Effect of lateral outflow on three-dimensional flow structure in a river delta, EarthArxiv

27 Spatial and temporal patterns in three-dimensional flow structure have been linked to 28 channel processes and morphology in many environments, including river meander bends, 29 confluences-diffluences, and bedrock canyons. However, there is not yet an understand30 ing of how channelized and gradually distributed lateral outflows that are often preva31 lent in river deltas influence three-dimensional flow structure and sediment transport mech32 anisms. This study presents an analysis of 3D flow structure data collected from Wax 33 Lake Delta, a naturally developing river-dominated delta in the northern Gulf of Mex34 ico. Three hydrographic surveys were conducted using a boat-mounted acoustic Doppler 35 current profiler (ADCP) at two sites: a channelized outflow zone and a distributary chan36 nel experiencing distributed lateral outflow. The flow structure was analyzed to iden37 tify secondary circulation cells induced by lateral outflow, which may influence the sed38 iment transport to the islands. Spatial patterns in flow structure were also compared to 39 previous numerical modeling and experimental studies on open channel diversions and 40 compound channels. A conceptual model is developed linking the formation of secondary 41 circulation cells and suspended sediment transport from the distributary channels to in42 terdistributary islands in a delta. The results suggest that a transition from advective 43 to turbulent diffusion transport mechanism may occur depending upon a threshold out44 flow momentum flux ratio which lies in between 0.211 km−1 and 0.375 km−1. This study 45 provides the first detailed quantification of flow structure in an actively prograding river 46 delta and offers important implications for coastal restoration by linking coastal sedi47 ment transport mechanism to patterns in flow structure. 48 Plain Language Summary 49 In a river delta, channels lose a significant amount of water to the islands because 50 of lateral discharge through small crevasse and also as overbank. With the water, sed51 iment and nutrients also get carried from the channels into the delta islands. This pro52 cess supports the deltaic ecosystem and influences the evolution of the delta. Although, 53 it is yet to be shown how such lateral discharge may affect the three dimensional flow 54 field in the delta channels and sediment transport mechanisms. Here we use high res55 olution three-dimensional velocity data from a river delta to determine the influence of 56 two different outflow processes on the nearby flow field. We observe strong coherent he57 lical circulations in the channels when the lateral outflow is concentrated in a small area 58 (i.e., a side channel) whereas weak transient structures when the lateral discharge gets 59 distributed over a large area (i.e., overbank flow). The results suggest the existence of 60 a threshold outflow momentum that triggers the formation of such coherent helical cir61 culations and induces changes to the sediment transport mechanism. The results of this 62 study have implications for better understanding of delta hydrodynamics and morpho63 logical evolution. 64

tems that often exhibit bed discordance, especially in the transition from main channels 141 to floodplains and small crevasses.

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In this study, the flow structure at two channel features in WLD were investigated: 214 CO and UO along the length of the channel. The CO study site was located at Mallard  A 1200 kHz Teledye RDI RiverPro acoustic Doppler current profiler (ADCP) was 228 used for the hydrographic surveys. All measurements were georeferenced using an ex-229 ternal Hemisphere A101 differential Global Positioning System (dGPS) mounted over 230 the ADCP. The ADCP transducer depth was kept at 0.3 m with a blanking distance of 231 0.25 m from the sensor head. Data from the measurement bins close to the bottom were 232 ignored automatically by the ADCP's auto-adaptive system to avoid sidelobe interfer-233 ence. Bin size for each ensemble was optimized by an auto-adaptive system that yielded 234 cell size ranging from 2 − 24 cm depending on the depth of that ensemble. The water 10 June survey (campaign 2) with two additional transects located further inside the lat-  (Table S5). 253 For the UO site (Fig. 1c), an initial survey of the Gadwall Pass was performed on  (Table S5).

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The cross-sections were spaced 500 m apart from each other, starting from N5. One ini-   In other words, the primary velocity at each vertical in this reference frame is equiva- The bathymetry data was interpolated from the ADCP transects. For higher res-296 olution bathymetry, additional zigzag ADCP surveys were performed at the field sites 297 to cover more areas along the channel. These bathymetry data were exported using VMT 298 in earth coordinates, and a Kriging interpolation was performed in ArcGIS R . The grid 299 size was 10 × 10 m for the CO system and 20 × 20 m for the UO sites. The resulting 300 bathymetry was triangulated for visualization in Tecplot 360 (Fig. 3). This method in-  . It is calculated as: which is the ratio of the product of fluid density (ρ), discharge (q), and velocity (v) at  (Table 1). For this 317 -10-manuscript submitted to JGR: Earth Surface study, ρ m and ρ l were assumed to be equal. q m , v m , q l , and v l were extracted from the 318 ADCP data (Table 1).

