B l o w i n g

S n o w

NUMERICAL METHOD

Equations

Numerical modelling and simulations of air flow fields
are performed with FLOW-3D(Hirt, 1975), a general pur-
posecomputerprogrambasedonfinite-volumetech-
nique.FLOW-3D usesthe Fractional Area/Volume Ob-
stacle Representation method or often referred to as the
FAVOR technique (Hirt,1993),tomodel obstaclesand
porous baffles.Obstacles are defined with zerovolume
porosityregions while thin porous bafflesare given by
area porosities.Inthe following transport equations,V
denotes the fractional volume open to flow and A is the
fractional area open toflow:

Continuity equation forthe airphase:

• Calculationofairvelocityprofile basicallybyensur-
  ing conservation ofmass and momentumforthe air-
  flow.
• Calculation of the friction velocity.
• Calculationofsnowdriftbasedonairvelocitiesand
  friction velocity from step 1 and 2, respectively.Snow
  transport isfirstevaluated by eq.4 and then byesti-
  mating some drift fromeq. 5.
• Evaluating of the snow surface. A new snow surface is
  formed where thesnow density is sufficiently high and
  thefrictionvelocityisbelowthethreshold valuefor
  snow drift. Erosion of old surfaces will occur at higher
  values of the friction velocity.

SIMULATIONOF CREEP, SALTATIONAND SUSPENSION

A scalar advection equation ( eq. 4) is used as the basis for
modelling of snow transport. Suspension by mean flow is
consideredby solving this advectionequation for the snow
phase based on the Eulerian wind velocity field. Thus the
airborne snow phase is treated as a dilute suspension, and
relative drift between snow and air phase is additionally
given by eq. 5. The drift velocity is a result of the balance
between pressure forces and interfacial drag forces. Drift-
fluxmodellingofsnowdriftwithoutaccumulationor
saltation can be found in Bang et al. (1994).
Modelling of saltation is boiled down to a vertical lift
problemregarding the snow phase.A vertical snow den-
sityprofilebasedonempiricalknowledge(Mellorand
Fellers,1986)ismaintained above thesnowsurface,by
introducing vertical transport in the advection equation.
Horizontal fluxes are then calculated as for suspension of
snow by the mean flow. The lifteffectisincluded until
the calculated frictionvelocity ineq.3decreases below
the threshold value forsaltation.The snow istherefrom
left to settle for possible accumulations. Deposition on the
snow surface is accomplished by accumulating a specific
part of the incoming snow fraction. It is also assumed that
theamountofsnowtransportbycreep issmall andin-
cluded in the saltation drifting process.

BOUNDARY CONDITIONS

Left inlet boundary condition

Measurements during blowingsnow conditions shows that
the mean wind profile is proportional to the logarithm of
height above the snow surface (Male, 1980), which also is
true fromobservations at non-blowing snow conditions.
Themean windprofileinsnowdriftseemstobemore
reducednear the surfacethan for situations without blow-
ing snow. This reduction in wind speed may be explained
byatransferofmomentumthrough thesaltatingparti-
cles, from the wind to the surface, or by the vigorous stir-
ring by saltating particles which results in a reduction of
the shear of the wind velocity (Maeno et al., 1979).
Mean inlet velocity is in agreement with field observa-
tions given bythe logarithmic profile:

=0

(1)

(2)

phase:

where a andb representviscous accelerations and flow
losses across porous baffles,respectively.

The friction velocity forthe airphase:

u_*= u (z) K/1n ( ----^z
z⁾
sno w

(3)

where u is the horizontal velocity at height z, k the von
Kármáns constant and z_{sno w} the surface roughness height
forcalculations ofthefrictionvelocity.A procedure for
calculating the friction velocityis proposed by Sundsbø
and Hansen (1996).

Scalar advection forthe snow phase:

V--
ðf ^ð
ðt^{+( fUA}
--
>_{) =-wF--}
ðz^{(fA z )}

(4)

w_Fis the terminal snowfall velocity and A_zis the frac-
tional area open to flow in vertical direction.

Relative velocity between the two phases:

--
U^>
r ^{=------------(rair-rsno w)}
K^{( 1-f}

(5)

Simulationprocedures

The air velocity model is based on a Eulerian description
that mainly involves solving Navier-Stokes equations to
obtain the mean velocity field.The following procedures
are repeated foreach time step:

130

u ( z) = ^u(--^z
K
--
*_{lnz) whemz>>z}
0
0

(6)

The inlet snow profile is given as a vertical mass concen-