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Step-pools are natural geomorphologic forms developed under the action of extreme floods1 in mountain streams with bed slopes ranging from 3 to 20%2,3. The step-pools are characterized by poorly graded bed materials intricately packed to form a step and pool sequence, generating high energy tumbling and tranquil mountain flows. The typical bed morphology is irregular and results in spatially and temporally varied hydrodynamics over various functional units within the step-pools such as step, tread, base of step, and pool region (Fig. 1b). The step denotes the portion of bed comprising boulders or bedrock outcrops jam-packed across the width of the channel. The pool consists of finer bed materials and deeper cross-sections as a result of scour due to submerged or unsubmerged hydraulic jumps generated in the pool. The base of step is the section immediately downstream of step unit where the flow over the step impinges into the pool with high amounts of turbulence and self-aeration. The tread is the region extending from the downstream end of the scour pool up to the step unit. Step-pool systems can also exist without the presence of a tread region. In that case, the pool region directly ends in a step unit4.Figure 1Details of step-pool systems in the present study: (a) Longitudinal section of the field site, (b) Longitudinal section of the laboratory model, (c) Photograph of the field site, (d) Photograph of the experimental setup.Full size imageThe evaluation of flow parameters in step-pool streams does not follow the general criteria recommended for lowland rivers. The commonly used flow friction factors such as Manning’s n and Chezy’s C cannot be applied here due to the non-uniform nature of flow at meso-scale. In step-pool mountain streams, the rational frictional coefficient to define flow resistance is the non-dimensional Darcy Weisbach friction factor5,6,7. Dedicated field and laboratory investigations of the step-pools are necessary to create a sufficient database for the development of accurate hydraulic models.In addition, the design of step-pools is adopted for stream restorations8,9, storm water conveyance systems10, and for creating close-to-nature step-pool fish passes11,12,13. Primal research on step-pools has been largely limited to the analysis of bed morphology14,15,16,17, flow resistance18,19,20,21,22 and sediment transport23,24 by considering the step-pool reach as a single system. A detailed review on the hydrodynamics of step-pools in mountain streams is available in Kalathil and Chandra7.The variations in the flow characteristics imposed by the various morphological units within the step-pool system (SPS) were not studied until the 2000s. Adverse pressure gradients in the pools and upstream of steps lead to increased turbulence, while favourable pressure gradients on steps suppress turbulence. Accordingly, pools are dominated by wake turbulence and the steps, treads and runs are governed by form or bed-generated turbulence. The wake turbulence in pools is characterized by recirculation eddies and its strength diminishes with increase in distance from the impingement point25,26. Incidentally, the variations in hydrodynamics within step-pool systems do not furnish considerable differences in the sediment transport estimation since the measured and computed magnitudes differ up to an order of three because of the limited sediment availability in mountain streams27,28. Nevertheless, updated knowledge on the flow dynamics at different regions within the step-pool reach will aid in providing guidelines for designing close-to-nature fish passes to enable target species to pass through the fluvial system29,30. In recent times, with increased demands to implement and maintain environmental flow schemes, cost-effective and eco-friendly structures such as step-pools provide a promising tool to facilitate economic development together with ecological conservation.The presence of a wide range of substrates (fine sand to boulders) and varying flow conditions in step-pools facilitate the inhabitation, migration, and dispersal of diverse aquatic species31. The productive range of water depth and flow velocity for inhabitation lies between 0.16 m to 0.5 m and 0.3 m/s to 1.2 m/s, respectively11. In addition to the range of flow depth and velocity requirements, hydraulic shear stress and turbulence characteristics also affect fish behaviour and locomotion32. Depending on the turbulence scale and intensities, various damages on the fish body or disorientation of the species may occur. Therefore, it is important to consider fish behaviour, life stage, swimming ability, and hydraulic conditions including velocity and turbulence characteristics in step-pool structures prior to its ecological applications. Adequate design guidelines for the construction of close to nature fish passes are not available due to lack of studies31,33.Limited research addresses the influence of bed morphology on