CN111881592B - River ice numerical simulation method considering river bed anchor ice - Google Patents

River ice numerical simulation method considering river bed anchor ice Download PDF

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CN111881592B
CN111881592B CN202010766130.1A CN202010766130A CN111881592B CN 111881592 B CN111881592 B CN 111881592B CN 202010766130 A CN202010766130 A CN 202010766130A CN 111881592 B CN111881592 B CN 111881592B
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CN111881592A (en
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潘佳佳
郭新蕾
王涛
付辉
李甲振
郭永鑫
施春蓉
路锦枝
杨涛
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China Institute of Water Resources and Hydropower Research
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Abstract

The invention relates to a river ice numerical simulation method considering river bed anchor ice, which comprises the following steps: collecting water ice data, calculating a one-dimensional shallow water equation set, water body net heat absorption capacity, water temperature, ice concentration in water, surface density of floating ice, ice flower layer thickness, ice cover thickness and anchor ice thickness, updating a river channel comprehensive roughness coefficient and simulating a river ice process and water level flow change. The method can accurately calculate the growth and ablation processes of floating ice, ice in water, ice cover and anchor ice, can simulate the generation, development, propagation and dissipation processes of anchor ice flood waves, and has high calculation precision; meanwhile, the method can evaluate the influence of the river ice process on the water level and flow change, has wide model application range and is suitable for the ice flood simulation with long duration in a large range.

Description

River ice numerical simulation method considering river bed anchor ice
Technical Field
The invention relates to a river ice numerical simulation method considering river bed anchor ice, and belongs to the technical field of hydraulic engineering.
Background
Due to the influence of seasonal air temperature, heat is continuously released from northern rivers in winter, ice in water, running ice and a frozen ice cover can be formed, and further the change of water level and flow is influenced. River ice accumulation under extreme conditions can cause ice to plug ice dams, inducing ice flooding. The ice in the water can be adhered to buildings in the water even blocking a water diversion port and a trash rack, and further causing water delivery difficulty in winter. Anchor ice is ice adhered or anchored on a bed surface and is a common phenomenon in rivers in cold regions. The growth of the anchor ice can block a water intake submerged in a river channel to form an anchor ice falling sill, and further flood discharge of the river channel in winter is influenced. The growth and release of large-area anchor ice on the river channel can cause the rapid change of the topography of the river bed, the change of the flow of the cross section and the mutation of the integral roughness of the bed surface, thereby causing the fluctuation of the water surface. The growth and release process of a large amount of anchor ice can cause the water depth and the flow rate to increase by more than 30 percent, even can induce the generation of chain type anchor ice flood waves, damage the stability of ice covers at the downstream of a river closing period and cause ice flood. The development of bank ice and ice covers can also reduce the river channel flow area, and further influence the water delivery flow of the canal. The growth and release of the river ice can obviously change the water delivery capacity of a canal, cause severe fluctuation of water level flow in winter, threaten industrial and agricultural production at both sides of the river channel and bring hidden troubles to the life and property safety of people.
Most of traditional river ice mathematical models aim at a single river ice process and cannot solve the problem of the river ice in the whole winter of a long river channel. The existing studies have the following limitations: firstly, the drag force of the river ice on water flow is not considered, and the water level flow change under the influence of the river ice cannot be accurately reflected; secondly, the problem of flood waves caused by growth and release of the anchor ice is ignored, and the generation, development, propagation and attenuation processes of the anchor ice flood waves cannot be accurately calculated; thirdly, the dynamic development process of floating ice, ice flow and ice cover is not considered, and the influence of the whole process of the river ice on the water delivery process of the canal cannot be accurately simulated; and fourthly, the coupling effect of river ice and water flow with large scale and long duration cannot be calculated, and the water delivery safety of northern rivers is influenced.
Therefore, it is necessary to develop a river ice numerical simulation method considering the bed anchor ice to satisfy the large-scale and long-duration river ice and water level flow simulation.
Disclosure of Invention
In order to overcome the problems of the prior art, the invention provides a river ice numerical simulation method considering the river bed anchor ice, which can meet the requirements of river ice and water level flow simulation with large scale and long duration and can be widely used for analyzing the river ice process and water level flow change of northern rivers.
