the modeling of the channel deformations in the rivers flowing into permafrost with an increase in...
TRANSCRIPT
The modeling of the channel deformations in the rivers flowing into permafrost with an increase in ambient temperatureE. Debolskaya, E. Zamjatina, I.Gritsuk and O. Maslikova
Water Problems Institute of RAS, Moscow, Russia ([email protected])
The purpose of this work is to investigate the influence of river flow during the increase of water temperature on the deformation of the coastal slopes, composed of permafrost rocks with the addition of ice layers.The method of investigation is laboratory and mathematical modeling.
Problem. Global climate changes in recent decades inevitably lead to more frequent catastrophic events. Their negative effects on rivers flowing into the permafrost zone, may be exacerbated by significant changes in bed deformations caused not only the influence of water flow, but significant changes of the bed due to the influence of increasing water and air temperatures on the structure of its constituent materials.
DESCRIPTION OF THE MODEL
Modeling of the ice plates melting - parameterization of the thermal effects
tL=
y
T
y
T
21
- the coefficients of thermal conductivity of ice and water, L - latent heat of ice melting,
Modeling of flow in the mainstream and thawed cavities - parameterization of the hydrodynamic regime
zuu ln bõ=u *
2
2u =bõ
3/1
2
H
gn=
2
n – the roughness coefficient in the Manning formula,
The transverse velocity is calculated from the equation of continuity
Modeling of the soil settlement and the sediment transport in the thawed cavities - parameterization of the channel deformations
bõ - the longitudinal component of shear stress on solid surfaces,
- the hydraulic friction coefficient.
- the coordinate of the interface, T - temperature, t – time.
where 21, - density of the ice,
The slide of soil lying above the thawed cavity filled with water, is described as a deflection of a beam on an elastic base and clamped at one end. The equation for maximum deflection of a beam, at which the separation of the soil can be described by the dependence
h
y=
Eh
y=
22
4
where y - transverse dimension of the thawed areas, σ - tensile strength , E - modulus of elasticity,
h - thickness of soil above the cavity
The erosion of the deposited soil is determined from the equation of mass conservation of sediment transported
01 =y
Q+
x
Q+p)z(
tsysõ
b
where p - porosity of the bottom material, Qsx, Qsy – the longitudinal and transverse components of sediment charge per unit width. To determine Qsx, Qsy Engelund dependencies were used
gd
gdu=Q
ss
äõsx 1/
0.052/3
2
gd
gdv=Q
ss
äysy 1/
0.052/3
2
where d – the average diameter of the soil particles, ρs - their density, ρ – the density of water.
Laboratory experiment and scheme of the cross-section with two plates of ice before and during melting
RESULTS
а
а
soil
ice
water
бh
y
The channel deformation of the Yenisei River under the influence of the flood wave. The coast erosion uncovered the whole ice mountain.
бh
y
бh
y
бh
y
бh
y
y
z ConclusionsThe erosion of the thawed cavities plays a less significant role in the overall picture of deformation than soil settlement.A significant increase of the roughness coefficients of the talik leads not only to substantial changes in the deformation within the taliks, but also to the appearance of the deformation in the bottom of the river bed of the stream, changing its mode from the non-critical to critical.The bed deformation of the rivers flowing in the permafrost zone is different significantly from the deformation of channels composed of soils not susceptible to the influence of the phase transition "water-ice," and can occur even under the nonerosive velocity of the water flow.
The time dependence of the phase transition boundary -1, its linear approximation – 2.
The vertical distribution of transverse velocities with depth.1 – on the section corresponding to the entrance of the talic2 - on the section corresponding to the output of the talic
The coastal relief in the cross-vertical projection after 1 hour of model time for different roughness in the thawed areas.
The relief of the coastal slope at the start of the numerical experiment - a, 60 minutes after the start of the numerical experiment – b, the photo of the coast slope 60 minutes after the start of the laboratory experiment - c