Hydrodynamics at the Junction of Silabati, Dwarakeswar and Rupnarayan Rivers at Bandar, Paschim Medinipur, West Bengal, India

Open access e-Journal Earth Science India, eISSN: 0974 – 8350

Vol. 6 (II), April, 2013, pp. 77-89 http://www.earthscienceindia.info/

Swapan Kumar Maity and Ramkrishna Maiti Department of Geography and Environment Management, Vidyasagar University Midnapur-721102, West Bengal, India Email: [email protected]; [email protected]

Abstract

The Rupnarayan river originates from Bandar as a combined flow of the Silabati and Dwarakeswar rivers and is characterized with huge siltation. Both riverine and maritime tidal processes are active in this channel. A close study on the processes acting at the junction is made to understand the relative importance of tide over fluvial processes. The hydrodynamic characteristics at the junction are very complex and unpredictable as many parameters influence the flow here. Geometric variables such as size, shape, slope and the angle of channels etc. and hydraulic variables like flow pattern, velocity, channel roughness, discharge ratio etc. are monitored after necessary measurement using compass, leveling instruments, echo-sounder, water current meter, GPS receiver etc. Cross channel distribution of depths are monitored by leveling instrument and echo-sounder at regular intervals for a lengths of more than 1 km along each of the incoming tributaries as well as combined flow to understand the nature of bed form specially channel gradient. The flow at junction is turbulent (Except along Dwarakeswar, where flow is laminar) and sub-critical in nature as indicated by Reynolds number and Froude number. The actual angle of junction of the river Silabati and Dwarakeswar are 230 and 360 respectively while the expected angles are 37046’37.4’’ and 560 20’12.16’’ (following Horton, 1945). Gradient of the Silabati, Dwarakeswar and Rupnarayan river bed are 0011’55.03’’, 0039’52.56’’ and 009’25.16’’ respectively. River Silabati is slightly sinuous but Dwarakeswar and Rupnarayan are straight channel near junction. Width-depth ratio of Dwarakeswar is very high (58.82) compared to Silabati (21.55) and Rupnarayan (43.24). Depth and velocity are inversely correlated in each of the three reaches. The discharge of Rupnarayan (59.289m3/sec.) is not equal to the cumulative discharge of Silabati and Dwarakeswar (51.13m3/sec.) due to tidal impulse. The availability of energy is more during high tide (13.25, 12.60 and 13.00 Joule for Silabati, Dwarakeswar and Rupnarayan respectively) than during low tide (11.80, 11.10 and 11.755 Joule). The widening of channel downstream of the junction (expected width, following Miller, 1958 is 66.66m but actual width is 80m) causes flow diversion that reduces the available energy downstream leading to sedimentation.

Key Words: Hydrodynamics, angle of junction, gradient, width-depth ratio, pool-riffle sequence, scouring.

Introduction

Practical considerations suggest the desirability of linking studies of drainage network topology and channel form with hydrodynamic characters. Flow in open channel junctions has always been interesting as a subject for investigation. The hydraulic and geometric characteristics at stream junction are difficult to understand due to its relative complexity and large parameters involved. Geometric variables like, size, shape, slope and the angle of confluence and flow variables like, Froude number, channel roughness, the ratio of

Hydrodynamics at the Junction of Silabati, Dwarakeswar and Rupnarayan Rivers at Bandar, Paschim Medinipur, West Bengal, India Maity and Maiti

discharges and the variation of fluid properties are the dominant interacting factors at junction.

Currently, most numerical models describing open channel networks provide the required equations to explain hydrodynamic nature of stream confluence using mass and energy conservation principles at stream junctions. Leopold and Miller (1956) presented a relation between channel width and stream order, and Miller (1958) analyzed the adjustments in channel form occurring at tributary junctions. Leopold and Wolman (1957) and Brice (1964) used the Sinuosity Index to separate straight from sinuous and meandering channels. Taylor (1944) at first used an analytical model to predict the tributary channel depth upstream of the junction. By using momentum equation and assuming hydrostatic wall pressure distribution Webber and Greated (1966) predicted the backwater effect across the junction. Hsu et al. (1998) applied overall mass and energy conservation to the junction and momentum conservation to control volumes in the junction and computed an energy loss coefficient as well as the depth ratio. Horton (1932) offered a quantitative model and rational explanation for angles of junction. He believed that angles of junction are determined at the time of origin of the stream network. Schumm (1956) observed that angles of junction change with the gradient ratio. Morisawa (1964) noted individual changes in angles of junction of stream, although the average angle of junction did not change significantly. Best and Reid (1984) performed an experimental study of junction flows with varying junction angles and flow ratios. They obtained the separation zone shape index defined as the ratio of the width to the horizontal length of the separation zone. Separation zone increases with the junction angle and the ratio of lateral to total discharge. Nazari (2003) has made some experimental studies on erosion and deposition in channel junction using the parameters like, discharge ratio, branch channel width and grain diameter. He concluded that the maximum scour depth does not occur at the junction itself but somewhere downstream of the main channel. Furthermore, as the width of branch channel decreases, the width of scour area increases more than the increase of scour depth.

