Flow Ratio and Temperature Effects on River Confluence Mixing: Field-Based Insights

Abstract

Understanding mixing behavior at river confluences is essential for effective watershed management in response to increasing environmental issues such as algal blooms and chemical pollution. This study focused on the confluence of the Nakdong and Geumho Rivers, employing high-resolution field measurements using an ADCP (M9) and YSI EXO sensors. Water temperature (°C) and electrical conductivity (μS/cm) data were collected under three representative conditions, including flow ratios of 0.91, 0.45, and 0.29, as well as 0.05, with a maximum temperature difference of up to 6 °C. Mixing behavior was three-dimensionally analyzed by integrating cross-sectional and longitudinal data, and the accuracy of visualization was evaluated using IDW and Kriging spatial interpolation techniques. The analysis revealed that under low flow ratio conditions, vertical mixing was delayed; the thermal stratification persisted up to approximately 3 km downstream from the confluence (Line 3), and complete mixing was not achieved until about 7 km downstream (Line 5) due to density currents. Quantitative comparison indicated that IDW (R² = 0.901, RMSE = 31.522) outperformed Kriging (R² = 0.79, RMSE = 35.458). This study provides a quantitative criterion for identifying the mixing completion zone, thereby addressing the limitations of previous studies that relied on numerical models or limited field data, and offering practical evidence for water quality monitoring and sustainable river management.

1. Introduction

River confluences are dynamic boundary zones where two water bodies with distinct geomorphological and hydraulic characteristics meet, resulting in the formation of complex flow structures. The degree and pattern of mixing at these sites are primarily governed by the flow ratio between the main river and its tributary, as well as by differences in their physical and chemical properties. Mixing does not occur instantaneously but generally progresses gradually over a certain distance downstream. Since tributaries often introduce physical and chemical characteristics that differ from those of the main river, accurately understanding their influence on the mixing process is essential for the effective management of river systems.

Furthermore, accurately simulating flow and sediment dynamics within such complex confluence zones plays a pivotal role in evaluating the effectiveness of engineering interventions and refining watershed-scale management strategies [1].

Previous studies have explored various aspects related to river confluences, such as mixing behavior, thermal stratification, and hydraulic characteristics. For example, Jang et al. (2006) analyzed the behavior of the Geum River and Miho Stream confluence under different inflow and slope conditions using the RMA-2 and SED2D models [2]. Lee et al. (2000) introduced a jet integral model to reproduce turbulent buoyant jets under stratified flow conditions [3], while Park et al. (2014) employed the W2 model to investigate thermal stratification and flow characteristics between Andong and Imha reservoirs [4]. Oh et al. (2015) applied the Kriging technique to evaluate seasonal water mass distribution in the Saemangeum estuarine system [5], and Seo et al. (2008) conducted numerical modeling on pollutant dispersion in the Han River tidal flat [6]. Yang et al. (2018) applied the HEC-RAS model to the Nakdong–Nam River confluence and combined SOM (Self-Organizing Map) with LOWESS (Locally Weighted Regression) to analyze temporal patterns of water level and water quality [7]. Gwak et al. (2017) identified spatial mixing characteristics by analyzing hydrodynamic and suspended particle properties based on field measurements [8]. Yuan et al. (2021) investigated sediment transport dynamics at the confluence of the Yangtze River and Poyang Lake [9], and Chabokpour et al. (2022) simulated pollutant dispersion behavior using the FLOW-3D model [10]. In addition, Shaheed et al. (2021, 2022) examined secondary flows, ecological impacts, and persistent downstream stratification at river confluences [11,12,13]. Choi et al. (2023) demonstrated that meandering, secondary flows, and water mass characteristics constrain mixing [14], while Choi et al. (2024) highlighted that seasonal thermal stratification causes slow vertical mixing in reservoirs [15].

Most of these previous studies have primarily relied on numerical modeling approaches or focused on stagnant or tidally influenced water bodies, while field data-based analyses of density currents induced by temperature differences remain relatively scarce. In addition, the majority of studies have been limited to two-dimensional or cross-sectional analyses. Therefore, this study aims to quantitatively assess the downstream shift in mixing completion under varying flow ratio and temperature difference conditions, to compare and validate the performance of interpolation techniques (IDW and Kriging) using field measurements for a more comprehensive evaluation, and to address this research gap by applying both two-dimensional and three-dimensional approaches.

