4.1. Hanging Dam Formation
Figure 4 shows the orthorectified aerial views of the hanging dam for all approach Froude numbers and two incoming ice supply rates upon reaching the final ice volume of 216 L. The hanging dam formed immediately at or very close to the lake inlet for lower approach Froude numbers (Fr = 0.19 and 0.23), and the formation shifted further downstream as the approach Froude number increased. Flow from a narrow river into a lake is analogous to a three-dimensional wall jet, where the flow is directed along a wall to an ambient fluid. A wall jet is defined as a shear flow directed along a wall where the streamwise velocity over some region within the flow exceeds that in the external stream at any downstream location because of the initially supplied momentum [
19]. The presence of a wall (ice cover) that directs the shear flow and the zero streamwise velocity at the wall (ice cover) due to the no-slip boundary condition are the primary similarities between a three-dimensional wall jet and the flow from a narrow river to a wide lake section. The high velocity of the wall jet for the approach Froude numbers 0.38, 0.56, and 0.69 did not allow under-ice deposition at the lake inlet, and the jet section can be seen in all these cases, where no ice was deposited immediately downstream of the river.
The spatial evolution of the hanging dam in terms of the maximum length along the centreline and the maximum width was analyzed for the three lowest Froude numbers (Fr = 0.19, 0.23, and 0.38), as the approach Froude number of an ice-covered river during the winter is typically of a low value.
Figure 5 shows the evolution of the dimensionless maximum centreline length (maximum centreline length/lake depth) of the hanging dam for various approach Froude numbers for the two incoming ice supply rates. Initially there was a rapid increase in the centreline length, but the length plateaued and approached a constant value when the t/t
final was approximately 0.2, where t is the time at a specific moment and t
final is the time taken to reach an ice supply volume of 216 L. This can be explained based on the momentum supplied by the velocity of the jet. Initially, the incoming ice supply to the flume is transported along the flow of the jet and deposited beneath the ice cover when the velocity is not adequate to transport the ice further downstream. The subsequent ice supply to the flume is deposited in the area in between the initially reached centreline length and the lake inlet, increasing the thickness of the accumulation. The final centreline length of the hanging dam has a direct relationship with the approach Froude number of the flow, where the centreline length increases when the approach Froude number increases, as ice is transported further downstream due to the high velocity of the jet at high approach Froude numbers.
The spatial evolution of the dimensionless maximum width (maximum width/lake depth) of the hanging dam is shown in
Figure 6. For all the cases, the maximum width of the hanging dam increased as more ice was supplied to the flume. Irrespective of the Froude number and incoming ice supply rate, the dimensionless maximum width of the hanging dam reached a constant value upon reaching the final volume of the hanging dam. Even though it is not possible to produce a similar plot for the evolution of the maximum thickness of the hanging dam, it would have increased with the increasing ice supply in a trend similar to that of the maximum width.
The final longitudinal profiles of the hanging dams obtained from photogrammetry at the centreline of the lake section for various Froude numbers are shown in
Figure 7. For the lowest-Froude number (Fr = 0.19) experiment, the hanging dam formed immediately at the lake inlet for both high and low incoming ice supply rates. The hanging dam formed immediately at the lake inlet only at the high incoming supply rate for the Froude number 0.23. As the Froude number increased, the hanging dam formed further downstream due to the high shear stress exerted by the flow of the jet. For all the approach Froude numbers, the maximum thickness of the hanging dam occurred closer to the lake inlet at the higher incoming ice supply rate when compared with the low incoming ice supply rate.
The maximum thicknesses of the hanging dam formation (T
max) for the two incoming ice supply rates and various approach Froude numbers are shown in
Figure 8. The highest thickness was observed at an approach Froude number of 0.38. The maximum thicknesses for the approach Froude numbers of 0.19 and 0.23 were just slightly lower than the maximum thickness at a Froude number of 0.38. For the low-Froude-number conditions, the maximum dimensionless thickness of the hanging dam plateaued around a dimensionless length of 0.68, which corresponds to a thickness of 0.25 m. The growth of the thickness of the hanging dam was hindered by several factors, such as the fixed lakebed that only allowed a flow depth of 0.12 m during the thick hanging dam formation, and the absence of cohesion due to freezing.
Figure 9 shows the side view of the hanging dam formation at the lake inlet for an approach Froude number of 0.19 after reaching the maximum thickness of 0.25 m. The maximum thickness of the hanging dam decreased with increasing approach Froude numbers because the velocity of the jet was high at higher Froude numbers and the hanging dam accumulation was pushed further downstream in the lake section. At a specific approach Froude number, the maximum thicknesses of the hanging dam reached similar values irrespective of the incoming ice supply rate. The maximum thickness of the hanging dam was governed by the fixed lakebed and the absence of cohesion in the HDPE pellets. The shear stress on the underside of the accumulation increases as the hanging dam grows in thickness and non-cohesive pellets easily erode due to this high shear stress. On the contrary, a hanging dam in a natural environment could reach extremely high thicknesses as long as there is a sufficient water depth such that the applied shear stress underneath the hanging dam is lower than the critical shear stress that initiates erosion. During the initial ice formation stages, the thermal effects of ice play an important role in forming an ice cover near the water surface. The thermal ice cover can grow in thickness, which may also contribute to a portion of the hanging dam, which was not simulated in this laboratory study.