In the present study attempts are made to analyze the geometric and hydraulic conditions like, angle of junctions, slope and shape of channels, velocity distribution, availability and conservation of energy, discharge ratio, suspended load concentration etc. at the junction of Silabati, Dwarakeswar and Rupnarayan rivers near Bandar in order to understand the relative importance of tide over riverine processes. The variation of available energy, relation between depth, discharge, gradient and energy availability, sinuosity index and pool-riffle sequence relationship etc. are explained. The expected hydro-geometric properties are calculated and compared with the actual values of the downstream channel, the Rupnarayan.

Study area

River Silabati and Dwarakeswar meet at Bandar, and the combined flow is named as Rupnarayan, which joins river Hoogly at Geonkhali covering a distance of 78 km. The study area extends between 22039’30’’N & 87046’12’’E and 22039’30’’N & 87047’15’’E to 22040’50’’N & 87046’12’’E and 22040’50’’N & 87047’15’’E at Bandar, Paschim Medinipur, West Bengal, India. The catchment area of both the tributaries has typical tropical monsoonal type of climate with an average rainfall of 1320mm to 1630mm. Annual temperature ranges from 11oC to 45oC. The angle of junction of river Silabati and Dwarakeswar with respect to river Rupnarayan are 230 and 360 respectively. The gradient of Dwarakeswar (0039’52.56”) is more than Silabati (0011’55.03”) and Rupnarayan (009’25.16”). The average elevation of the

Open access e-Journal Earth Science India, eISSN: 0974 – 8350

Vol. 6 (II), April, 2013, pp. 77-89 http://www.earthscienceindia.info/

junction is 12 m. from mean sea level. The junction area is characterized by a sequence of pools and riffles. Semi-diurnal tide is active here and tidal impulse penetrates a little beyond Bandar. Tidal bore of lower magnitude is an important phenomenon at that junction.

Fig.1: Study area.

Hydrodynamics at the Junction of Silabati, Dwarakeswar and Rupnarayan Rivers at Bandar, Paschim Medinipur, West Bengal, India Maity and Maiti

Materials and Methods

Topographical maps and District Planning Maps have been collected from Survey of India and National Atlas and Thematic Mapping Organization (NATMO) respectively. Discharge of water is measured in the field and related data were collected from the Sectional Office at Ghatal, under the Irrigation and Waterways Department of Government of West Bengal. Bathymetric close grid survey of the study area was made using Leveling instrument and Echo sounder interfaced with Position Fixing System (GPS). Angle of junction of two upstream tributaries was measured by prismatic compass. Velocity is measured by Digital water current meter and floating method at different sections along three rivers at junction. Zone of scouring was depicted by monitoring of depth, velocity and orientation of river bank. Pool-riffle sequence was identified by constructing the bathymetric contour map at junction and subsequently the average distances between pools and riffles are measured. Simultaneous tidal observations were available at an interval of half-an hour at Bandar Gauge Station in the river Rupnarayan. Water samples during high and low tide were collected to measure the suspended load concentration. Some bed samples were collected and grain size analysis was done at laboratory in the Department of Geography, Vidyasagar University. ERDAS IMAGINE 8.5, ArcGIS 9.2 and Microsoft Office Excel etc. have been used for the preparation of maps and diagrams.