This study focuses on the confluence of the Nakdong and Geumho Rivers, with the objective of quantifying the effects of discharge ratio and thermal gradients on mixing behavior. By distinguishing the spatial patterns of mixing zones and analyzing thermal stratification characteristics, this research provides new insights into confluence dynamics and contributes to evidence-based water quality management.

2. Materials and Methods

2.1. Study Area and Data Collection

2.1.1. Study Area

Specifically, this study aims to quantify the effects of discharge ratio and temperature gradient on mixing behavior at the confluence of the Nakdong and Geumho rivers (Figure 1). By distinguishing the spatial patterns of mixing zones and analyzing thermal stratification characteristics, this research provides new insights into confluence dynamics and contributes to the establishment of evidence-based water quality management strategies.

The study area covers a 7 km stretch downstream of the confluence, ranging from 3.5 km to 10.5 km. Approximately 1 km upstream of the confluence is the Gangjeong-Goryeong Weir, the largest multi-purpose weir in Korea, whose discharge operations induce thermal stratification and serve as a primary driver of frequent temperature differences at the confluence.

In addition, industrial wastewater generated from the Seongseo Industrial Complex is continuously discharged into the Jincheon Stream, which joins the main river near the confluence. The downstream section of the confluence also receives a large inflow of domestic and industrial sewage from Daegu Metropolitan City. Consequently, water quality deterioration and algal blooms frequently occur, particularly around the Jincheon Stream confluence. Due to these overlapping influences, the investigated section is considered a representative reach for analyzing mixing behavior in complex riverine environments.

2.1.2. Field Observations

The fundamental data set was originally collected and analyzed in the context of the author’s master’s thesis [16].

Field surveys were carried out using a YSI EXO multiparameter water quality sensor and a SonTek Acoustic Doppler Current Profiler (ADCP, M9) to collect hydrodynamic indicators and water quality parameters.

The study reach was defined as the section extending from 3.5 km to 10.5 km downstream of the Nakdong–Geumho confluence. To evaluate longitudinal mixing characteristics along the downstream flow path, a total of five cross-sectional survey lines (Line 1–Line 5) were established.

The channel distances between the survey lines were set as 1 km between Line 1 and Line 2, and 2 km intervals from Line 2 to Line 5. The 1 km section between Line 1 and Line 2 represents the immediate post-confluence zone, where rapid hydrodynamic and mixing changes occur, including velocity shear, recirculation, and stratification formation. In particular, the approximately 1 km reach from the confluence to the Samunjin Bridge was designated with a shorter interval to capture the initial mixing process at high resolution. The 2 km intervals from Line 2 to Line 5 were established to represent the gradual progression of mixing while maintaining spatial representativeness and improving survey efficiency (Figure 2).

At each transect, five measurement points (P1–P5) were established at equal intervals across the channel width. P1 was located closest to the left bank, P5 closest to the right bank, and P2, P3, and P4 were positioned at equal spacing between P1 and P5.

For sampling, operations were conducted under stable meteorological conditions with low wind speeds. Prior to each survey day, the YSI EXO sensor was calibrated using standard solutions, while the ADCP was checked for compass calibration and depth cell settings at the start of sampling. At each measurement point, water temperature (°C) and electrical conductivity (μS/cm) were recorded using the YSI EXO sensor at 1 s intervals from the surface layer to the bottom layer, with the boat held stationary at a single point. In addition, for each transect, the ADCP was employed to simultaneously measure flow velocity and discharge using acoustic signals.

Through the combined use of the YSI EXO and ADCP, high-resolution water quality and hydrodynamic data were synchronously acquired in the confluence region.

2.2. Characterization of Transverse Mixing Patterns

To analyze lateral mixing dynamics, this study utilized high-resolution field measurements of electrical conductivity (EC) and water temperature to examine both surface and vertical mixing characteristics.