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For the purpose of this study, the momentum flux ratio was divided by the length 320 of outflow zone along the primary axis of the main channel to yield momentum flux ra-321 tio per unit length of outflow or outflow momentum flux ratio, M r . For CO, the length 322 (L) is the lateral channel width. Eq. 1 thus is modified as, For, UO conditions, eq. 2 is modified as the following, where M rl denotes the momentum flux lost due to lateral outflow for a outflow distance

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To estimate the sediment entrainment and transport capacity of the secondary cir-332 culation, the sediment settling velocity at WLD was calculated using the formula pro-333 vided by Dietrich (1982).
where R f denotes the dimensionless settling velocity, g = 9.81 m/s 2 is the gravitational 337 acceleration, and v s is the settling velocity. The submerged specific gravity of sediment where ρ the density of fluid (water) and the density of quartz (2.65 g/cm 3 ) is used as 342 the density of sediment (ρ s ) for this study. R f is calculated using a relationship based  (Table 1).

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-11-manuscript submitted to JGR: Earth Surface Primary velocity directions for both surveys did not show any significant change 359 with tide. Separation zones upstream of the lateral channel were observed along both 360 banks (Fig. 4). Moreover, the lateral channel bottom was at a higher elevation than the 361 main channel bottom representing a discordant bathymetric feature (Fig. 3). The ve-362 locity magnitude into the lateral channel was approximately 50% of that in the main chan-363 nel (Table 1). No shallow bar was observed on the opposite bank of the main channel 364 (Fig. 3).

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Inside the lateral channel, two zones of flow were observed. The flow close to the 366 right bank (looking downstream) had a significantly lower velocity than the left bank.

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The high velocity core in the lateral channel shifted from the left bank to the middle of 368 the channel gradually as the water moved further inward (Fig. 4). Additionally, the right 369 bank had a shallow elongated bar, and the left bank was scoured (Fig. 3). During falling  -13-manuscript submitted to JGR: Earth Surface Backscatter intensity was found comparatively higher inside the lateral channel and 373 in the right bank (looking downstream) separation zone both in falling and rising tides 374 (Fig. 5). For the rising tide (Fig. 5b), the intensity was even higher at the discordant crevasse 375 located on the opposite bank. The secondary velocity in Rozovskii reference frame for both rising and falling tide 378 at transect M2 shows a large channel-wide clockwise circulation in the main channel (Fig. 6a).

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The width of the separation zone at M2 on the right bank was ∼15 m and it was ∼10  For transect M3 (Fig. 6c), that extended into the lateral channel, the above-mentioned Transects M2 and M4 are from campaign 2 (rising tide) and transect M3 data is from campaign 1 (falling tide). The inset shows the location of the transects.
The dominant channel-wide clockwise secondary circulation also prevailed through 394 the transects M4 (Fig. 6b) and M5 (Fig. 7a and 7c). This observed clockwise cell thus 395 extends from upstream M2 to the downstream M5 transect, which is longer than 50 flow 396 -16-manuscript submitted to JGR: Earth Surface depths (a channel width). Additionally, a clockwise secondary circulation can also be ob-397 served in the depression zone of M4 ( Fig. 6b and S3a). At transect M5, a counter-clockwise 398 cell was observed in the depression zone during falling tide (Fig. 7a), whereas a clock-399 wise cell was observed there during rising tide (Fig. 7c). Large transverse current towards 400 the main channel from the island was observed both at M4 (Fig. S3d) and M5 (Fig. 7d) 401 during campaign 2 compared to the smaller transverse current from the same direction 402 during campaign 1 (Fig. S3b and 7b). approaching 3 cm/s which was comparatively weaker than that observed in the main chan-408 nel, and approximately 5% of the primary velocity. Further inside the lateral channel, 409 the coherent counterclockwise rotating flow structure started to break down (Fig. 8c) 410 as the depth gradually decreased and the high-velocity core, along with the channel thal-411 weg, moved to the center of the lateral channel. In the rising tide survey, the circulation 412 cell was observed to break down inside the channel at a distance of 2.6-4.5 lateral chan-413 nel widths (Table 1).   (Fig. S2).