The entire calculations associated with the present analysis were made based on the following equations:

Pattern of flow is identified using the following formula: Re = VR/η …………… (1) and η=μ/ρ …………… (1a) (Reynolds, 1883)

Dynamic viscosity is taken from the empirical table proposed by Roberson, J.A., and Chow, V.T. (1980)

Nature of flow is understood by calculating the Froude Number. Fr = v/√gD …………… (2)(Froude, 1895)

Amount of water discharge is calculated following Leopold and Maddock (1953): Q= WDV …………… (3) b f m Again W= aQ , D= cQ and V= kQ So, Q= aQbxcQfxkQm ………….. (3a) b+f+m= 1 …………. (3b) and a …………(3c)

The expected width of the downstream is calculated following Miller (1958): wc= k1 (wa + wb) …………………. (4)

The angle of junctions of two up streams with respect to the downstream is predicted by the formula: Cos α = Sm/Sn ……………………. (5) (Horton, 1945)

Slope of the river bed is calculated by the equation: θ = tan-1[r/h] ……………………. (6)

Open access e-Journal Earth Science India, eISSN: 0974 – 8350

Vol. 6 (II), April, 2013, pp. 77-89 http://www.earthscienceindia.info/

Sinuosity Index (SI) is calculated following Leopold and Wolman (1957) and Brice (1964). SI= Thalweg length/ Valley length ………….. (7) (Leopold and Wolman, 1957) SI= Length of channel/ Length of meander belt axis ………….. (8) (Brice, 1964).

The available stream energy passing through open channel is expressed as energy equation: H= Z+d cosθ +V2/2g …………….. (9) (Bernoulli, 1941)

Analysis of mean grain size is done following the equation Graphic mean= (φ16 +φ50 +φ84)/3 ……………… (10) (Folk and Ward, 1957)

Here, Re = Reynolds Number, V= mean velocity of flow, R= hydraulic radius, η=kinematic viscosity, μ= dynamic viscosity, ρ= density of water, Fr = Froude Number, g = gravitational constant, D = water depth, Q= discharge, W= width of channel, b= width exponent, f= depth exponent, m= velocity exponent, wa and wb are the width of two upstream tributaries and wc is the width of the downstream, α is the angle of junction, Sm is the gradient of the downstream and Sn is the gradient of the upstream tributaries, θ is the slope of river bed, r is the difference of vertical elevation between two points and h is the horizontal distance between the same points, d= depth, Z= elevation above datum, v= mean velocity.

Result and discussion

Hydraulic monitoring was made during the time when the flow of the tributaries are less than average annual peak and analysis of the data reveals that the hydraulic and geometric characteristics of the region is unpredictable and quite different from the normal stream flow. Moreover, the tidal impact has made the situation more problematic and chaotic. The values of Reynolds number (Re) at Silabati (6714.57) and Rupnarayan (6277.445) indicate the turbulent flow pattern but the flow is transitional in Dwarakeswar River (Re= 1187.624). The nature of flow is sub-critical in the entire stream segment at junction as indicated by Froude Number (Froude, 1895). Tidal effect is feeble; channel cross section is symmetrical and shallow. The channel is straight and movement of water is smooth that does not allow sufficient turbulence. The actual angle of junction is less than the possible angle causing the upstream migration of point of junction. Horton (1945) mentioned that if the tributary approaches the main stream at an angle less than that predicted, the flow in the tributary will be diverted toward the main stream in the vicinity of the junction. The resulting oversteepened gradient on the upstream side of the junction causes rapid erosion, whereas aggradations (lessened erosion) occur on the gentler downstream side. As a result the point of junction will migrate upstream, increasing the angle of junction until it matches the predicted angle. Average slope/gradient of Silabati, Dwarakeswar and Rupnarayan river bed are 0011’55.03’’, 0039’52.56’’ and 009’25.16’’ respectively. Stream gradient has an impact on erosion and deposition at junction and migration of the junction point. Howard (1971) remarked that if the channel gradient are such that S1 ≥ S2 ≥ S3 (S1 and S2 are gradient of two upstream tributary, S3 is the gradient of downstream), then stream 1(Dwarakeswar) might be subject to advantageous capture by stream 2(Silabati) or stream 3(Rupnarayan) and stream 2 by stream 3. If streams adjust their angles of junction to their respective gradients, then the areal pattern of the stream network should be influenced by this tendency.