The data were collected during the third year of a long-term monitoring program and included discharge (CMS) measurements for the Nakdong River (mainstream) and the Geumho River (tributary).

For comparative analysis, the discharge ratio (R) was defined as the ratio of the tributary discharge to the mainstream discharge, expressed as R = Q_tributary/Q_mainstream. The mainstream discharge was normalized to 1.0, and the tributary discharge was expressed as a relative proportion to this baseline. Based on this definition, three representative cases were distinguished.

Based on this discharge ratio, three representative cases were classified to reflect different hydrological conditions. A higher value indicates a greater contribution of tributary discharge, while a lower value indicates a smaller contribution. CASE 1, with a discharge ratio of 0.88, represents a high-flow condition with a dominant tributary contribution, whereas CASE 2, with a discharge ratio of 0.45, represents an intermediate-flow condition. CASE 3 corresponds to low tributary discharge conditions and is further subdivided into CASE 3-1 (0.05) and CASE 3-2 (0.29). These classifications are summarized in

Table 1. Summary of flow conditions and discharge ratios for each CASE scenario.

	CASE 1	CASE 2	CASE 3-1	CASE 3-2
Mainstream flow rate (CMS)	287.26	30.35	858.76	18.32
Tributary flow rate (CMS)	253.4	13.8	40.7	5.25
Flow ratio	0.88	0.45	0.05	0.29

.

Transverse mixing behavior was evaluated using contour maps of surface electrical conductivity (EC) and by analyzing vertical EC and temperature profiles for each case. Surface contour maps were used to identify surface mixing completion zones, while vertical profiles were employed to assess vertical stratification, delayed mixing patterns, and asymmetries. In particular, distinct temperature gradients were observed in CASE 3-1 and CASE 3-2, prompting additional analysis of thermocline characteristics. The depth of the thermocline was measured along Line 3, approximately 3 km downstream from the confluence, which was identified as the location where thermal stratification was most pronounced.

2.3. Investigation of Longitudinal Mixing Characteristics

Methodology for Longitudinal Mixing Analysis

To quantitatively determine mixing characteristics along the main flow direction of the river, the longitudinal axis was defined as the Y-axis and the transverse axis as the X-axis. To minimize interpretation errors caused by spatial discontinuities along the X-axis, longitudinal analysis was performed using the Y-axis, which was aligned with the natural flow direction of the river.

The longitudinal profile was established by sequentially connecting the measurement points P1, located on the left bank, from Line 1 to Line 5, thereby forming a continuous longitudinal section extending 7 km. Mixing behavior was evaluated under the three predefined discharge ratio conditions, and for each condition, longitudinal profiles of electrical conductivity (EC) and temperature were generated.

To visualize the spatial variations along the longitudinal reach, the Inverse Distance Weighting (IDW) interpolation method was applied using SURFER software (Sufer 25.1.229).

Electrical conductivity (EC) and temperature values collected from the five transects were interpolated to generate contour plots, enabling a detailed evaluation of mixing progression over the 7 km river section.

A comparative assessment with the Kriging interpolation method was also conducted; however, the IDW technique demonstrated superior performance in reliably capturing longitudinal mixing gradients and was therefore adopted as the final approach.

To quantify the visualization of spatial interpolation, a Mixing Efficiency Index (MEI) was calculated for each transect.

The MEI is defined as follows:

$$\mathrm{M}\mathrm{E}\mathrm{I}=1-{\displaystyle \frac{\sigma }{\mu }}$$

(1)

Here, σ denotes the standard deviation of vertical water temperature and electrical conductivity across the transect, and $\mu$ represents the mean value. An MEI value closer to 1 indicates a homogeneous mixing state, whereas lower values represent incomplete mixing. In this study, values of MEI greater than or equal to 0.94 were considered to indicate complete mixing.

