Field observations - CR97_070009

Figure 3. Ice jam failure with ice fully mobilized; view is looking downstream

Objective and approach

REVIEW OF ICE JAM MODELING

Season of occurrence

Figure 7. Freezeup jam following shoving and thickening

Figure 9. Cross section of a breakup jam

Figure 10. Mid-winter breakup jam on the Kennebec River in Maine

Dominant formation process

Analysis of stationary jams

Figure 12. Idealization of ice jam evolution with time

Figure 13. Forces acting on an ice cover

Analysis of stationary jams-continue - CR97_070021

Figure 14. Dimensionless stability parameter

Analysis of stationary jams-continue - CR97_070023

Numerical modeling

Numerical modeling-continue

Summary - CR97_070026

LABORATORY EXPERIMENTS - CR97_070027

Experimental setup - CR97_070028

Figure 16. Plastic beads used to simulate ice

Observations of shoving and thickening

Observations of shoving and thickening-continue

Equilibrium thickness evaluations

Figure 18. Measured velocity profile with fitted log-law equations for the ice and bed-affected areas

Figure 19. Slope vs. discharge, showing inrease in slope after jam failure

Discussion - CR97_070035

FORMULATION - CR97_070036

Development of equations

Figure 24. Longitudinal and cross-sectional views of ice and water flow areas

Conservation of water momentum

Conservation of water momentum-continue

Figure 26. Two-layer approach designation of shear stress due to water flow

Figure 27. Shear stress due to water flow for cases of a moving jam

Figure 28. Shear force on the ice jam underside vs. ice velocity

Conservation of ice momentum

Conservation of ice momentum-continue

Substituting for Ffi gives

Integration yield

Conservation of water mass

Discretization of the system of equations

Discretization of the system of equations-continue - CR97_070050

Figure 30. Computational grid used for the numerical simulations

Discretization of the system of equations-continue - CR97_070052

Discretization of the system of equations-continue - CR97_070053

Solution of the system of equations

Solution of the system of equations-continue

Ice cover stability, solution methods, and boundary conditions

Ice cover stability, solution methods, and boundary conditions-continue

Fully coupled solution

Loosely coupled solution

Figure 34. Block diagram for the loosely coupled solution scheme

Static-unsteady thickness solution

NUMERICAL MODEL DESCRIPTION

Table 1. List of baseline testing parameters

Baseline runs-continue

Figure 36. Output plots of solution variables for baseline run

Figure 36. Continued - CR97_070066

Figure 36. Continued - CR97_070067

Model rigor

Courant number sensitivity

Figure 44. Final jam thickness profiles for θi = 1.0 and θ = 0.55, 0.6, 0.66, 0.8, and 1.0

Alternate boundary conditions

Effects of variable length steps

Figure 49. Final jam thickness profile for length step reduced to 25 m

UNSTEADY JAM DYNAMICS

Effects of ice momentum-continue

Comparison with steady-state models

Figure 54. Discharge record during breakup jam initiation and failure

Dimensionless momentum parameter

Table 2. Ice parameters for channels at different bed slopes

Table 3. Characteristics of various inflow hydrographs

Effects of hydrograph shape on jam thickening

Figure 62. Effect of tp on final jam thickness profile shape

SUMMARY - CR97_070083

CONCLUSIONS - CR97_070084

RECOMMENDATIONS FOR FUTURE RESEARCH

LITERATURE CITED - CR97_070086

LITERATURE CITED-continue - CR97_070087

Report Documentation Page - CR97_070088

CR97_07