y
Ice
η(x,t)
υ(x,t)
Y(x,t)
Water
D(x,t)
d(x,t)
u(x,t)
Bed
yb(x)
x1
x2
x(horizontal
z
)
t
η(x,t)
Ai
d(x,t) δ
A
D(x,t)
b(δ)
d(x,t)
Y(x,t)
dδ
δ
y b (x)
x
z
Figure 24. Longitudinal and cross-sectional views of ice and water flow areas, showing
coordinate system used in equation development.
where
ρi =
ice density
υ =
ice velocity
Ai =
cross-sectional area of the jam
p =
porosity of the jam
si =
specific gravity of ice.
The first and third terms in eq 36 represent the mass flux of ice, while the second
and fourth terms represent the pore water. Pore water is only contained in that
portion of the ice area below the phreatic surface (siAi). The experiments of White
(1991) show that the velocity of flow through a stationary frazil cover is negligibly
small (105 m/s), resulting in negligible mass exchange between the pore water
and the underlying water flow. Hence, there is no term for seepage flow through
the jam provided. Pore water is assumed to move at the same velocity as the ice
and since ρi = siρ, the ice and pore-water terms may be combined. Setting eq 36
31
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