force *F*″merge1 can be approximated as the lateral pressure exerted by ice moving

from channel 2, σz2, multiplied by the contact area parallel to the direction of flow

in channel 1, η2(*b*2/sin α + *b*e). The length *b*e can only be estimated, because no

predictive relationship presently exists for it. As an approximation, *b*e ≈ *b*s, though

Ice will not jam if Σ*F * *F*merge > 0, because the net force driving ice in channel 2 is

of ice moving from channel 1.

Equation 21 can be used in quasi-steady formulation of ice movement and jam-

ming in confluences. A difficulty in the formulation is estimation of the width *b*3

set *b*3 *b*c ≈ *b*3. This approximation is somewhat crude, but reasonable given all the

other uncertainties associated with estimation of jam behavior. Inclusion of *F*′merge1

and *F*″merge1 would modify the force formulation, such as proposed by Uzuner

and Kennedy (1976), for a static floating ice jam:

ρ η

(

)

(η1σ x1 ) - *y *η1τxy1

+ *s*i1ρ*g*η1 sin(θ + ϕ)1 -

τi1 cos i

ρ * x*1

(22)

- σ z2 η2 (

) - 1σ z2 η2 ( s

)=0

where σx, τxy, τi, are the normal stress in the streamwise direction, the shear stress

at the banks, and the shear on the underside of the cover, respectively. The angle θ

39

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