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List of Figures

1.1 Snow transport modelling: a state of the art

Presenting a global state of the art of snow transport and deposition studies is not the purpose of this thesis, more focused on a numerical model. However, an overview of this field is necessary to situate this work in its context (a more extensive panorama can be found in [Castelle 1995]). We will therefore introduce some basic concepts, and different approaches followed by other researchers.

Figure 1.2: “the influence of snow drift over flat ground around an ordinary ten-foot fence, with one inch space between the vertical boards” (Johnson 1852) cited in [Sundsbo 1997]

1.1.1 Basic phenomenon

It is generally accpeted that snow is transported by wind following three different modes, in the very same manner as sand, displayed in figure 1.3 [Mellor 1965, Kobayashi 1972]:

• creeping: particles are rolling on the ground;

• saltation: they take off almost vertically, and fly along a parabolic trajec-tory; they can be ejected by strong enough eddy or by the shock of landing particles;

• suspension: during the saltation phase, particle can be taken in larger scale eddies and fly for longer distance.

Although the same components are present (turbulent wind flow and solid par-ticles), these three modes are treated separately by all the authors. Each pro-cess is identified to a governing equation [Anderson et al. 1991] and prediction

wind

saltation

creeping suspension

~.001m .001<h<.4m .05<h<100m

Figure 1.3: snow transport by wind is split into three modes: creeping of particles at ground level, ballistic saltation trajectories and suspension of particles over long distances [Castelle 1995].

models usually take into account only the main modes involved in the studied phenomenon.

This approach has been proven successful, for example, the erosion of a wind-facing step [Castelle 1995] or a numerical model for suspension transport [Martinez 1996]. However, beside these rather theoritical questions, many efforts (often by the same persons) have been achieved to answer field problems, such as the deposit around a fence, a building, an alpine crest etc. with the same kind of methods.

1.1.2 Modelling outdoor situations

Statistic or fully-dedicated models

Outdoor observations are recorded to build a statistics data base: this approach have been proposed by [Tabler 1980a] for deposits around fences. The prediction for a new case is therefore based on comparison with the nearest records. How-ever, such a model can only be applied to a limited range of situations covered by the data base, and results can hardly be extrapolated.

Other forecasting tools, based on semi-empirical models have been developed:

• the deposit over an alpine governed by the addition of two transport modes:

the potential (stationary) flow and a plume model for the turbulent non-steady effects [F¨ohn et Meister 1983];

• the situation in the canadian prairie decomposed in two processes: salta-tion and suspension, based on semi-empirical observasalta-tions (Prairie Blowing Snow Model PBSM) [Pomeroy 1988].

However, this models are dedicated to particular cases, and cannot be directly used on more general problems. Another direction to explore was therefore the indoor wind tunnels.

Indoor wind tunnel

Perhaps the most natural approach, when predicting snow or sand deposits around structures, was to use indoor wind tunnels. However, some similarity criterion must be observed to recover the outdoor situation:

• Iversen have defined a set of criterias to model snow deposit around fences [Iversen 1980];

• the same ideas have been adapted to model snow erosion/deposition at an alpine pass [Castelle 1995].

However, since the advent of powerful computers, numerical wind tunnels are not out of reach anymore.

Figure 1.4: ouput from [Uematsu et al. 1991] around a fence, where wind flow is plot in the upper part; snow drift rate and snow depth are confronted to outdoor results in the lower part of the figure.

Classical numerical models

Very early, computers have been used to model fluid flows. It has therefore been natural to incorporate a solid phase to the fluid one and simulate the deposits.

One of the earliest three-dimensional models have been proposed by [Uematsu et al. 1991], and a result is shown in figure 1.4. The static wind flow, and the lack of an

im-plementation of a particle saturation process cause some differences with reality.

However, this model was applied to true 3D configurations, such as the deposit around a cube.

More recent approaches have used commercial fluid solvers, such asFlow-3D, and later added a solid particle phase. [Sundsbo 1997] focuses on snow deposit around man made structures, such as fences and overall 3D complex buildings and has proposed very accurate results. [Gauer 1999], with the same kind of physically-based approach, addresses alpine terrain questions, comparing fully 3D numerical simulations around large crest areas with field measurements.

As in many other fields, classical numerical models are directly based on theorit-ical ones. This approach can be broken down in three layers:

1. based on observations, the main components or of the phenomenon (at least the supposed most relevant ones) are pointed out;

2. following argument and deduction, these extracted variables are mixed into a set of governing equations;

3. to be numerically handled (for an extrapolation purpose for instance), these equations must be transformed into a computable form.

At each of these levels, simplifications are assumed, a priori decisions are taken. The more complicated the phenomenon is, the less a consensus can be reached by different approaches.

This chain process is of course not unique to the problem adressed in this thesis. However, transport of solid particles by a fluid is a very good example of a complex system. Therefore, the approach introduced in the following section, radically different from the classical numerical models and aimed to served a very wide range of purposes, suits perfectly our problem.