The purpose of the invention is realized as follows:
a river ice numerical simulation method considering river bed anchor ice calculates a one-dimensional shallow water equation set by considering the drag force of the river ice on water flow, and calculates the water temperature change by the energy conservation principle; the method comprises the following steps of calculating the growth and ablation process of the river ice through water body heat exchange, and updating the water level flow change under the influence of the river ice, wherein the method specifically comprises the following steps:
step 1, collecting water ice data: collecting or measuring water ice data including river terrain, water level, flow, water temperature, ice concentration in water and heat exchange coefficient between water and air in a research area;
step 2, calculating a one-dimensional shallow water equation set: based on the water ice data collected in the step 1, solving a one-dimensional shallow water equation set considering the river ice influence by adopting a four-point hidden-format Prisman method;
Figure BDA0002614665250000021
Figure BDA0002614665250000022
wherein t is time; x is the distance in the direction of flow; a is the area of the cross section; ρ is the density of water; q is river flow; h is water level; p is a radical ofbIs the wet week of the riverbed part; p is a radical ofiIs the wet week of surface river ice; b isoThe width of the open flow part of the cross section; tau isbIs the riverbed shear stress; tau isiThe drag force of the surface floating ice; tau isaDrag of surface air; g is the acceleration of gravity;
step 3, calculating the net heat absorption capacity of the water body: calculating the net heat absorption capacity of the river water body by adopting the following equation;
φss-φsk＝pbφb-B(1-fB)(1-Ca)φwa-[(1-fB)BCa+CbPb+fBB]hwi(Tw-Tf)
in the formula, phissHeat flux absorbed for the surface and wet perimeter of the water body; phi is askHeat flux released for the surface and wet weeks of the body of water; phi is abHeat transfer flux to the riverbed; phi is awaIs the heat flux between water and air; f. ofBThe ratio of the bank ice to the river width is shown; caThe surface density of the floating ice on the surface; cbThe proportion of the anchor ice covered on the wet circumference of the riverbed; h iswiIs the heat exchange coefficient between water and ice; t iswThe water temperature is adopted; t isfThe freezing temperature of the water body; b is the width of the cross section of the river channel; pbIs the wet week of the riverbed part;
step 4, calculating the water temperature and the ice concentration in the water: calculating the average water temperature and the ice concentration in water of the river section by adopting the following simultaneous equation;
Figure BDA0002614665250000023
Figure BDA0002614665250000024
in the formula, CvIs the ice concentration in the water; cpThe specific heat capacity of the water body; l isiLatent heat of fusion of ice; e is the rate of ice ablation in the water; rhoiIs the density of ice;
step 5, calculating the surface density of the floating ice: calculating the surface density of the surface floating ice by adopting the following equation;
Figure BDA0002614665250000025
in the formula, hiEffective ice thickness for ice floes; vbThe rate of ice flotation in the water; alpha is the probability of ice floating in water; beta is the probability of the ice on the surface being washed into the ice in the water; ranFor release of anchor iceA rate; u is the average flow velocity of the section;
step 6, calculating the thermal growth and the ablation thickness of the ice: the thermal growth and ablation thickness of the ice were calculated using the following equations:
Figure BDA0002614665250000031
in the formula, hiaIs the heat exchange coefficient between ice and air; t isiIs the ice surface temperature; t isaIs the air temperature; e.g. of the typefPorosity of the ice flower layer;
step 7, calculating the thickness of the ice flower layer: calculating the thickness of the ice flower layer by adopting the following equation;
Figure BDA0002614665250000032
in the formula, hfIs the thickness of the ice flower layer;
step 8, calculating the thickness of the ice cover: setting the ice sealing position or ice blocking starting point of the river channel section, and calculating the critical Froude number and the corresponding ice cover thickness of different river ice accumulation up-tracking modes;
the average froude number of a section is calculated using the following equation:
Figure BDA0002614665250000033
in the formula, FrAverage Froude number of cross section; d is the average water depth of the section;
calculating critical Froude numbers of different ice cover development modes, and judging whether the ice cover is in a tiling and upward tracing mode, a hydraulic thickening mode or a mechanical thickening mode;
Figure BDA0002614665250000034
Figure BDA0002614665250000035
wherein, FrpCritical Froude number for tiled up-trace mode; frcCritical froude number for hydraulic thickening mode; phi is afIs an empirical coefficient related to the ice cube size; e.g. of the typepPorosity of ice cap;
if Fr＜FrpThe ice cover is developed according to a flat-laying up-tracing mode, and the ice thickness is the thickness of single-layer floating ice; if Frp＜Fr＜FrcThen the ice cover thickness is calculated according to the following equation:
Figure BDA0002614665250000036
if Fr＞FrcThen the ice cover thickness is calculated according to the following equation:
