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

*A*i =

cross-sectional area of the jam

*p* =

porosity of the jam

*s*i =

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 (*s*iAi). 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 = *s*iρ, the ice and pore-water terms may be combined. Setting eq 36

31