3. Research Analysis Results and Discussion

3.1. Transverse Mixing Response to Flow Discharge Ratio

Comparative Analysis of Surface and Vertical Mixing Profiles

• CASE 1

The analysis was first classified into three major cases based on the discharge ratio. CASE 1 corresponds to a high flow ratio condition, in which the discharges of the Nakdong River (mainstream) and the Geumho River (tributary) were measured as 287.26 CMS and 253.40 CMS, respectively, resulting in a discharge ratio of approximately 0.91. This comparable magnitude of discharge indicates an almost 1:1 balanced state between the two rivers. As shown in the surface contour map (Figure 3), mixing was completed immediately downstream of the confluence, due to the balanced discharge conditions.

Prior to the confluence, the water temperature and electrical conductivity values of each river were as follows: Nakdong River—27.0 °C, Geumho River—25.5 °C, and Jincheon Stream—26.5 °C, indicating a temperature difference of approximately 1.5 °C between the mainstream and the tributary. In terms of electrical conductivity, the Nakdong and Geumho Rivers both exhibited similar values of about 300 μS/cm, whereas the Jincheon Stream, influenced by the Seongseo Industrial Complex, showed a relatively higher value of about 400 μS/cm.

The vertical profiles of water temperature and electrical conductivity for CASE 1 are presented in Figure 4. According to the conductivity profiles, mixing was nearly completed from Line 1, where the discharges of the two rivers were comparable, and fully completed at Line 2. This was evidenced by the uniform distribution of conductivity values around 300 μS/cm, which corresponded to the pre-confluence values of the Nakdong and Geumho Rivers.

The temperature profiles showed relatively higher values at P1 and P2, where the Jincheon Stream and the Geumho River entered, while P5 reflected the characteristics of the Nakdong River. Although minor temperature differences were observed among points, water temperature remained vertically uniform within each flow, and no distinct thermal stratification was detected. Therefore, under high flow ratio conditions, effective mixing was found to begin from Line 2.

• CASE 2

In CASE 2, the discharges of the mainstream and tributary were measured as 30.35 CMS and 13.80 CMS, respectively, resulting in a discharge ratio of approximately 0.45. This indicates a moderate tributary contribution relative to the mainstream. As shown in the surface electrical conductivity (EC) contour map (Figure 5), high-EC water masses introduced from the Geumho River and Jincheon Stream overlaid the mainstream flow immediately after the confluence. The influence of the tributaries extended downstream from Line 1 to approximately 300 m, and surface mixing was found to be completed just before Line 2.

Prior to the confluence, the water temperatures of each river were measured as follows: Nakdong River—22 °C, Geumho River—24 °C, and Jincheon Stream—23 °C, with the Geumho River showing the highest temperature. The temperature difference between the Nakdong and Geumho Rivers was approximately 2 °C. In terms of electrical conductivity, the Nakdong River exhibited a relatively low value of about 300 μS/cm, whereas the Geumho River and Jincheon Stream showed much higher values of approximately 700 μS/cm and 900 μS/cm, respectively. These contrasting water quality characteristics reflect a clear distinction between the mainstream and tributaries influenced by industrial activities.

The vertical profiles of electrical conductivity and water temperature for CASE 2 are presented in Figure 6. In the vertical distribution of conductivity, high concentrations were observed at P1 and P2 of Line 1, indicating the early influence of tributary inflows. Vertical mixing began around Line 3 and was found to be completed by Line 5, as evidenced by the uniform distribution of conductivity. According to the vertical temperature profiles, surface water temperature at Line 1 was about 24 °C, while the bottom layer was about 22 °C. Moving downstream, surface temperature increased to approximately 26 °C, while the bottom temperature decreased to about 20 °C, resulting in a maximum vertical temperature difference of up to 6 °C.

However, despite this temperature gradient, distinct vertical stratification among surface, middle, and bottom layers did not develop, suggesting that no pronounced thermal stratification occurred under these conditions.

• CASE 3-1

CASE 3-1 corresponds to an extremely low flow ratio condition, in which the discharge of the Nakdong River (mainstream) and the Geumho River (tributary) were measured as 858.76 CMS and 40.70 CMS, respectively, resulting in a discharge ratio of approximately 0.05. According to the surface contour map (Figure 7), the mainstream began to hydraulically dominate the tributary from about 300 m downstream of Line 1, with the Nakdong River flow visually overriding the influence of the Geumho River. This pattern was further observed near Line 3, where partial vertical mixing of tributary water masses occurred in the surface layer as the Nakdong River flow shifted toward the left bank.