The locations of the maximum thicknesses of the hanging dam (L
max) for various approach Froude numbers and the two incoming ice supply rates are shown in
Figure 10. The maximum thicknesses of the hanging dam occurred further downstream as the approach Froude number increased due to the high-velocity jet coming out of the river that pushed the formation downstream. The maximum thicknesses for lower incoming ice supply rates were located further downstream when compared with the locations of the higher supply rates for the same Froude number. During the ice supply stage of hanging dam formation, both deposition and erosion processes happen at the same time at different locations, making the process quite dynamic. Erosion is facilitated through the shear force exerted by the jet flow, and if the incoming ice supply from upstream is not adequate to maintain the rate of erosion, the subsequent depositions happen further downstream.
The areal extents of the hanging dam (A
max) for various approach Froude numbers and two incoming ice supply rates are shown in
Figure 11. The areal extent of the hanging dam increased with increasing Froude numbers, and the areal extent for the lower incoming ice supply rate experiment was higher than that of the high ice supply rate experiment for the same approach Froude number. At a low ice supply rate, the rate of supply was not adequate to overcome the rate of erosion; therefore, the eroded ice was transported in both the streamwise and spanwise directions and became deposited at a location further away from the high erosive power of the jet. This also means that if the incoming ice supply from upstream is abruptly terminated and the water discharge is maintained the same, the hanging dam will evolve with erosion and finally reach a stable state. An erosion experiment was conducted to further investigate this theory.
4.3. Comparison to Field Data
The experimental results were qualitatively compared with two hanging dam occurrences in the field using optical imagery from satellites and hydrometric data. The first case was the hanging dam formation at the confluence of the Dauphin River and Lake Winnipeg in central Manitoba. The Dauphin River is about 52 km long and drains into Lake Winnipeg. Based on the difference in the channel slope, this river can be classified into two reaches: an upper reach with a slope of 0.029% over 40 km and a lower reach with a slope of 0.16% over 11.2 km. The steep lower reach of the river has open-water areas with velocities that exceed 1.5 m/s and can generate a significant volume of frazil ice during the freeze-up season [
20]. A hanging dam forms at the outlet to Lake Winnipeg when the frazil ice is deposited under the lake ice cover [
21]. The ice-affected water levels in the steep lower reach can rise 4–5 m or more above those of the open-water conditions due to thick ice jams [
22].
The shape and areal extent of the hanging dam were visible from satellite images when the lake ice cover was relatively thin, typically at the end of the winter during the months of April and May. Optical imagery was obtained from Landsat 8/9 and Sentinnel-2 satellites from the US Geological Survey’s EarthExplorer [
23,
24] for days with low cloud coverage.
An HEC-RAS model of the Dauphin River [
22] was used to estimate the Froude number at the most downstream cross section of the river. The mean monthly discharge and the mean monthly water level at the Dauphin River Water Survey of Canada gauge (05LM006) were used as the upstream and downstream boundary conditions for the HEC-RAS model, respectively. The model was set to run in a steady state for each month during the ice-affected period (from November to April), and the Froude number at the downstream cross section of the river was obtained. The average ice-affected Froude number for 2017–2018 was estimated as 0.06 from HEC-RAS model simulations.
The ice discharge in a river is correlated to the air temperature. A field estimation of the incoming ice discharge in the Dauphin River was previously conducted using an analysis of unmanned aerial vehicle (UAV) videos taken at a site 25 km upstream of the lake inlet for the 2017–2018 season. The ice discharge was calculated using Equation (3), where Q
ice is the ice discharge (m
3/s), V
ice is the average surface ice velocity (m/s), N is the average surface ice concentration (-), B is the river width (m), and t
ice is the average thickness of a surface ice floe (m):
The average thickness of the ice floes was considered a major unknown when using this method and was estimated to vary between 0.05 m and 0.15 m according to field measurements. The ice discharge in the river for the 2017–2018 season was calculated to vary between 1.1 m
3/s and 3.4 m
3/s [
22]. The corresponding volumetric incoming ice discharge (q
i) at the lake inlet was calculated to vary between 0.004 m
3/s/m and 0.01 m
3/s/m using Equation (4), where the width of the river immediately upstream of the lake inlet was determined to be 120 m using the bathymetry data:
Figure 15a shows the hanging dam formation at the Dauphin River–Lake Winnipeg confluence for the 2017–2018 season, where the average approach Froude number is equal to 0.06. This case from the field can be compared with the lowest Froude number experiment shown in
Figure 15b, where the approach Froude number was 0.19 and the incoming ice supply rate was 0.001 m
3/s/m. In both cases, ice deposition occurred immediately at the lake inlet, where the flow velocity was reduced due to the abrupt increase in the channel width and depth. Ice was deposited in a semi-circular shape around the inlet of Lake Winnipeg, similar to the experimental case, suggesting that there was a high incoming ice supply during the formation stage of this hanging dam. In comparison, the ratio of the lake width (at the bay where the Dauphin River enters Lake Winnipeg) to the Dauphin River width was 17, whereas the physical model had a lake width–river width ratio of 13. The field observations and analysis by Wazney [
22] indicated that the ice discharge in the Dauphin River was as high as 3.4 m
3/s, based on the thickness of the ice floes, during the 2017–2018 freeze-up season.
