n

σn

t

Y

σ xy c

X

σt

σxx

boo m

σ yx

σ yy

in which

boom

The hydrodynamics model is verified by simulating

τsx,τsy = components of wind drag in *x*- and

flow in a rectangular ice-covered channel of length 2000

m, width 500 m, bed elevation at upstream 5 m, bottom

τwx,τwy = components of water drag in *x*- and

slope 0.0001, and bed Manning's coefficient of 0.03.

The ice cover thickness is selected to be 1.06 m, with a

Manning's coefficient 0.03. Water discharge is 2500

Since the ice element is essentially stationary, the force

m3/s and downstream water surface elevation is 0.2

balance conditions ∑ *F*x = 0 and ∑ Fy = 0 reduce the

m. The simulated water surface profile is compared with

above equations to the following, by neglecting the

the result of the one-dimensional backwater calculation

higher order terms

in Figure 6.

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Analytical solutions for idealized ice jams in a

straight, uniform, rectangular channel with a uniform

The normal and shear stresses acting on the boom

current are developed for verifying the numerical model.

segment *ab *are

The numerical simulation results are compared with

analytical solutions for ice accumulation in a channel

σ n = σ xx cos2 (*n*, *x*) + σ yy cos2 (*n*, *y*) +

of length 5000 m, width 500 m, constant water velocity

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of 0.6 m/s, and zero water surface slope. A boom is

+ 2σ xy cos(*n*, *x*) cos(*n*, *y*)

placed at 500 m and assumed 100% effective, i.e., no

ice is allowed to pass it. Initially, 900 ice parcels of size

σ t = (σ yy - σ xx ) cos(*n*, *x*) cos(*n*, *y*) +

(46)

50 50 m having a thickness of 0.2 m and a

+ σ xy cos2 (*n*, *x*) - σ yx cos2 (*n*, *y*) .

concentration of 0.6 are placed over the water surface

from the upstream boundary and the boom. In the

The normal and tangential components of the load per

simulations, this ice cover was allowed to move and

unit length of the boom are

consolidate behind the boom under the action of the

current drag. No additional ice was added during the

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simulations. The model parameters used are

summarized in Table 1.

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