Prior to the confluence, the measured water temperatures were 13.5 °C in the Nakdong River, 16.0 °C in the Geumho River, and 17.5 °C in the Jincheon Stream, with a maximum temperature difference of approximately 4 °C between the Nakdong River and Jincheon Stream. Electrical conductivity was measured as 400 μS/cm in the Nakdong River, 500 μS/cm in the Geumho River, and 650 μS/cm in the Jincheon Stream, indicating a distinct contrast with a difference of about 250 μS/cm between the mainstream and the tributary.

In the vertical temperature profiles of CASE 3-1 (Figure 8), a much more distinct thermocline was observed compared to CASE 1 and CASE 2. Clear signs of thermal stratification appeared from Line 2, and at Line 3, a pronounced thermocline developed at a depth of 2–3 m. In particular, at Line 3, the surface temperature decreased sharply from 15.5 °C to 13.5 °C within the first meter, yielding a temperature gradient of 2 °C/m and a corresponding density difference of approximately 0.289. Generally, a 1 °C/m temperature gradient under warmer conditions induces greater density variation than under cooler conditions; thus, the thermal stratification in this case was even more strongly emphasized.

Additionally, the vertical conductivity profiles (Figure 8) showed high conductivity values at P1 and P2 of Line 1, reflecting the influence of the Seongseo Industrial Complex. As thermal stratification became more distinct at Line 2 and Line 3, the conductivity distribution also exhibited a pattern similar to that of the temperature distribution, suggesting the presence of electrical conductivity-induced density stratification. Even at Line 5, vertical mixing was not fully achieved, confirming that stratification within the water mass persisted throughout the downstream reach.

• CASE 3-2

CASE 3-2 corresponds to a moderately low flow ratio condition. The discharges of the mainstream and tributary were measured as 18.32 CMS and 5.25 CMS, respectively, resulting in a discharge ratio of approximately 0.29. This indicates that the tributary contribution was relatively minor compared to the mainstream. According to the surface electrical conductivity contour map (Figure 9), high-EC water masses originating from the Geumho River and Jincheon Stream appeared just upstream of Line 1. However, from Line 1 onward, the mainstream flow of the Nakdong River hydraulically overwhelmed the tributary influence, and surface mixing was visually interpreted to be effectively completed.

Prior to the confluence, water temperatures were measured as 27 °C in the Nakdong River, 24.5 °C in the Geumho River, and 25.5 °C in the Jincheon Stream, with the Nakdong River exhibiting the highest temperature. A distinct temperature difference of approximately 2.5 °C was observed between the Nakdong and Geumho Rivers. Electrical conductivity values were 300 μS/cm in the Nakdong River, 650 μS/cm in the Geumho River, and 850 μS/cm in the Jincheon Stream, demonstrating a considerable water quality contrast between the tributaries (Geumho and Jincheon Streams), which are influenced by the Seongseo Industrial Complex, and the mainstream (Nakdong River).

The vertical profiles of water temperature and electrical conductivity for CASE 3-2 are presented in Figure 10. Along Line 1, the temperature profile indicated relatively high surface temperatures in the mainstream, which can be attributed to the influence of the Gangjeong–Goryeong Weir. By Line 2, vertical mixing appeared to be largely completed. In contrast, the conductivity profiles showed high values in the tributary inflows, particularly from the Jincheon and Geumho rivers, reflecting again the influence of industrial inputs.

As a result, the presence of density currents was observed between Line 2 and Line 3. At Line 2, density-driven currents developed in the surface water mass due to elevated conductivity from tributary inflows. Finally, by Line 5, vertical mixing was found to be fully completed, indicating that the water masses became ultimately homogenized in the downstream reach.

3.2. Flow Ratio-Diven Longitudinal Mixing Evaluation

3.2.1. Evaluation and Selection of Spatial Interpolation Techniques

The total length of the study reach was 7 km, divided into five sections from Line 1 to Line 5. The river width varied between 358 m and 510 m across the sections, and five observation points (P1–P5) were arranged laterally from the left bank to the right bank.

