Fluvial thermal erosion: heat balance integral method

Abstract

In periglacial regions, frozen river banks are affected by thermal and mechanical erosion. In Siberia, bank retreats of up to 40 m per year are observed. This thermal erosion occurs during a few weeks, at springtime, for high enough water temperatures and river discharges. Until now, models of thermal erosion have been based on the assumption of a constant thermal erosion rate. We have developed a more general model at variable rate, whose solution is calculated using the integral method. Results of this model are compared with experiments, carried out in a cold room. A hydraulic channel allows measurements of the thermal erosion rate of a ground ice sample subjected to a turbulent water flow. Once validated, the model is applied to the periglacial river study case. The model has contributed to better understanding of the roles of each parameter during the thermal erosion process. High water temperature, discharge and ice temperature produce major thermal erosion, whereas the ice content in the soil tends to slow down the thermal erosion process. The effects of water temperature are predominant. An acceleration phase characterized by an increase of the thermal erosion rate occurs at the beginning of the thermal erosion process. The duration of such an acceleration phase is systematically studied. A relatively long acceleration phase is related to a low ablation rate. During the flood season, when the water temperature is increased to 18°C, this acceleration phase lasts only a few minutes. However, for data typical of periglacial rivers, when the water temperature is close to the melting point, the acceleration phase can last a few days. Figure 3. Experimental data. Effects of water temperature, discharge and ice temperature on the location of the moving surface s(t). This figure is available in colour online at www.interscience.wiley.com/journal/espl 1834 R. Randriamazaoro et al.Figure 4. Evolution of the thermal erosion rate for different water temperatures, discharges, ice temperatures and ice contents. The reference case (bold line) corresponds to ice at −7·5°C in contact with a water flow at 5·5°C and a Reynolds number equal to 15 900. corresponds to 90% of the final erosion rate and gives the duration of the acceleration phase (A.P.). This figure is available in colour online atFigure 6. Applications to an arctic river. Effects of water temperature, discharge, ice temperature and ice content on the thermal erosion rate and the duration of the acceleration phase. Bold line, reference case. , duration of the acceleration phase. Synthesis and DiscussionWater temperature and discharge can be represented by the heat flux exchanged by convection at the interface between the water flow and the permafrost (Equation (21) and Figure 7).

Erosive flood events on the surface of Mars: Application to Mangala and Athabasca Valles

“…The dependence of e on θ w is found from considering Fig. 4 of Randriamazaoro et al (2007), and their discussion, as well as the results of a constantrate melting model (Costard et al, 2003), which together imply that e is proportional to θ w . Finally, after studying the bottom-left graph of Fig.…”

“…the erosion of the cryosphere that forms the bedrock by disaggregation of silicates as interstitial ice is melted. We have modified a treatment of thermal erosion of the frozen banks of periglacial rivers on Earth (Randriamazaoro et al, 2007) for application to Mars, where the ground temperature is much less, using the following analysis. The primary controlling parameters of the erosion rate, e, are the Reynolds number, Re, and the water temperature, θ w .…”

“…The dependence of e on Re is found from the asymptotes of the top right-hand graph of Fig. 4 in Randriamazaoro et al (2007); taking values from this graph enables one to plot erosion rate against (Re/15900). The dependence of e on θ w is found from considering Fig.…”

A model of river bank deformations under the simultaneous effect of waves from a hydropower plant and warming

“…The observations of coastal erosion of the Lena River and measurement of the water temperature allowed establishing a direct dependency for the increase of the volume of the deformations caused by thermoerosion on the increasing temperature of the water during the flood (Coastard et al 2007, Dupeyrat et al 2011. Simulation of this dependency in the work of Randriamazaoro et al (2007) showed that the erosion rate can increase by an average of 20% with an increase of the water temperature by 2°C. These results were used to test the model presented Fig.…”

“…This structure of the banks makes the abrasion processes even more pronounced (Dallimore, et al 1996, Coastard et al 2007, Bowden 2010. The laboratory experiments and field observations (Randriamazaoro et al 2007, Dupeyrat et al 2011 showed that thermoerosion plays a significant role in the deformation of the banks composed of permafrost with the inclusion of layers of ice. Sometimes the effect of thermoerosion is greater than that of mechanical erosion.…”