Figure 16a shows the hanging dam on 3 May 2018 during the breakup season. The higher river discharge and warmer water temperature seem to have caused the hanging dam to have eroded (either mechanically, thermally, or likely a combination of both) along a preferential path.
Figure 16b shows the aerial view of the hanging dam 35 min after setting an approach Froude number of 0.33 during the erosion experiment, where the erosion was caused by the higher river discharge. In both cases, the open-water jet section that results from the higher river discharge is clearly visible. The thermal effect on erosion is an important difference between a field study and a laboratory study. In the Dauphin River field study, rising air temperatures might have contributed to the erosion of the hanging dam, whereas the erosion in the experiments was caused entirely by the flow of the jet.
Another hanging dam can be found downstream of the Keeyask Generating Station on the lower Nelson River, Manitoba. The Keeyask Generating Station is located between the outlet of Split Lake and the inlet to Stephens Lake, with average winter flows of 3300 m3/s. The lower Nelson River is a complex, fast-flowing hydraulic system that contains reaches that are separated by rock controls, rapids, and lakes. The ice processes in this river are complex due to the presence of rapids that produce a large quantity of frazil ice during the winter and the interconnected system of river reaches and lakes. During the winter, a large hanging dam forms at the inlet to Stephens Lake that is located immediately downstream of the Gull Rapids. There is a 13 m drop in elevation from Gull Lake to Stephens Lake, and the majority of the drop spans across the Gull Rapids.
The lake ice cover on Stephens Lake forms in early fall, causing the frazil ice generated in the Gull Rapids to collect at the leading edge of the ice cover. The ice cover progresses upstream until reaching the rapids section downstream of the Keeyask Generating Station, where it stalls. The incoming frazil ice from upstream is deposited beneath the ice cover forming a hanging dam at this location. This hanging dam initially grows very rapidly, but the growth rate slows down later depending on whether an ice bridge forms upstream of Gull Lake. The frazil ice supply from upstream is reduced substantially if the ice cover bridges upstream of Gull Lake, which impacts the size of the hanging dam formation [
25].
The size and the location of the hanging dam at this site can be seen in satellite imagery when the lake ice cover is thin, typically in mid-May. Satellite images of the hanging dam from Sentinel-2 and Landsat 8/9 satellites were obtained from the US Geological Survey’s EarthExplorer [
23,
24] for a period of 10 years from 2013 to 2023. The hanging dam was not visible in some years due to high cloud coverage.
Figure 17 shows the hanging dam downstream of the Keeyask Generating Station in 2013 and 2023. The areal extent of the hanging dam has decreased over the years, and a significant difference in the areal extent can be observed when comparing the formation of 2013 with that of 2023.
The Keeyask Generating Station started operations in March 2022, which is the main difference between the 2012–2013 and 2022–2023 seasons. The ice boom installed at Gull Lake and the flow control procedures taken by the generating station as part of their operations may have ensured the formation of a competent ice cover upstream of the rapids section, lowering the frazil ice production. There are open water sections visible in the 2013 satellite image upstream of the hanging dam location, but these sections are ice-covered in the 2023 satellite image.
The mean daily air temperatures at Gillam Airport (the closest meteorological site to the Keeyask Generating Station) were analyzed for the two winter seasons (October–May) for 2012–2013 and 2022–2023. The cumulative degree days of freezing (CDDF) for the 2012–2013 winter were calculated as 3323, while the 2022–2023 winter had 3065 cumulative degree days of freezing, indicating that the 2022–2023 winter was warmer than the 2012–2013 winter.
The results presented in this paper comprise the first published qualitative laboratory data on hanging dam formation, but there are several limitations of this study that need to be highlighted. The thermal effects on the hanging dam formation were not taken into consideration, as it is practically difficult to incorporate the thermal component in a laboratory environment. Frazil ice is cohesive and easily freezes together, unlike the HDPE pellets that were used as simulated ice in this laboratory study. In a natural river, hanging dams can attain extremely high thicknesses if the applied shear stress beneath them is less than the critical shear stress that initiates erosion. In this laboratory study, the flow depth was limited; therefore, the maximum thicknesses of the hanging dam reached similar values for all the different ice supply rate conditions.
The under-ice roughness, shear stress, and velocity change as the accumulation increases in thickness. Quantifying these parameters would be beneficial when validating numerical models as well as provide an additional insight when making comparisons with field data. An acoustic Doppler velocimeter (ADV) was considered to obtain the velocity measurements in this study, but it could not be used during the ice supply stage because the ADV probe disturbed the hanging dam formation. The use of an alternative technique to measure the velocity beneath the hanging dam is suggested for future studies, as it will be a valuable addition to the existing hanging dam literature.