The Kriging interpolation method considers not only spatial distance but also directionality, and is therefore widely applied in river studies where flow paths are clearly defined. However, in this study, interpolation analysis focused on the longitudinal axis (Y-axis) rather than the transverse axis (X-axis). In particular, since the length of the longitudinal reach was limited to 7 km, applying Kriging could generate interpolated values influenced by relatively distant points, potentially reducing local representativeness and accuracy.

To more effectively capture local variability, the Inverse Distance Weighting (IDW) method was selected. This approach emphasizes proximity by assigning greater weights to closer points. For methodological verification, both Kriging and IDW were applied to the same dataset, and the visual outputs of each method were compared. When applied to electrical conductivity (EC) data obtained from the Nakdong–Geumho River confluence, IDW provided a finer representation of spatial gradients and better preserved localized features compared to Kriging (Figure 11).

In addition to visual assessment, a quantitative evaluation was performed by comparing interpolated electrical conductivity (EC) values with actual measurements. For this purpose, statistical indicators including the coefficient of determination (R²) and the root mean square error (RMSE) were used. The Kriging method yielded R² = 0.79 and RMSE = 35.458, whereas the IDW method achieved improved predictive performance with R² = 0.901 and RMSE = 31.522 (

Table 2. Comparison of interpolation performance between Kriging and IDW.

Kriging Method		IDW Method
R2	RMSE	R2	RMSE
0.790	35.458	0.901	31.522

), (Figure 12). Based on these comparative results, the IDW method was determined to be the most appropriate interpolation technique for this study.

3.2.2. Analysis of Vertical Interpolation Patterns for Temperature and EC

• CASE 1

Figure 13 presents the spatial interpolation results obtained using the IDW method for CASE 1. In the visualized interpolation map, the grid points are arranged from right to left, starting with P1 (tributary side) to P5 (mainstream side), and vertically from Line 1 at the top to Line 5 at the bottom. Under the high flow ratio condition of CASE 1 (R = 0.88), substantial discharges from both the mainstream and tributary induced immediate mixing at the confluence, which was clearly reflected in the interpolation patterns.

According to the temperature contour map, P1 and P2 on the tributary side of Line 1 exhibited a vertically consistent low-temperature distribution, whereas P3 and P4 maintained relatively higher temperatures throughout the water column. Although thermal mixing progressed more slowly than electrical conductivity (EC), the stratified thermal layers gradually showed signs of integration.

Quantitative assessment using the Mixing Efficiency Index (MEI) indicated that, in CASE 1, both temperature and EC achieved MEI values of 0.99 at Line 2, confirming that vertical mixing was completed (

Table 3. Mixing Efficiency Index (MEI) under CASE 1 conditions.

	Line1	Line2	Line3	Line4	Line5
Water Temperature MEI	0.93	0.99	0.98	0.98	0.99
Conductivity MEI	0.92	0.92	0.99	0.99	0.99

).

• CASE 2

Figure 14 presents the vertical spatial interpolation results for CASE 2. In the electrical conductivity contour map, high conductivity values introduced from the Jincheon Stream were observed at P1 of Line 1. In addition, elevated conductivity near the surface was evident at all points of Line 2, indicating the continued influence of the upstream tributaries. By Line 5, vertical differences in conductivity had almost disappeared, suggesting that vertical mixing was largely completed at this location.

In the water temperature contour plot, the thermal gradient between the surface and bottom layers appeared relatively small, and the spacing of the isotherms was not clearly pronounced. Examination of the vertical temperature distribution from the water surface to the riverbed revealed gradual changes in color gradients and widely spaced isotherms. This indicates that no distinct thermocline was formed, supporting the conclusion that thermal stratification did not occur under the CASE 2 conditions.

Quantitative assessment using the Mixing Efficiency Index (MEI) showed that, in CASE 2, both temperature and conductivity converged to values above 0.94 at Line 5, confirming that vertical homogeneity had been achieved (

Table 4. Mixing Efficiency Index (MEI) under CASE 2 conditions.

