been known to progress by juxtaposition at veloci-

analyses had been static in that they neglected the

ties more than three times greater than the critical

angular momentum of the rotating blocks). They

velocity they predicted. Using a different ap-

found that the Froude criteria of Pariset and

proach, Tremblay and Thibeault (1980) proposed

Hausser (1961) and Ashton (1974) underpredicted

a critical velocity criterion for the Milles Iles River

the critical Froude number for stability, particu-

(Quebec) based on the Chezy formula that in-

larly for small ratios of floe thickness to depth.

cluded floe size and ice discharge.

They did find good agreement, however, with the

Later researchers (e.g., Uzuner and Kennedy

shallow water criterion for stability presented by

1972, 1974; Ashton 1974; Uzuner 1975; Michel 1978;

Daly (1984):

Tatinclaux and Gogus 1981) used both laboratory

experiments and analysis to arrive at a rational

4 1 - *t*s β

3

Froude number to describe the limits of the rota-

≤

tional stability of the ice floes. Generally, a densi-

3

2

2

*t*b *t*b ρi

(2)

metric Froude number was used, with a length

1 - 1 - -

*H * *L * ρ

scale based on some ratio between the ice block

thickness and water depth, modified by the dif-

ference in the densities of water, ρ, and ice, ρi.

where *t*b is ice block thickness, *L *is ice block length,

Ashton (1974) successfully described the experi-

mental data using an analysis based on the "no-

that is independent of underturning velocity, and

spill" condition, which postulates that the limit of

block length, thickness, and density, determined

rotational stability occurs when the upper, up-

to be equal to 0.262. A definition sketch is given in

stream corner of the block becomes submerged.

Figure 2. The submerged depth of the ice block, *t*s,

He assumed that the underturning moment was

is calculated using

because of the constriction caused by the block.

Despite the obvious problem that the constriction

ρ

of flow would be negligible in deep water,

(3)

ρ

Ashton's criterion was widely adopted.

Daly and Axelson (1990) demonstrated that

floating blocks have a well-defined maximum

Daly (1984) noted that this equation, developed

righting moment. They noted that the limit of ro-

as a simple curve fit to data from Uzuner and

tational stability has been reached when the

Kennedy (1972), Ashton (1974), and Larsen (1975),

underturning moments exceed this maximum and

is not strictly applicable to deep water (ice block

a no-spill condition was not necessary. They de-

thickness-to-depth ratios less than about 0.1).

veloped an analytical expression for the limit of

More recently, Andres (1999) has proposed the

rotational stability in terms of the hydrostatic right-

use of a dimensionless stability number to deter-

ing moment of the block, expressed in the form of

mine whether juxtaposition or shoving will domi-

a densimetric Froude number. Their work was

nate the ice cover formation process under differ-

incorporated by McGilvary and Coutermarsh

ent hydrologic and meteorological conditions. His

(1992) in a dynamic analysis of ice block stability

analysis includes the effects of temperature in the

based on careful measurements of the pressure

form of air temperature (*T*a), the thermal conduc-

distributions around the leading edge and under-

tivity of the ice (*k*i), and the latent heat of fusion of

side of a model ice floe for various flow depths

the water (*L*f). The dimensionless stability num-

(Coutermarsh and McGilvary 1991, 1993). This

ber takes the form

pressure distribution, produced by the accelera-

tion of the flow as it passed under the block, cre-

ates an underturning moment acting on the block

(4)

that could cause underturning in both deep and

shallow water.

McGilvary and Coutermarsh (1992) further ex-

where *Q *is discharge, *B *is river width, and *S*f is

tended the analysis by including the angular mo-

the water slope. A typical value of the latent heat

mentum of the block, and demonstrated that the

of fusion of water is 334 J/g (Batchelor 1967). The

angular momentum could be an important factor

thermal conductivity of the ice is related to tem-

in causing blocks to underturn (all of the previous

perature by the following equation (USACE 1999):

3