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The average velocity at Gadwall Pass during campaign 3 was significantly lower 428 as a consequence of smaller discharge through the channel compared to campaigns 1 and 429 2. During the rising tide, there was an increase in velocity near transect N7 relative to 430 N5 (Fig. 9a). This increase might be attributed to the interaction with subaqueous chan-431 nels near the transect location. The velocity core visible at the right bank of N7 grad-432 ually disappeared at transect N10, which lost 54% of flow due to significant lateral out-433 flow. During campaign 4 (Fig. 9b), the high-velocity core strengthened at N10 and moved In campaign 3, the backscatter intensity dropped at the location of transect N9 (Fig. 10). 439 Also at N9 the backscatter is higher (∼7dB) over the subaqueous levees than the main 440 channel. Additionally, this transect had 30% discharge loss relative to N5 due to lateral 441 outflow (Fig. S2).

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During the UO outflow surveys on campaigns 3 and 4, no significantly coherent sec-444 ondary structures were observed at any of the transects (Fig. 11a and b). During rising 445 tide, there's a hint of a loosely coherent counter-clockwise rotating structure in the mid-446 dle of transect N9 (Fig. 11a), although it was not observed during falling tide (Fig. 11b). 447 Therefore, tides seem to have an effect on the secondary structures in the unchannelized 448 zone that may also be driven by modulation of the water-level gradient. Minimal tur-449 bulent exchange in this unconfined part of the delta has also been previously reported.

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Thus the incoherence of flow structures is expected as also the channel discharge was con-451 siderably lower. The transverse flow was observed to be directed from the right bank to 452 the left bank (looking downstream) during both campaigns 3 and 4 (Fig. S4). The results from this study provide an insight into the lateral outflow process in 455 deltaic systems and how it impacts the three-dimensional flow structure, sediment trans-456 port mechanisms, and delta morphology. Coffey and Shaw (2017) suggested that lateral 457 outflow is a vital mechanism for delta growth and maintenance. Besides, flow loss through 458 lateral outflow is also responsible for modulating the velocity and sediment transport trends 459 in the lowermost reach of a river (Esposito et al., 2020). Accordingly, lateral outflow is 460 likely a salient feature of prograding deltas, making the lateral outflow observed at WLD 461 more of the norm rather than the exception. Therefore, results from this study and the  tered by tides, but the depth-averaged velocity demonstrated a significant change (Fig. 4).

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The bathymetry for transects M4 and M5 (Fig. 3) (Table 1) suggesting sedimen-490 tation may have occurred during both surveys. Varying M r with discharge, tides, and 491 storms may modify the zone as temporally erosional or depositional. Although, the hy-492 drodynamic parameters suggest deposition at the depression zone during survey times, 493 the data is not enough to predict the trend of long term erosion or deposition.

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At transect M4 and M5, water was observed to enter the channel from the island, 495 which altered the flow structure patterns. At transect M5 (Fig. 7), a small crevasse on 496 the right bank induced a counter-clockwise rotating cell in the right bank of the main 497 channel (Fig. 7a) during campaign 1. The circulation cell was not present during cam-498 paign 2 and only one clockwise rotating secondary structure could be identified in the 499 main channel (Fig. 7c). The transverse velocity vectors (Fig. 7d) indicate a large trans-500 verse current from the floodplain to the channel on campaign 2 compared to the smaller 501 flow during campaign 1 (Fig. 7b). A similar observation was made at transect M4 ( side the lateral channel (Fig. 3). The associated counter-clockwise rotating secondary 519 circulation (Fig. 8) observed at transects L3 and L4, may scour the channel bed in the 520 left bank, entrain and carry the scoured sediment near the right bank, where the flow 521 is slower (Fig. 4). This mechanism may lead to the formation of the elongated shallow 522 bar in the reduced velocity zone on the right bank. In addition, we observed this coher-   The effect of vegetation was integrated in the field data, and it is currently not con- is required to come to a more precise limit for the threshold.