the turbulence characteristics in step-pools. Wohl and Thompson4 studied the variations in flow profiles at different locations in a step-pool with the use of an electromagnetic current meter of sampling frequency 0.5 Hz. The study was limited to the analysis of mean velocity and coefficient of variation in velocity which is sometimes used synonymous to turbulence intensities. Although flow profiles showed variations in pattern, ANOVA and ANCOVA results were rather inconclusive regarding the dependence of flow parameters on the bed form types. Later on, Wilcox and Wohl34 and Wilcox et al.35 conducted three-dimensional velocity measurements using SonTek FlowTracker operating at 1 Hz sampling frequency to study the spatial variation of velocity and turbulence intensities in step-pools. The pools exhibit increased levels of turbulence intensities and less velocity reduction in cases where the upstream step-units do not span the entire width of the channel and effects as leaky or porous steps35. The turbulence characteristics in terms of the root mean square of the fluctuating velocities showed considerable differences between step, tread and pool. However, due to the low sampling frequency of the velocity measuring instrument, the accuracy of turbulence analysis is questionable. Considering the complex terrain in step-pool streams and practical difficulties in the use of high frequency instruments that require proper stationing and continuous power supply, it is arduous to produce good quality data of the fluctuating velocities. To bridge the gap in research on the fluctuating velocity components in step-pools, extensive laboratory studies are required.In this context, to shed light upon the variation of hydraulic parameters with the morphological units, we discuss the results from a physical model downscaled according to field measurements conducted in a step-pool stream in Erumakolli, Wayanad, India. Figure 1 shows the longitudinal sections and photographs of the field site and the laboratory experimental setup. The field investigation comprised the measurements of bed material size, bed topography and flow velocity measurements. The physical model study discusses the variation in the turbulence characteristics across steps, treads and pools. The analysis is limited to the vertical distribution of velocity magnitude and turbulence intensities across the morphological units, the propagation of velocity magnitude and Reynolds shear stress in the flow direction, relationship between the turbulent kinetic energy and velocity magnitude, and the evaluation of energy dissipation factor in the step-pools. The present study is the foremost attempt in the analysis and discussions of turbulence fluctuations, Reynolds shear stresses and energy dissipations in self-formed step-pool systems.Experimental setup validationThe laboratory experimental setup was created by establishing dynamic similarity between the field and the laboratory model through Froude’s Model Law. Model scales less than 10:1 can successfully simulate field conditions in the case of turbulent self-aerated flows36. A length scale ratio of 3.3: 1 was chosen for creating the physical model. The corresponding velocity scale and discharge scale are (3.3)1/2: 1 and (3.3)5/2: 1, respectively. The laboratory step-pool system is self-formed under a formative discharge and is not expected to generate the exact bed topography as observed in the field. However, effect of the influencing parameters such as D84, step-height, bed slope, and discharge on the velocity and turbulence characteristics would be adequately simulated. A comparison of the thalweg velocity and Froude number over step, tread and pool at d = 0.6 H between the field and laboratory data is presented in Table 1, where d is the depth of measurement and H is the total flow depth at that point. Since the measured data is location specific and due to the limitations in the number of data points available, only the reach scale average values of velocity and Froude number was used to estimate the error. An absolute error of 0.04 m/s (6.3%) and 0.02 (4.9%) was observed between the field and laboratory up scaled data for thalweg reach average velocity and Froude number, respectively.Table 1 Comparison of the thalweg velocity and Froude number for step, tread and pool at d = 0.6 H between the field and laboratory data.Full size tableVelocity and turbulence intensitiesThe velocity and turbulence characteristics pertinent to accurate design and model development of step-pools are velocity magnitude (VR), turbulence intensities (TI), normalized turbulent kinetic energy (K), and energy dissipation factor (EDF). We obtained velocity data in the physical model using Nortek Vectrino 3-D Acoustic Doppler Velocimeter. A total of 16 thalweg velocity data at d = 0.6H and 24 vertical velocity profiles at 1 cm intervals have been retained after velocity filtering and processing (see “Methods”), where d is the depth of measurement and H is the total flow