An accurate assessment of the stage-discharge relationship in open channel flows is necessary and important to the design and management of hydraulic structures and engineering in practical hydrosystems such as rivers and streams. While the flow structures and patterns at open channel junctions are interesting and have been widely studied in the literature, this paper focuses further on the effect of flow junctions on stage-discharge relationship at mountain river confluences. In this study, both the flume and physical model experiments are designed and performed carefully to test and analyze the complex flow structures and characteristics at river confluences with different configurations and hydraulic conditions. The impacts of the flow junctions on the traditional stage-discharge relationship are analyzed in this study. The results of this study are discussed in the paper for the understanding of flow structures at flow junctions and the design and management of hydraulic structures in river engineering.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

The power of the river does not always work to the benefit of living things; rather, it has the ability to destroy human society and has negative effects on the environment. River Teesta has a prodigious significance on the riverine dweller and its changing precarious behaviour has repercussions on the lives of millions. Utilizing satellite images and 41 years of temporal analysis, the mapping of channel extraction and channel shifting has been demonstrated. Delineating the exact channel boundary is a laborious operation, but MNDWI technique is really valuable in this situation to produce valuable results. Descriptive statistics are used to analyze the Teesta River's active flow line migration trend and channel migration behaviour. A particular river's oscillating character over time has both beneficial and detrimental power, destroying important resources for environmental sustainability and human society while also providing fertile mother earth as a source of wealth. As a result, another goal of the current study was to determine how vulnerable riverine residents were. A livelihood vulnerability index (LVI) based on the riverine inhabitants' exposure, sensitivity, and capacity for adaptation was created. According to the findings, the river's erratic behaviour is putting the people who live beside it in danger. Therefore, it is vitally necessary to implement a capable management strategy to stop bank failure at the Teesta-Dharala confluence in order to save the riverine residents.

Vegetation has a significant influence on velocity distribution and turbulent energy in a confluence channel. A laboratory measurement with ADV was used to investigate the flow through a Y-shaped confluence channel partially covered with rigid vegetation on its inner bank. In this study, the flow velocities in cases with and without vegetation were measured by the ADV in a Y-shaped confluence channel. The results clearly show that the existence of non-submerged rigid plants has changed the internal flow structure, that the velocity in the non-vegetated area is greater than in the vegetated area, and that there is a large exchange of mass and momentum between the vegetated and non-vegetated areas. The velocity on both sides is significantly reduced when vegetation is present. In the vicinity of tributaries, due to the presence of vegetation, the high-velocity area moved rapidly to the middle of the non-vegetated area, and the secondary flow phenomenon disappeared. In the mainstream, when vegetation was present, circulation disappeared, and the degree of lateral mixing decreased. The presence of vegetation caused a great change in the internal flow structure and made the flow in non-vegetated areas more intense.

This study investigates the mean annual water temperature trends at the confluence of the Sava and Danube Rivers, along with air temperature trends at the Belgrade meteorological station, spanning from 1956 to 2020. Results reveal a consistent increase in temperature across all three measuring stations, with the Danube experiencing a rise of 0.34°C/10 years, the Sava at 0.44°C/10 years, and Belgrade's air temperature increasing by 0.39°C/10 years. Employing the RAPS method, sharp rises in water temperature were pinpointed in 1989 for the Sava and 1990 for the Danube, while Belgrade's air temperature surge began in 1998. The highest intensity of air temperature increase within the recent period (1998-2020) was observed at the Belgrade observatory, reaching 0.76°C/10 years. Notably, the Sava exhibited a faster increase in water temperature over the last thirty years compared to the Danube. August marked the peak average water temperature for both rivers, while July recorded the highest average air temperature in Belgrade. Despite differing flow rates, both rivers exhibit similar hydrological regimes, with maximum flows occurring in April and minimum flows in August for the Sava, and October for the Danube. Seasonal temperature increases were most pronounced in summer, notably in August, with the smallest rises occurring during cold periods. Additionally, an inverse proportional relationship between mean annual water temperatures and discharges was observed at both river stations.