Figure BDA0002614665250000041
in the formula, phi is the internal friction angle of ice; tau iscShear stress of the river bank to ice; tau isgThe gravity component of the ice cover along the flow direction; mu is the internal friction coefficient of the river ice;
step 9, calculating the thickness of the anchor ice: calculating the thermal growth and the ablation thickness of the anchor ice, judging whether the anchor ice is released or not, and calculating the corresponding release volume of the anchor ice, wherein the growth rate of the anchor ice is calculated according to the following equation:
Figure BDA0002614665250000042
in the formula, hanThe thickness of the anchor ice; e.g. of the typeaPorosity of the anchor ice; cvThe concentration of ice in the suspension water; gamma is the adsorption rate of ice in water on the riverbed; phi is aanThe net heat exchange capacity between the water body and the anchor ice;
step 10, updating the comprehensive roughness coefficient of the river channel: calculating the comprehensive roughness of the river channel considering the influence of the anchor ice by adopting a piecewise linear formula, wherein the calculation equation is as follows:
Figure BDA0002614665250000043
in the formula, nbi0The comprehensive roughness coefficient of the river channel is considered to be influenced by the anchor ice; n isbThe coefficient of roughness of the river channel without anchor ice is shown; dsThe median particle size of the riverbed silt;
step 11, simulating a river ice process and water level flow change: and calculating all factors including water level, flow, water temperature, ice thickness, ice concentration and anchor ice thickness time by time according to all the equations, and simulating the river ice process and the corresponding water level flow change.
Further, the judgment of whether the anchor ice is released or not in the step 9 is carried out according to the following equation: if the equation is established, the anchor ice is completely released; if the equation is not satisfied, the anchor ice is not released;
Figure BDA0002614665250000044
in the formula, WbIs the net buoyancy of the anchor ice body; fbThe tensile resistance between the anchor ice and the river bed; ρ is the density of water;
Figure BDA0002614665250000045
is the anchor ice volume.
The invention has the advantages and beneficial effects that: the invention provides a river ice numerical simulation method considering river bed anchor ice, which can accurately calculate the growth and ablation processes of floating ice, ice in water, ice cover and anchor ice, can simulate the generation, development, propagation and dissipation processes of anchor ice flood waves, and has high calculation precision; meanwhile, the method can evaluate the influence of the river ice process on the water level and flow change, has wide application range of the model, and is suitable for the ice flood simulation with a large range and a long duration; in addition, the invention considers various river ice types and two-layer movement of water flow and flowing ice, and provides theoretical basis and calculation tool for preventing and controlling the ice-filled ice dam of the northern river.
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The invention is further illustrated by the following figures and examples.
FIG. 1 is a schematic illustration of a glacier process;
FIG. 2 is a flow chart of a method according to an embodiment of the invention;
FIG. 3 is a process of calculating the flow boundary of the upstream river of the region and the flow of two tributaries according to an embodiment of the present invention;
FIG. 4 is a flow process simulated and measured at 364 km upstream in accordance with an embodiment of the present invention;
FIG. 5 is a diagram illustrating simulated and measured water level at 364 km upstream in accordance with an embodiment of the present invention;
FIG. 6 is a simulated and measured water temperature process at 364 kilometers upstream in accordance with an embodiment of the present invention;
FIG. 7 is a simulated and measured distance of the leading edge of the ice cover from the upstream dam in accordance with an embodiment of the present invention;
FIG. 8 shows simulated anchor ice thickness and river channel aggregate roughness coefficient for the Canadian Pisrefer river embodiment of the invention.
Detailed Description
Example (b):
the embodiment is a river ice numerical simulation method considering river bed anchor ice, which comprises the following steps:
step 1, collecting water ice data: collecting or measuring water ice data including river terrain, water level, flow, water temperature, ice concentration in water and heat exchange coefficient between water and air in the research area.
Step 2, calculating a one-dimensional shallow water equation set: based on the water ice data collected in the step 1, solving a one-dimensional shallow water equation set considering the river ice influence by adopting a four-point hidden-format Prisman method;
Figure BDA0002614665250000051
Figure BDA0002614665250000052
wherein t is time; x is the distance in the direction of flow; a is the area of the cross section; ρ is the density of water; q is river flow; h is water level; p is a radical ofbIs the wet week of the riverbed part; p is a radical ofiIs the wet week of surface river ice; b isoThe width of the open flow part of the cross section; tau isbIs the riverbed shear stress; tau isiThe drag force of the surface floating ice; tau isaDrag of surface air; g is the acceleration of gravity.