depth at that point. The velocity measurements were confined in the range of 0.003 m/s to 0.796 m/s, bounding the productive range for aquatic species inhabitation in field scale (0.005 m/s to 1.446 m/s).The propagation of flow in a step-pool system is illustrated in Fig. 2. The x-axis shows the measurement sections along the longitudinal direction (X) for step-pool system 2 (see “Methods”). The variable on the y-axis z + H − d denotes the elevation of the measurement point above the datum which is set at the deepest scour point of X = 2.60 m. Where, z is the vertical distance from the datum to the bed surface, H is the total flow depth at the point, and d is the depth of measurement with respect to the free surface. The first vertical corresponding to X = 2.40 m is at a distance of 0.15 m downstream of a step unit. Any data collected closer to the steps were removed in data filtration. The average velocity at d = 0.6H is shown in the plot legend. The lowest velocity is observed at the deepest scour section of X = 2.60 m.Figure 2Variation of resultant velocity magnitude VR in the longitudinal direction of the SPS 2.Full size imageTo examine the statistical differences in the distribution of velocity and turbulence intensities across the morphological units, the 24 vertical velocity measurements comprising longitudinal and cross-stream points have been subjected to Kruskal–Wallis ANOVA. The earlier studies that sought to distinguish the morphological units on the basis of velocity components performed one-way ANOVA on the datasets. Although the measurements on steps, treads and pools are independent of each other and randomly sampled, the available data fails to uniformly conform to normal distribution, which is a prerequisite for ANOVA test. Therefore, the present work revisits this analysis for velocity components, velocity magnitude and turbulence intensities using Kruskal–Wallis ANOVA which is a non-parametric test that does not assume a normally distributed dataset. The analysis is conducted on the ranks of the data values rather than the data values, and tests whether the median values are significantly different from each other. A resultant p value of 0 from the analysis indicates that there is significant difference between the groups, while a p value of 1 indicates vice-versa. The null hypothesis of Kruskal–Wallis ANOVA is that the sample groups come from the same population. Closeness of the p value to 0 is a measure of the confidence in rejecting the null hypothesis. In the present study, data points were categorized with respect to d/H values to normalize the effect of depth on the velocity variations, and the data points confined in the range d/H = 0.50–0.70 were considered for the test (Case I). The d/H is thus selected to obtain a wider range of data points pertaining to the average velocity which is typically at d/H = 0.6. The non-parametric test was also repeated for depth averaged values (Case II) to produce similar results. Except in the case of cross-stream velocity v, all other groupings showed significant difference between the median values for step, tread and pool data points. The p values of 0.24 and 0.41 were obtained for the hypothesis test on v for Case I and Case II, respectively. This shows that the variation in the cross-stream velocity is independent of the morphological type and is not a characteristic feature of step-pool system in a straight channel. The step-pool system that encounters bends within the reach may have an influence on the cross-stream velocity component. The results of the statistical analysis and box-plots of the velocity magnitude and turbulence intensities for both Cases I and II are given in Table 2 and Fig. 3, respectively. A negligible absolute error of 0.027 m/s and 0.031 m/s in velocity magnitude was obtained between the mean and median of Cases I and II, respectively. Whereas, a maximum absolute error of 0.134 and 0.087 was observed in the respective turbulence intensities. However, the differences in the methods are not substantial enough to alter the results of the hypothesis testing.Table 2 Comparison and analysis results of Kruskal–Wallis ANOVA for data points in the range of d/H = 0.50–0.70 and depth-averaged values at various verticals across the morphological units.Full size tableFigure 3Distribution of resultant velocity magnitude VR and turbulence intensities TI of the fluctuating velocities, u′, v′, and w′ for different morphological unit: (a) Case I: data points confined to d/H = 0.50–0.70. (b) Case II: depth-averaged values at each vertical.Full size imageThe average values of TIu′, TIv′, and TIw′ combining the 24 verticals (d/H ranging from 0.20 to 1.00) are 0.065,0.055 and 0.097 for steps, 0.146, 0.110, and 0.165 for treads, and 0.453, 0.265, and 0.523 for pools, respectively. The values show an increase of 55%, 50% and 41% for TIv′ with respect to TIu′ for step, tread and pool, respectively, while a sizeable increase of 597%, 382% and 439% for TIw′ with respect to