Hydrodynamics at the Junction of Silabati, Dwarakeswar and Rupnarayan Rivers at Bandar, Paschim Medinipur, West Bengal, India Maity and Maiti

Table-1: Reynolds number, Froude number, gradient and angle of junction. River Reynolds Froude Number Gradient/Slope Angle of junction Number (Fr = v/√gD) (degree) (Re = ρ. VL/μ) Actual Possible Silabati 6714.57 0.06079 0011’55.03’’ 23 37046’37.4’’ Dwarakeswar 1187.624 0.04849 0039’52.56’’ 36 56020’12.16’’ Rupnarayan 6277.445 0.0798 009’25.16’’ Not applicable Not applicable

The actual width of the river Silabati and Dwarakeswar is 50m., but it is 80m. for Rupnarayan. The expected width of Rupnarayan is 66.66m (Miller, 1958). He mentioned that the formula is most applicable in cases where joining tributaries are approximately equal in size. In the study area the equal size of both the upstream tributaries should support the expected width of Rupnarayan River. The increase volume of water due to tidal effect is one important cause for the extra width of Rupnarayan River at junction. This sudden widening causes flow separation leading to increased sedimentation. Width-depth ratio of Dwarakeswar is very high (58.82) compare to Silabati (21.55) and Rupnarayan (43.24). The width-depth distribution has an impact on the pattern and distribution of velocity at junction. The asymmetrical cross-section of Silabati causes asymmetrical distribution of velocity. Maximum velocity (0.4228 m/sec during low tide and 0.4559 m/sec during high tide) is observed at the surface level just above the thalweg towards left bank. In Dwarakeswar river high width-depth ratio has reduced the maximum flow velocity (0.1859 m/sec during low tide and 0.2103 m/sec during high tide). The distribution of velocity is symmetrical in Rupnarayan and maximum velocity (0.5912 m/sec during high tide and 0.5544 m/sec during low tide) is observed at the middle of the cross-sectional area above thalweg (1.85m). Inverse relation between depth and velocity is noticed in all the reaches, which is shown in Fig 6. The discharge of Silabati and Dwarakeswar River during period of survey is 32.486 and 18.650 m3/sec respectively. The discharge of Rupnarayan (59.289 m3/sec) is not equal to the cumulative discharge of Silabati and Dwarakeswar (51.13 m3/sec). Hsu et al. (1998) applied the formula of overall mass conversation (Q1 + Q2 = Q3, whereQ1, Q2 and Q3 are the discharge of 1st tributary, 2nd tributary and downstream respectively) at junction. Tidal influx along the Rupnarayan is more and so, it accounts for almost 10 cumecs of extra discharge. Though the discharge of Rupnarayan is more but sudden widening of it at junction reduces channel depth causing the decline of available stream energy.

Concentration of suspended sediment is more (1.75, 2.00 and 2.25gm/liter) during high tide than low tide (1gm/liter) in three reaches at junction respectively. The junction area is characterized by a sequence of pools and riffles. The average observed and expected distance between pools and riffles is measured and calculated which is shown in Table-4. Observed distance between pools and riffles is less in Silabati (360.5m and 380m respectively) than those in Dwarakeswar (577.5m and 600m) and Rupnarayan river (455m and 435m). Richards (1982) mentioned that systematic downstream variation in velocity is associated with the development of pools and riffles, spaced at a distance of 5-7 w (w is the average width of channel). It can also be linked with Sinuosity index and energy fluctuation (Brice, 1964) in stream channel. More sinuosity of Silabati river (SI=1.13) than Dwarakeswar (SI=1.046) and Rupnarayan (SI=1.0562) causes frequent fluctuation of velocity and energy. That is why the average distance between pools and riffles are comparatively less in Silabati than other two channels.

Open access e-Journal Earth Science India, eISSN: 0974 – 8350

Vol. 6 (II), April, 2013, pp. 77-89 http://www.earthscienceindia.info/

Fig.2: Contour map at the junction.

Hydrodynamics at the Junction of Silabati, Dwarakeswar and Rupnarayan Rivers at Bandar, Paschim Medinipur, West Bengal, India Maity and Maiti

Table-2: River width, width-depth ratio and water velocity. River Width (m.) Width- Velocity of water (m. /sec.) depth High tide Low tide ratio Maximum Minimum Maximum Minimum Silabati 50 21.55 0.4559 0.1069 0.4228 0.1069 Dwarakeswar 50 58.82 0.2103 0.0.06 0.1859 0.0806 Rupnarayan 80 (possible stream 43.24 0.5912 0.2122 0.5544 0.1859 width is 66.66m. following Miller, 1958)

Fig.3: Cross and long profiles at junction.