Step 3, calculating the net heat absorption capacity of the water body: calculating the net heat absorption capacity of the river water body by adopting the following equation;
φss-φsk＝pbφb-B(1-fB)(1-Ca)φwa-[(1-fB)BCa+CbPb+fBB]hwi(Tw-Tf) (3)
in the formula, phissHeat flux absorbed for the surface and wet perimeter of the water body; phi is askHeat flux released for the surface and wet weeks of the body of water; phi is abHeat transfer flux to the riverbed; phi is awaIs the heat flux between water and air; f. ofBThe ratio of the bank ice to the river width is shown; caThe surface density of the floating ice on the surface; cbThe proportion of the anchor ice covered on the wet circumference of the riverbed; h iswiIs the heat exchange coefficient between water and ice; t iswThe water temperature is adopted; t isfThe freezing temperature of the water body; b is the width of the cross section of the river channel; pbIs the wet week of the riverbed part.
Step 4, calculating the water temperature and the ice concentration in the water: calculating the average water temperature and the ice concentration in water of the river section by adopting the following simultaneous equation;
Figure BDA0002614665250000061
Figure BDA0002614665250000062
in the formula, CvIs the ice concentration in the water; cpThe specific heat capacity of the water body; l isiLatent heat of fusion of ice; e is the rate of ice ablation in the water; rhoiIs the density of ice.
Step 5, calculating the surface density of the floating ice: calculating the surface density of the surface floating ice by adopting the following equation;
Figure BDA0002614665250000063
in the formula, hiEffective ice thickness for ice floes; vbThe rate of ice flotation in the water; alpha is the probability of ice floating in water; beta is the probability of the ice on the surface being washed into the ice in the water; ranIs the release rate of the anchor ice; u is the cross-sectional average flow velocity.
Step 6, calculating the thermal growth and the ablation thickness of the ice: the thermal growth and ablation thickness of the ice were calculated using the following equations:
Figure BDA0002614665250000064
in the formula, hiaIs the heat exchange coefficient between ice and air; t isiIs the ice surface temperature; t isaIs the air temperature; e.g. of the typefPorosity of the ice flower layer.
Step 7, calculating the thickness of the ice flower layer: calculating the thickness of the ice flower layer by adopting the following equation;
Figure BDA0002614665250000065
in the formula, hfIs the thickness of the ice flower layer.
Step 8, calculating the thickness of the ice cover: setting the ice sealing position or ice blocking starting point of the river channel section, and calculating the critical Froude number and the corresponding ice cover thickness of different river ice accumulation up-tracking modes;
the average froude number of a section is calculated using the following equation:
Figure BDA0002614665250000066
in the formula, FrAverage Froude number of cross section; d is the average water depth of the section;
calculating critical Froude numbers of different ice cover development modes, and judging whether the ice cover is in a tiling and upward tracing mode, a hydraulic thickening mode or a mechanical thickening mode;
Figure BDA0002614665250000067
Figure BDA0002614665250000068
wherein, FrpCritical Froude number for tiled up-trace mode; frcCritical froude number for hydraulic thickening mode; phi is afIs an empirical coefficient related to the ice cube size; e.g. of the typepPorosity of ice cap;
if Fr＜FrpThe ice cover is developed according to a flat-laying up-tracing mode, and the ice thickness is the thickness of single-layer floating ice; if Frp＜Fr＜FrcThen the ice cover thickness is calculated according to the following equation:
Figure BDA0002614665250000071
if Fr＞FrcThen the ice cover thickness is calculated according to the following equation:
Figure BDA0002614665250000072
in the formula, phi is the internal friction angle of ice; tau iscShear stress of the river bank to ice; tau isgThe gravity component of the ice cover along the flow direction; mu is the internal friction coefficient of the river ice.
Step 9, calculating the thickness of the anchor ice: calculating the thermal growth and the ablation thickness of the anchor ice, judging whether the anchor ice is released or not, and calculating the corresponding release volume of the anchor ice, wherein the growth rate of the anchor ice is calculated according to the following equation:
Figure BDA0002614665250000073
in the formula, hanThe thickness of the anchor ice; e.g. of the typeaPorosity of the anchor ice; cvThe concentration of ice in the suspension water; gamma is the adsorption rate of ice in water on the riverbed; phi is aanThe net heat exchange capacity between the water body and the anchor ice;
judging whether the anchor ice is released or not according to the following equation: if the equation is established, the anchor ice is completely released; if the equation is not satisfied, the anchor ice is not released;
Figure BDA0002614665250000074
in the formula, WbIs the net buoyancy of the anchor ice body; fbThe tensile resistance between the anchor ice and the river bed; ρ is the density of water;
Figure BDA0002614665250000075
is the anchor ice volume.
