Unsteady Ice Jam Processes
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
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