TIu′, which evidently indicates the dominance of vertical fluctuations in the pools. The pattern of variation of turbulence intensities at step, tread and pools can be better understood with the help of vertical profiles. Figure 4 shows the vertical profiles of velocity magnitude and turbulence intensity profiles corresponding to step, tread and pool regions in different step-pool systems, namely, SPS 1, SPS 2, and SPS 3 (see “Methods”). Compared to the velocity profiles in step and tread, a visible mid-profile shear layer can be seen in the pool. Previous researchers have identified the presence of mid-profile shear in regions of wake turbulence. Thompson and Wohl4 illustrated the shear layer downstream of steps with the help of velocity profiles in step-pool systems. Baki et al.37 illustrated the presence of shear layer in the wake turbulence regions of a rock-ramp fish pass. A staggered arrangement of natural boulders of equivalent diameter 14 cm was used to prepare the rock-ramp bed. The wake area downstream of the boulders is similar to the downstream of steps in step-pool systems. Fang et al.38 illustrated the shift in the vertical profile of Reynolds shear stress due to near-bed and boulder-induced shear stresses. In the present study, the shear layer is prominent in SPS 3, milder in SPS 1 and fairly non-existent in SPS 2 which corresponds to the profile at X = 2.40 m in Fig. 2. The shear layer is generated due to the momentum exchange occurring in the pools consequent to flow impingement. The occurrence of the shear layer and the magnitude of velocity shift depend on the characteristics of the upstream step unit and spacing between the upstream step and point of interest. In the case of leaky step units where some portion of the step cross section is devoid of elevated step units, the flow passes through without causing consideration impingement to the downstream pool. Hence, the flow does not produce a downstream wake region resulting in the absence of shear layers in the vertical profile. The same can be observed from Fig. 4e, where the vertical section in SPS 2 existed downstream of a leaky step unit, which also lead to lower levels of energy dissipation and less velocity reduction.Figure 4Variation of resultant velocity magnitude VR and turbulence intensities TI of the fluctuating velocities, u′, v′, and w′ along the depth: (a) VR at Step, (b) TI at Step, (c) VR at Tread, (d) TI at Tread, (e) VR at Pool, and (f) TI at Pool.Full size imageThe magnitude of turbulence intensities is lower on step and tread, and maximum in the pools as can be observed in Fig. 4b, d and f, respectively. The fluctuations are higher in the pools due to the varied velocity distribution and wake turbulence characteristics in the pools.Reynolds shear stressReynolds shear stress is the stress generated due to the momentum exchange between the fluctuating velocity components. The range of shear stress in the flow medium has implications in the suitability of a flow body to various aquatic lives since high levels of shear stress may even lead to major injuries or mortality to the species. The vertical profiles of the time averaged and normalized Reynolds shear stress in the x–z plane in the longitudinal direction is shown in Fig. 5. The x-axis shows the normalized Reynolds shear stress (- overline{{u^{{prime }} w^{{prime }} }} /V_{max }^{2}) for each section, where Vmax = 0.796 m/s is the maximum velocity measured during the experimental runs. The variable on the y-axis follows the same convention as described in Fig. 2. The fluctuations in the profile are more in the deeper locations in the pool (X = 2.40 m to 2.80 m) due to the increased turbulence at the bottom as a result of flow impingement. The error bar shown for X = 2.50, 2.90 and 3.05 is calculated from the additional 4 verticals measured in the cross-stream direction, for each of the sections. The maximum Reynolds shear stress variation is observed in x–z plane compared to x–y and y–z planes, with normalized values ranging from − 19.477 to 13.729. The absolute maximum value of 19.477 amounts to 12.34 N/m2 in model scale and 40.73 N/m2 in prototype scale. Reynolds shear stress as low as 30 N/m2 can cause reduction in startle response in some species39. Therefore, ensuring acceptable limits of turbulence fluctuations is essential in the design for artificial constructions of the step-pool morphology. While recreating the morphology for a fish pass design, control can be placed on the pool volume, characteristic grain size (equivalent to step height) or allowable discharge to reduce the turbulence levels in pools. However, this entails detailed study into the cause and effect of these parameters on the hydrodynamics.Figure 5Variation of time averaged and normalized Reynolds shear stress in the x–z plane (( – overline{{u^{{prime }} w^{{prime }} }} /V_{max }^{2} )) in the longitudinal direction of SPS 2 (Vmax = 0.796 m/s).Full size imageTurbulent kinetic energyAnother indicator of turbulence characteristic