	Line1	Line2	Line3	Line4	Line5
Water Temperature MEI	0.96	0.97	0.95	0.93	0.94
Conductivity MEI	0.69	0.83	0.89	0.92	0.94

).

• CASE 3-1

Among the analyzed scenarios, CASE 3-1 exhibited the most pronounced stratification, where density currents induced by electrical conductivity and a distinct thermocline were observed simultaneously. As shown in the spatial contour map of electrical conductivity (Figure 15), elevated concentrations originating from the Jincheon Stream were clearly distributed at P1 of Line 1. This thermocline facilitated the formation of conductivity-induced density currents, resulting in a stratified layering structure that persisted through Line 5, indicating that vertical mixing was not fully achieved.

Figure 15 also presents the water temperature contour map for CASE 3-1. At P1 and P2 of Line 1, elevated surface temperatures were observed, attributed to inflows from the Jincheon and Geumho Rivers. In contrast, the Nakdong River mainstream maintained relatively lower temperatures, showing little mixing with the tributary water masses. This vertical separation and persistence of stratification clearly support the presence of a thermocline, and the stratified thermal structure remained evident even at Line 5, further indicating that vertical temperature mixing was not completed under the CASE 3-1 conditions.

Quantitative assessment using the Mixing Efficiency Index (MEI) confirmed this result. At Line 5 in CASE 3-1, the MEI values were 0.93 for temperature and 0.90 for conductivity, both failing to converge to values above 0.94, thus indicating that complete vertical mixing had not occurred(

Table 5. Mixing Efficiency Index (MEI) under CASE 3-1 conditions.

	Line1	Line2	Line3	Line4	Line5
Water Temperature MEI	0.92	0.92	0.91	0.92	0.93
Conductivity MEI	0.84	0.88	0.89	0.87	0.90

).

• CASE 3-2

In CASE 3-2, no thermocline was formed; however, density currents induced by electrical conductivity were observed. As shown in the electrical conductivity contour map (Figure 16), high-conductivity water masses from the Jincheon and Geumho Rivers were clearly detected at P1 and P2 of Line 1. This influence spread downstream in an L-shaped pattern, extending beyond Line 3 and reaching P3. By Line 5, vertical mixing was fully achieved, as indicated by the uniform conductivity distribution across the entire water mass.

In the water temperature contour map of Figure 16, the inflow of high-temperature water masses was identified at P1 of Line 1. However, unlike CASE 3-1, no thermocline was formed; instead, immediate vertical mixing occurred. This was reflected in the uniform temperature distribution observed across all transects and points, indicating that thermal integration within the water mass was rapidly achieved under the CASE 3-2 conditions.

Quantitative assessment using the Mixing Efficiency Index (MEI) confirmed this result. In CASE 3-2, the MEI values for temperature and conductivity were 0.99 and 1.0, respectively, verifying that complete mixing was achieved in this reach (

Table 6. Mixing Efficiency Index (MEI) under CASE 3-2 conditions.

	Line1	Line2	Line3	Line4	Line5
Water Temperature MEI	0.99	0.99	0.99	0.99	0.99
Conductivity MEI	0.67	0.80	0.84	0.92	1

).

4. Discussion

This study aims to demonstrate that mixing behavior at river confluences can lead to environmental issues such as oxygen depletion caused by stratification, abnormal algal growth, and water quality deterioration. The analysis revealed that as the discharge ratio decreases, the mixing completion point shifts further downstream, and under conditions of both low discharge ratio and temperature differences, thermal stratification was observed (

Table 7. Flow Ratios by CASE.

	CASE 1	CASE 2	CASE 3-1	CASE 3-2
Flow Ratio	Large	Medium	Small	Small
Water Surface Mixing Completion	Line 1	Line 2	Line 3	Line 1
Vertical Mixing Completion	Line 2	Line 5	After Line 5	Line 5
Thermal Stratification	X	X	Thermal Stratification	Density Stratification

).