Step 10, updating the comprehensive roughness coefficient of the river channel: calculating the comprehensive roughness of the river channel considering the influence of the anchor ice by adopting a piecewise linear formula, wherein the calculation equation is as follows:
Figure BDA0002614665250000076
in the formula, nbi0The comprehensive roughness coefficient of the river channel is considered to be influenced by the anchor ice; n isbThe coefficient of roughness of the river channel without anchor ice is shown; dsThe median particle size of the riverbed silt;
step 11, simulating a river ice process and water level flow change: and (3) calculating each element including water level, flow, water temperature, ice thickness, ice concentration and anchor ice thickness time by time according to the equations (1) - (16) to simulate the river ice process and the corresponding water level flow change.
The simulation is as follows:
taking the winter river ice simulation of the Canadian Pistriffer river 2014-2015 as an example, the method comprises the steps of collecting data such as the terrain, the water level, the flow, the water temperature, the ice concentration in water, the heat exchange coefficient between water and air and the like of the Pistriffer river, and providing initial conditions, boundary conditions and basic data for the one-dimensional river ice numerical simulation. Fig. 3 shows the upstream flow boundary of the calculation region and the flow boundaries of the two branches of the calculation region.
Calculating water level, flow, water temperature, ice thickness, ice concentration, anchor ice thickness and the like time by time according to equations (1) to (16), simulating the river ice process and corresponding water level flow change, and the simulation results are shown in fig. 4 to 8. Fig. 4 shows the comparison of the simulated flow process and the measured value at 364 km, fig. 5 shows the comparison of the simulated water level process and the measured value at 364 km, and fig. 6 shows the comparison of the simulated water temperature process and the measured value. FIG. 7 further shows the simulated ice cover leading edge position compared to the observed values. FIG. 8 reflects the anchor ice growth release process and river roughness change. The result shows that the water level, the flow, the water level and the river ice process simulated by the method are consistent with the measured values, have higher calculation precision and can be widely applied to river ice process simulation of northern rivers.
Finally, it should be noted that the above is only for illustrating the technical solution of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred arrangement, it should be understood by those skilled in the art that the technical solution of the present invention (such as the application of various formulas, the sequence of steps, etc.) can be modified or equivalently replaced without departing from the spirit and scope of the technical solution of the present invention.

Claims (2)

1. A method for numerical simulation of river ice in consideration of anchoring ice at a river bed, the method comprising the steps of:
step 1, collecting water ice data: collecting or measuring water ice data including river terrain, water level, flow, water temperature, ice concentration in water and heat exchange coefficient between water and air in a research area;
step 2, calculating a one-dimensional shallow water equation set: based on the water ice data collected in the step 1, solving a one-dimensional shallow water equation set considering the river ice influence by adopting a four-point hidden-format Prisman method;
Figure FDA0002614665240000011
Figure FDA0002614665240000012
wherein t is time; x is the distance in the direction of flow; a is the area of the cross section; ρ is the density of water; q is river flow; h is water level; p is a radical ofbIs the wet week of the riverbed part; p is a radical ofiIs the wet week of surface river ice; b isoThe width of the open flow part of the cross section; tau isbIs the riverbed shear stress; tau isiThe drag force of the surface floating ice; tau isaDrag of surface air; g is the acceleration of gravity;
step 3, calculating the net heat absorption capacity of the water body: calculating the net heat absorption capacity of the river water body by adopting the following equation;
φss-φsk＝pbφb-B(1-fB)(1-Ca)φwa-[(1-fB)BCa+CbPb+fBB]hwi(Tw-Tf)
in the formula, phissHeat flux absorbed for the surface and wet perimeter of the water body; phi is askHeat flux released for the surface and wet weeks of the body of water; phi is abHeat transfer flux to the riverbed; phi is awaIs the heat flux between water and air; f. ofBThe ratio of the bank ice to the river width is shown; caThe surface density of the floating ice on the surface; cbThe proportion of the anchor ice covered on the wet circumference of the riverbed; h iswiIs the heat exchange coefficient between water and ice; t iswThe water temperature is adopted; t isfThe freezing temperature of the water body; b is the width of the cross section of the river channel; pbIs the wet week of the riverbed part;