to the morphological units in the present study is Turbulent Kinetic Energy (TKE) which is a measure of kinetic energy per unit mass of the turbulent flow. It is an important parameter that determines the locomotive characteristics of various species40 and key to evaluating the energy loss to fishes41. In the present study, normalized form of turbulent kinetic energy (K) follows an inverse power relation to the velocity magnitude as shown in Fig. 6. The x-axis is normalized using Vmax and TKE is normalized by the transformation (K = sqrt {{text{TKE}}} /V_{R}). The data is inclusive of all the depth-wise data points measured over step, tread and pool regions along the thalweg. Larger values of K occurred in pools followed by tread and step regions. The pattern is comprehensible from visual observation of the flow field, where the flow occurs as high-velocity sheet with limited agitation over tread and step, resulting in plunging flow with recirculating eddies in the pools. A non-linear curve fitting of type Power-Allometric 1 was used to generate the empirical equation (K = aleft( {{{V_{R} } mathord{left/ {vphantom {{V_{R} } {V_{max } }}} right. kern-nulldelimiterspace} {V_{max } }}} right)^{b}), where a = 0.12398 and b = − 0.89947 with a standard error of ± 0.01018 and ± 0.03398, respectively. The coefficient of determination of the plot is 0.93.Figure 6Variation of normalized turbulent kinetic energy K with the time-averaged thalweg velocity ratio VR/Vmax (Vmax = 0.796 m/s).Full size imageEnergy dissipation factorThe energy dissipation factor (EDF) is an engineering design parameter that checks the turbulence level in the fish pathways. The flow energy must be sufficiently dissipated to ensure velocity levels less than 2 m/s. The EDF is also representative of the eddies and turbulence generated due to flow impingement into pools. Contrary to the conventional pool fish passes and slot fish passes, the pool cross-sections in natural step-pools are not uniform33. The pool dimensions vary along the reach and accordingly reflects in the EDF values. Hence, calculation of EDF using the equation (EDF=gamma QS/A) would result in considerable errors since A is not a constant within and across step-pool systems, where γ is the specific weight of water, Q is the discharge, S is the bed slope and A is the cross-sectional area of the pool. Here, the EDF calculations were based on the basic equation (EDF = gamma QDelta H/forall), where ΔH is the drop in water elevation level per pool and (forall) is the pool volume. The step-pool systems 1, 2 and 3 have been evaluated for EDF. The pool volume was calculated applying the trapezoidal rule to the wetted areas of cross-sections in pool spaced at 10 cm apart. The wetted area was calculated from the measured bed and water elevation levels. The region starting immediately downstream of the steps up to the exit slope of the scour pool is considered for calculating the pool volume. Table 3 presents the pool dimensions and EDF values obtained in the present study. The EDF values obtained for step-pool systems 1, 2, and 3 were 321, 207, and 123 W/m3 in model scale, respectively. The results corresponds to 590, 380, and 226 W/m3 in prototype scale. However, a value of 150 W/m3 should not be exceeded to ensure acceptable levels of turbulence in the pools33. Specific EDF criteria for various fish species are available to design fish passes accommodating the requirements of the predominant fish population42.Table 3 Computation of energy dissipation factor in step-pool systems 1, 2 and 3.Full size tableConsidering the range of shear stresses and energy dissipation factors obtained in the present study, it can be inferred that construction of step-pool fish passes simulating the field parameters may not provide adequate flow conditions for a step-pool type fish pass. For the design of step-pool type fish passes, the pool volumes should be back calculated from the EDF equation for specific species. The translation of the pool volume in terms of the width of channel, pool length and pool depth will ensure lower levels of turbulence intensities and shear stresses in the passage. Since the interest towards close-to nature fish passes have been developed only in the recent years, specific guidelines for step-pool type fish passes are yet to be formulated. This calls for research in artificial step-pool constructions based on the pool and turbulence requirements of the dominant target species. Nevertheless, the nature of hydrodynamics in the self-formed and artificially constructed would coincide since the step-pool bed morphology has an inherent tendency to attain a state of maximum resistance. The concept of creating artificial structures is limited to providing and placing the bed materials into required bed slopes and approximate design dimensions. The ultimate bed morphology of the structure will be modelled over time by the hydraulic force of the flowing water. More

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