disorganize its action in the area (the widen shape is important as it also accelerates the wind at the ground level).

against the cornice growing. Instead of regular mining with explosive during the whole winter, the idea is to build works in order to modify cleverly the wind flux, such as:

• fences, to store snow windwards the crest,

• slanted screens¹, to acclerate the wind parallel to the slope, thus breaking the cornice,

• wind-veerings, vertical crossbars, to alter the wind flux pattern.

The question is therefore to place these works in the most efficient position to avoid the emergence of the cornice, and to see how side effects (growing of an important wind slab, for example) can emerge.

Therefore, it was a natural application (at least a challenge) for our numerical model. Simulations were performed over two landcape profile, called profiles 1 and 3.

Marlennaz - profile 1

In the profile 1 situation, where a slanted screen has already been built, simu-lations were ran with and without the work: snow deposits (figure 3.30), wind vorticity (the wind velocity field rotational, in figure 3.31) and flying particle

1The french term is “toit buse”, something like “shaft roof”, and the term “slanted screen”

is a personal traduction. In the same manner, “wind-veering” is an approximative translation for “vire-vent”.

Figure 3.30: La Marlennaz - profile 1. Computed deposits the crest are plotted every 6000 time steps, with (right) or without (left) a slanted screen. As observed outdoor, the screen is efficient to limit the growing of the cornice. In such a simulation, the lattice resolution is coarse, and cell size effects are visible (such as the deposited particle concentration nearby each landscape stair step); however, averaging the deposit over thex−dimension lower this model artefact.

distribution (figure 3.32) have been compared. Later, different slanted screens angles and locations along the profile have also been tested (figure 3.33).

Marlennaz - profile 3

This profile is more challenging from two points of view:

Figure 3.31: La Marlennaz - profile 1. Vorticity plot, where one can see the action of the slanted screen (the darker, the higher the vorticity).

1. the interesting part of the profile is the main slope break; however, it is located leewards a small little crest, whose influence is hard to estimate a priori;

2. no works have yet been built (except regular avalanche barriers in the slope), but some are planned in this area: therefore the question of what and where to build them is of a practical importance.

The computed deposit over the naked crest is compared with two slanted screens configurations in figure 3.34. According to the model results, a slanted screen at the slope breaking would clearly get rid of the cornice.