Open access e-Journal Earth Science India, eISSN: 0974 – 8350

Vol. 6 (II), April, 2013, pp. 77-89 http://www.earthscienceindia.info/

The difference between actual and expected distance between pools and riffles in all the streams is due to downstream variation of velocity and energy (Langbein and Leopold, 1964). In natural channels, pool-riffle bed morphology controls hydraulic patterns, which in turn controls bed scour, sediment sorting, and deposition in streams; thus, a feedback loop occurs with average spacing between pool-riffle sequences (Bledsoe and Watson, 2001; Schwartz and Herricks, 2007). In the study area one important scouring zone is identified, 1.38 km. away from the junction towards downstream and is located near right bank which is concave in shape. Nazari (2003) concluded that the maximum scour depth doesn’t occur at the junction itself but somewhere downstream of the main channel. Two or more small scouring zones are also identified in other reaches.

Table-3: Water discharge, sinuosity index and concentration of suspended sediment. River Water discharge Concentration of suspended load (m3/Sec.) Sinuosity Index (gm/liter) High tide Low tide Silabati 32.486 1.13 1.75 1 Dwarakeswar 18.650 1.046 2.0 1 Rupnarayan 59.289 (Expected water 1.0562 2.25 1 discharge is51.13 m3/Sec.)

The availability of stream energy is determined by the depth of river, gradient and flow velocity (Bernoulli, 1941). At all the reaches the availability of energy is more during high tide (13.25, 12.60 and 13.00 Joule for Silabati, Dwarakeswar and Rupnarayan respectively.) than that during low tide (11.80, 11.10 and 11.755 Joule). So, tidal impulse is very significant to increase available stream energy at junction during high tide. The available energy of Rupnarayan River, in the absence of tide is calculated to be 11.45 Joule. The extra energy of 0.355 Joule, mainly contributed from tidal impulse may have significant effect on hydro-dynamics of junction. Tidal asymmetry is very significant (nearly 5.5hours) here as the high tide duration is 3 to 3.5 hours where as the low tide duration is 9 to 8.5 hours. So stronger and swifter high tide is more effective at junction during lean period due to low flow of riverine discharge at that time. Though the impact of tide is observed at the junction and it is relatively important over riverine processes but the tidal effects continuously increase towards downstream of the Rupnarayan river. As a result huge amount of marine water and sediment penetrate inward of the Rupnarayan river during high tide but during low tide the free discharge of the same is resisted because of weaker riverine flow as well as slower low tide flow for longer duration being characterized by tidal asymmetry. That is why sediments are deposited towards downstream of the river, having a cumulative effect to obstruct the free discharge of Silabati and Dwarakeswar.

Hydrodynamics at the Junction of Silabati, Dwarakeswar and Rupnarayan Rivers at Bandar, Paschim Medinipur, West Bengal, India Maity and Maiti

Fig.4: Velocity distribution at junction during high tide.

Open access e-Journal Earth Science India, eISSN: 0974 – 8350

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Fig.5: Velocity distribution at junction during low tide.

Hydrodynamics at the Junction of Silabati, Dwarakeswar and Rupnarayan Rivers at Bandar, Paschim Medinipur, West Bengal, India Maity and Maiti

Table-4: Average distance between pools and riffles, mean grain size and available stream energy. River Average distance (m.) between Mean Available stream energy grain (H= Z+ dcosθ+V2/2g) pools riffles size High tide Low tide observed expected observed expected (mm.) Silabati 360.5 250-350 380 250-350 0.35 13.25 Joule 11.80 Joule Dwarakeswar 577.5 250-350 600 250-350 0.33 12.60 Joule 11.10 Joule Rupnarayan 455 400-560 435 400-560 0.30 13.00 Joule 11.755 Joule

Fig.6: Relation between depth and velocity at junction.

Conclusion The hydrodynamic characteristics of the junction are still firmly empirical, but proper understanding and modeling is becoming more important as the situation is more complex and unpredictable (Bennett, 1974). Hydro-dynamic processes acting in the junction under

Open access e-Journal Earth Science India, eISSN: 0974 – 8350

Vol. 6 (II), April, 2013, pp. 77-89 http://www.earthscienceindia.info/

study is far complex as both riverine and marine processes are active. Tidal actions are more prominent along downstream segment, the Rupnarayan, where tidal asymmetry plays important role for increased sedimentation downstream. Hydro-dynamic property of the junction cannot be explained through well accepted models as incorporate only riverine processes which consider unidirectional flow of water. The junction under study, experiences bi-directional flow of unequal intensity. It may be inferred from the present study that the riverine processes are over powered by marine processes throughout the years, except few days of peak discharge during monsoon. Hydro-dynamic properties of channels are adjusted to such complex situation.

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(Submitted on: 24.9.2012; Accepted on 13.4.2013)