step 4, calculating the water temperature and the ice concentration in the water: calculating the average water temperature and the ice concentration in water of the river section by adopting the following simultaneous equation;
Figure FDA0002614665240000013
Figure FDA0002614665240000014
in the formula, CvIs the ice concentration in the water; cpThe specific heat capacity of the water body; l isiLatent heat of fusion of ice; e is the rate of ice ablation in the water; rhoiIs the density of ice;
step 5, calculating the surface density of the floating ice: calculating the surface density of the surface floating ice by adopting the following equation;
Figure FDA0002614665240000015
in the formula, hiEffective ice thickness for ice floes; vbThe rate of ice flotation in the water; alpha is the probability of ice floating in water; beta is the probability of the ice on the surface being washed into the ice in the water; ranIs the release rate of the anchor ice; u is the average flow velocity of the section;
step 6, calculating the thermal growth and the ablation thickness of the ice: the thermal growth and ablation thickness of the ice were calculated using the following equations:
Figure FDA0002614665240000021
in the formula, hiaIs the heat exchange coefficient between ice and air; t isiIs the ice surface temperature; t isaIs the air temperature; e.g. of the typefPorosity of the ice flower layer;
step 7, calculating the thickness of the ice flower layer: calculating the thickness of the ice flower layer by adopting the following equation;
Figure FDA0002614665240000022
in the formula, hfIs the thickness of the ice flower layer;
step 8, calculating the thickness of the ice cover: setting the ice sealing position or ice blocking starting point of the river channel section, and calculating the critical Froude number and the corresponding ice cover thickness of different river ice accumulation up-tracking modes;
the average froude number of a section is calculated using the following equation:
Figure FDA0002614665240000023
in the formula, FrAverage Froude number of cross section; d is the average water depth of the section;
calculating critical Froude numbers of different ice cover development modes, and judging whether the ice cover is in a tiling and upward tracing mode, a hydraulic thickening mode or a mechanical thickening mode;
Figure FDA0002614665240000024
Figure FDA0002614665240000025
wherein, FrpCritical Froude number for tiled up-trace mode; frcCritical froude number for hydraulic thickening mode; phi is afIs an empirical coefficient related to the ice cube size; e.g. of the typepPorosity of ice cap;
if Fr＜FrpThe ice cover is developed according to a flat-laying up-tracing mode, and the ice thickness is the thickness of single-layer floating ice; if E isrp＜Fr＜FrcThen the ice cover thickness is calculated according to the following equation:
Figure FDA0002614665240000026
if Fr＞FrcThen the ice cover thickness is calculated according to the following equation:
Figure FDA0002614665240000027
in the formula, phi is the internal friction angle of ice; tau iscShear stress of the river bank to ice; tau isgThe gravity component of the ice cover along the flow direction; mu is the internal friction coefficient of the river ice;
step 9, calculating the thickness of the anchor ice: calculating the thermal growth and the ablation thickness of the anchor ice, judging whether the anchor ice is released or not, and calculating the corresponding release volume of the anchor ice, wherein the growth rate of the anchor ice is calculated according to the following equation:
Figure FDA0002614665240000031
in the formula, hanThe thickness of the anchor ice; e.g. of the typeaPorosity of the anchor ice; cvThe concentration of ice in the suspension water; gamma is the adsorption rate of ice in water on the riverbed; phi is aanThe net heat exchange capacity between the water body and the anchor ice;
step 10, updating the comprehensive roughness coefficient of the river channel: calculating the comprehensive roughness of the river channel considering the influence of the anchor ice by adopting a piecewise linear formula, wherein the calculation equation is as follows:
Figure FDA0002614665240000032
in the formula, nbi0The comprehensive roughness coefficient of the river channel is considered to be influenced by the anchor ice; n isbThe coefficient of roughness of the river channel without anchor ice is shown; dsThe median particle size of the riverbed silt;
step 11, simulating a river ice process and water level flow change: and calculating all factors including water level, flow, water temperature, ice thickness, ice concentration and anchor ice thickness time by time according to all the equations, and simulating the river ice process and the corresponding water level flow change.
2. The method of claim 1, wherein the determination of whether the anchor ice is released in step 9 is made according to the following equation: if the equation is established, the anchor ice is completely released; if the equation is not satisfied, the anchor ice is not released;
Figure FDA0002614665240000033
in the formula, WbIs the net buoyancy of the anchor ice body; fbThe tensile resistance between the anchor ice and the river bed; ρ is the density of water;
Figure FDA0002614665240000034
is the anchor ice volume.
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