Environmental Engineering Reference
In-Depth Information
(
ε
0
h
in equation [2.33)] as well as by mixing the flow (fourth and fifth terms in
equation [2.33)] and maintaining the suspension against sedimentation flow mixing
(last term on the right-hand side of equation [2.33]).
Although originally devoted to submarine turbidity currents, this model has been
applied to airborne avalanches, with only small modifications in the entrainment
functions [FUK 90, GAU 95]. A new generation of powder-snow avalanche models
has recently appeared [HUT 96]. Some rely on the numerical resolution of local
equations of motion, including a two-phase mixture approximation and closure
equations (usually a
k −
model for turbulence) [NAA 97, SAM 93, SCH 87].
Other researchers have tried to establish the relation existing between a dense core
and an airborne avalanche because they think that, most often, a powder-snow
avalanche is tightly related to a denser part that supplies the airborne part with snow
[EGL 83, ISS 98, NAZ 91]. Though these recent developments are undoubtedly a
promising approach to modeling powder-snow avalanches, their level of sophistication
contrasts with the crudeness of their basic assumptions as regards the momentum
exchanges between phases, turbulence modification due to the dispersed phase, and
so on. At this level of our knowledge of physical and natural processes, it is of great
interest to continue to use simple models and to fully explore what they can describe
and explain.
2.2.5.
Three-dimensional computational models
The rapid increase in computer power has allowed researchers to integrate
local motion equations directly. Compared to the depth-averaged models, the
problems in the development of three-dimensional computational models mainly
concern numerical treatments. For instance, the treatment of the free surface poses
complicated issues. Naturally, problems linked to the constitutive equations reliable
for snow are more pronounced compared to intermediate models since the entire
constitutive equation must be known (not just the shear and normal stress). The
development of three-dimensional models is currently undertaken mainly for airborne
avalanches generally using finite-volume codes for turbulent flows. Examples include
the models by Naaim and Gurer [NAA 97], Hermann
et al.
[HER 93] and Scheiwiller
et al
. [SCH 87].
2.2.6.
Small-scale models
A few authors have exploited the similarities between avalanches and other
gravity-driven flows. For instance, Hopfinger and Tochon-Danguy used the analogy
between airborne avalanches and saline density currents to perform experiments
in the laboratory in a water tank [HOP 77]. In this way, examination of various
aspects of airborne dynamics has been possible: effect of a dam, structure of the
