NOMENCLATURE
αh
Fraction of water flow depth affected by the bed friction
εij
Generalized eddy viscosity coefficients
εij
Strain rate tensor
φ
Internal friction angle of ice
φB
Boundary friction angle
γ2
Wind drag coefficient
η
Water surface elevation
η′
Elevation of the undersurface of the ice layer
λ
Seepage flow coefficient
Nonlinear viscosity coefficient in constitutive law
θa
Angle between the wind direction and the x-axis
ρ
Water density
ρa
Air density
ρi
Ice density
σ
Internal ice stress
τax, τay
Components of wind drag on ice
→
τb
Shear stresses on the riverbed
τix, τiy
Components of seepage flow water drag on ice
→
τs
Shear stresses at the icewater or airwater interface
τwx, τwy
Components of lower-layer-flow water drag on ice
Ab
Flow area affected by the bed resistance
Ai
Flow area affected by the ice resistance
ca
Wind on ice drag coefficient
cf
Bed resistance coefficient
cw
Water on ice drag coefficient
→
Wind drag on ice
Fa
Fc
Ice cohesive force
Ff
Frictional force between ice and the solid boundary
FN
Normal ice force against the solid boundary
→
Water drag on ice
Fw
G
Gravitational force attributable to water surface slope
Gx, Gy
Components of gravitational force attributable to water surface slope
h
Water depth below the reference level
H
Total water depth
H′
Water depth beneath the ice layer
Hu
Net water depth in the ice layer
k
Dimensionless empirical coefficient for seepage flow formula
K
Hydraulic conveyance
Ki
Conveyance of flow carried by ice
Kl
Conveyance of the lower water layer
Ks
Conveyance of seepage flow
Kt
Total conveyance of flow
Ku
Total conveyance of flow in the upper ice layer
Mi
Ice mass per unit area
Ms
Average surface area per volume of ice
nb
Manning's coefficient of river bed
ni
Manning's coefficient of ice
N
Ice concentration
p
Ice porosity
P
Internal ice pressure term in the constitutive law
v
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