ness coefficient assignment as a function of thickness based on the data of

Nezhihovskiy (1964). The program then automatically updates the HEC-2 input

file to reflect these new values of ice thickness and roughness. Iterations continue

until a specified tolerance is met. Considerable judgment is necessary in the jam-

toe area, where ice thickness conditions cannot be expressed adequately by the

Lal and Shen (1991) developed the jam model RICE, which is intended to simu-

late unsteady conditions of water flow, water temperature, ice concentration, and

thermal growth and decay of ice. In their model, ice travels downstream at the

water velocity until it reaches some location where a jam forms, by either ice-piece

juxtaposition or the narrow-jam or wide-jam accumulation modes. The wide-jam

mode is taken to be governed by the ice force balance equation proposed by Pariset

et al. Lal and Shen did recognize that as progression (by shoving) is taking place,

there is a simultaneous change in the flow hydraulics. They take care of flow changes

by solving the equilibrium thickness and step-backwater equations simultaneously

in the reach where the jam is thickening. The RICE model has been used success-

fully in simulations of ice conditions on the St. Lawrence, Niagara, Ohio, and Yel-

low rivers, though, like other models, it requires significant calibration to match

field data.

Tsai et al. (1988) developed a jam model to investigate ice transport in rivers and

ice jam initiation. They used a one-dimensional numerical scheme for solving the

ice transport equations, i.e., conservation of ice momentum, ice mass, and ice area.

The equations are solved in a Lagrangian form, where the trajectories of ice ele-

ments at fixed Eulerian grid points at the beginning of a time step are traced on the

the end of the time step. The de Saint Venant equations for unsteady water flow are

solved using a four-point implicit finite-difference scheme. The ice transport and

water flow equations are loosely coupled by first solving the water flow equations

and then the ice transport equations based on the new values of the water flow

variables.

Shen et al. (1990) elaborated further aspects of this model, examining the vari-

ous plausible constitutive relationships possible for describing the internal stresses

and bank shear. For example, they describe a rapid flow regime as one in which the

ice concentration is low and interaction between ice particles is minimal. Commen-

surately, they characterize a slow flow regime as one in which higher (multi-layer)

ice concentrations typically form, and where internal resistance is attributable to

prolonged interaction of contacting particles. Their expressions for the streamwise

stress σx and the stress normal to the bank τxy are equivalent to those for passive

pressure resistance, as described by Pariset et al. The authors state the model

appears to adequately describe the time and location of jam initiation in river chan-

nels, but that more research is necessary to improve the constitutive laws.

While considerable progress has been made in modeling the unsteady flow

associated with stationary ice jams, the unsteady aspects of ice movement have

not been adequately addressed. Most models treat shoving and thickening as an

instantaneous phenomenon, with no consideration for the effects of ice momen-

tum on the resulting jam thickness and profile. Physics and field observations sug-

gest that ice momentum should substantially affect jam thickness.

The following sections describe laboratory and numerical experiments aimed at

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