In addition, through the analysis of vertical mixing completion points at the Nakdong–Geumho River confluence, a predictive model for estimating the confluence mixing completion point was developed, expressed as y = 14.238e^(−1.387x) with R² = 0.7787 (Figure 17). Although predictive accuracy may be limited at the initial stage due to the unique characteristics of each river, it is expected that as more data are accumulated and the reliability of the model improves, the field-based monitoring and analytical framework presented in this study can be extended to other confluence systems. This will facilitate the establishment of a more integrated analytical approach for evaluating mixing behavior in complex riverine environments.

This study provides sufficient evidence that flow ratios at river confluences can induce downstream environmental problems.

The Nakdong River mainstream, characterized by a low Froude number but dominated by momentum inertia, and the Geumho River tributary, with a high Froude number functioning as a jet but quickly subordinated to the mainstream inertia, exhibited stratification in which surface jets persisted over long distances. This led to enhanced lateral mixing and suppressed vertical mixing, demonstrating a typical inertia-dominated mixing behavior at river confluences.

Through longitudinal analysis, this study identified both the mixing completion zones across surface and water masses as well as the stratification occurrence zones. These findings are expected to contribute to establishing effective countermeasures against water quality problems or preventing their occurrence. In particular, the results can be applied to determine dam release timing and discharge volumes in order to prevent downstream water quality deterioration.

Nevertheless, this study has limitations in that the measurements were conducted during a restricted period under specific hydrological conditions, thereby not fully capturing seasonal variability or temporal changes in mixing behavior. Although the analysis was based on high-resolution temperature and electrical conductivity data, direct indicators of turbulence dynamics were not included, which may limit detailed explanations of mixing mechanisms. However, the conclusions derived from longitudinal analyses of observed temperature and conductivity data at the confluence remain valid.

Future studies should incorporate extended investigations considering seasonal variations, diverse flow conditions, and the effects of multi-purpose dam operations. In addition, the development of predictive models based on machine learning (ML) and artificial intelligence (AI) will be actively explored.

In conclusion, this study demonstrated that the location of the mixing completion point shifts downstream depending on the discharge ratio at river confluences, and that thermal stratification can occur under specific combinations of flow ratio and temperature differences. Importantly, this work highlights the significance of applying longitudinal analysis to interpret confluence behavior. The results are expected to serve as a valuable foundation for water quality management and environmental policy.

5. Conclusions

Recent incidents such as drinking water supply problems, large-scale algal blooms, and chemical spill accidents have highlighted the environmental vulnerability of river confluences. Confluences are zones where complex hydrodynamic interactions frequently occur and can exert significant impacts on water quality. Therefore, systematic investigations and the accumulation of baseline data for such areas are urgently needed.

This study analyzed density currents under various hydrological conditions and applied a two-dimensional/three-dimensional (2D/3D) analytical framework to elucidate mixing behavior at the river confluence.

The following key findings were obtained: Based on water temperature and electrical conductivity data, analysis of variations in discharge ratio and temperature gradient revealed that as the discharge ratio decreased, the mixing completion point shifted further downstream, while stratification induced by density currents inhibited vertical mixing. Thermal stratification was primarily observed under conditions of low discharge ratios combined with moderate temperature differences. Comparative analysis of surface contour maps and cross-sectional profiles indicated that the spatial location of mixing completion varied depending on vertical and surface variables. Longitudinal profile analysis enabled identification of the mixing completion points across both the surface and the entire water column, showing predictable spatial trends between transects. Spatial interpolation techniques effectively visualized heterogeneous mixing patterns, demonstrating the utility of 2D/3D data for evaluating confluence dynamics. A comparative assessment of IDW and Kriging interpolation in the longitudinal direction showed that IDW achieved superior statistical performance (R² = 0.901, RMSE = 31.522) and was therefore determined to be the most suitable method for this study. Furthermore, analysis of vertical mixing completion points at the Nakdong–Geumho confluence yielded a predictive model (y = 14.238e^(−1.387x), R² = 0.7787). Finally, the Mixing Efficiency Index (MEI) was applied to quantitatively verify the mixing completion points under each discharge ratio condition, with values above 0.94 defined as indicative of complete mixing.