Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method

River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.

Dramatic thinning of Alaskan river ice and its climatic controls

River ice thickness(RIT)directly influences human activities,such as rural transportation and subsistence activities,in addition to ecosystem and hydrology processes in the Arctic.Knowledge of RIT response to the rapid Arctic warming is very limited or essentially lacking.The scientific objective of this study is to investigate changes and variations in RIT and their response to rapid Arctic warming.We used ground-based measurements of 45 river gauge sites from 1961 through 2015 spanning 12 river basins across Alaska.The results indicate that the long-term mean maximum river ice thickness(MRIT)ranged from 40.3±12.7 cm in the southeast to 187.3±31.9 cm in northwest Alaska.MRIT decreased dramatically from 1961 to 2015,on average,at a rate of−0.26±0.17 cm per year,and RIT declined significantly in all months from October through March,and more rapidly in winter than in autumn and spring.The impacts of air temperature and snowfall on MRIT change were analysed,and their relative influences were 74%and 26%,respectively.Specifically,an increase in air temperature was the primary factor contributing to MRIT decrease,while increasing snowfall,and snow on river ice enhanced MRIT decline.Seasonally,snowfall was the primary regulator for thickness change and higher air temperature resulted in RIT declining in autumn,while ice thickness decrease was mostly driven by warming in spring.However,neither air temperature nor snowfall is the primary control factor for declining RIT in winter,and further work needs to be done to detect the reason.

Analyses of the stability of submerged ice blocks

This paper proposes the critical conditions for a submerged ice block beneath an intact ice cover to become unstable,as a fundamental component of any numerical model to successfully predict the ice jam formation or the ice jam release events.The flume model experimental and numerical simulation methods are both applied to analyze the stability of submerged ice blocks.The flume model experiment is first conducted,and the experimental results indicate that the influencing factors of the stability of a submerged ice block include the relative length,the relative water depth and the relative width.It was shown that the effect of the relative width on the stability of submerged ice blocks was not well studied.Based on the experimental results,the k-eturbulence model is applied to establish a 3-D numerical model for studying the pressure distribution beneath submerged ice blocks.The effects of the relative width on the Venturi pressure and the leading edge pressure are evaluated.Finally,according to the force balance equation and the moment balance equation,this paper proposes a computational formula for the sliding and underturning critical conditions of submerged ice blocks,and the results are in good agreement with the experimental results.

NUMERICAL SIMULATION OF STREAMBED HEAT TRANSFER

Conductive heat exchange between streambed and the water contacted is a significant heat balance component in a full thermal budget model, especially in ice covered rivers or shallow streams. A numerical model based upon a finite difference solution of the unsteady heat dispersion equation is formulated to predict heat conduction between water and streambed with emphasis on its application to the diurnal temperature variations of shallow or ice covered streams.