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The objective of this study was to explore the higher-order turbulence statistics of flow and turbulent length scales around a complex pier (CP) and compare the results with those for a simple pier (SP). The velocity data were recorded in a laboratory flume using particle image velocimetry (PIV). The PIV data were analysed to estimate the velocity fluctuations of third order, turbulence production and dissipation rates, turbulent length scales and the contributions of burst–sweep events to the total Reynolds shear stress around the piers mounted on a rigid flat surface. The skewness and advection coefficients indicated a more asymmetric distribution of velocity fluctuations for the SP than for the CP. Ejection and sweep events illustrated the dominance of similar strengths for an extended period, downstream of the piers. The upstream turbulent kinetic energy production was similar for both piers, while the upstream dissipation rate was higher for the CP. The length scales were greater at the upstream for the case of the SP while, downstream, they were greater for the CP. The findings of this work demonstrate the importance of a pile cap in restricting downward-moving flow by showing a lower magnitude of scour-inducing turbulence parameters for the CP as compared with the SP.

This study investigates the turbulent flow properties experimentally in the vicinity of two side-by-side circular cylinders, along with the influence of the third cylinder of the same dimension placed in the upstream and successively in the downstream forming an equilateral triangle. Three-dimensional stereoscopic particle image velocimetry (PIV) was employed to collect the instantaneous velocity data around the arrangements. The study highlights the prime parameters of turbulence such as the mean velocities, Reynolds stresses, turbulent kinetic energy (TKE), quadrant analysis, and Q-criteria for vortices, which are responsible for the development of various problems such as scour-hole around the cylindrical pier arrangements, disturbance around industrial and marine structures. The spectral analysis was performed to examine the energy distributions, vortex-shedding frequencies with corresponding Strouhal numbers. Dominant vorticity locations were identified from the contours of Q-criteria. The magnitude of turbulence characteristics was reduced by 15–20% (turbulence intensity reduced by 20% and TKE by 15%) when the third cylinder was placed the upstream of side-by-side cylinder group. Streamlines are also studied to visualize the flow patterns for a better understanding of physics in the presence of the third cylinder. The maximum energy of vortices obtained from the spectrum analysis showed that the vortices generated were less when the third cylinder is placed upstream.

A series of flume experiments were conducted with varying the flow discharges at the Fluvial Mechanics Laboratory of Indian Statistical Institute (Kolkata) to understand the co-evolution patterns of generating bed forms and the corresponding flow turbulence. Instantaneous bed elevations and velocity components were recorded continuously for sufficient time using high resolution instruments, such as, Ultrasonic Ranging System and acoustic Doppler velocimeter, at some spatial location over the deformed bed for each flow discharge. Increase in mean bed elevations and bed-slopes was found to be increased in discharge. Heavy-tailed nature of the probability density functions of magnitude of bed elevation increments, magnitude of single continuous bed elevation increments and instantaneous Reynolds shear stresses along three planes were analyzed using Pareto and truncated Pareto distributions. The spectral analysis of bed elevations revealed that the slope of log–log linearity increased with increase in flow discharge. Wavelet cross-correlations depicted strong dependence of bed form evolution on the corresponding instantaneous Reynolds shear stress along xz-plane. A Gram–Charlier type of distribution was used to estimate the probability density function of fluctuating velocity components, instantaneous Reynolds shear stresses along three planes and the joint probability density functions of the fluctuating velocity components, which showed good fit with the experimental data.

This paper presents the spatio-temporal variations in bed elevations and the near-bed turbulence statistics over the deformed bed generated around the submerged cylindrical piers embedded vertically on loose sediment bed at a constant flow discharge. Experiments were carried out in a laboratory flume for three blockage ratios in the range of 0.04–0.06 using three different sizes of submerged cylinders individually placed vertically at the centerline of the flume. Clear-water experimental conditions were maintained over the smooth sediment bed surface with a constant flow discharge ( $$Q = 0.015\,{\rm m}^3/{\rm sec}$$ ), thereby giving three different cylinder Reynolds numbers $$Re_{D_c} = \frac{U_mD_c}{\nu }$$ (=10200, 12750, 15300) away from the cylinder locations, where $$U_m$$ is the maximum mean velocity, $$D_c$$ is the cylinder diameter and $$\nu$$ is the kinematic viscosity of fluid. Instantaneous sand bed elevations around the cylinders were recorded using a SeaTek 5MHz ultrasonic ranging system of net 24 transducers to estimate bed form migration, and the near-bed velocity data at transducer locations over the stable deformed bed around the pier-like structures were collected using down-looking three-dimensional (3D) Micro-acoustic Doppler velocimeter to estimate the bottom Reynolds shear stresses and the contributions of bursting events to the dominant shear stress component. The flow perturbation generated due to relatively lower flow blockage ratio favored to achieve the stable bed condition more rapidly than the others, and larger upstream scour-depth and deformed areas were noticed for greater flow blockage ratio due to larger cylinder diameter. For larger blockage ratio in the upstream of scour-hole near the bed, occurrences of probabilities of both boundary-ward interactions (Q1 and Q3) were the dominant; whereas in the downstream of the scoured region, occurrences of probabilities of second and third quadrant events (Q2 and Q4) were dominant. On the other hand, for the lower blockage ratio, quadrant (Q2) was dominant over Q4 in the downstream of scour-hole, and in the upstream of scour-hole, quadrant Q4 was the dominant.

Experiments are conducted in a laboratory flume on the propagation of a surface wave against unidirectional flow with a sediment bed. This paper presents the spatial variation of bed forms induced by the wave-blocking phenomenon by a suitably tuned uniform fluid flow and a counter-propagating wave. The occurrence of wave-blocking is confirmed by finding a critical wave frequency in a particular flow discharge in which the waves are effectively blocked and is established using the linear dispersion relation. The novelty of this work is to identify the wave-blocking and its influence on the development of bed forms over the sediment bed. Interesting bed form signatures are observed at a transition of bed forms in three zones, with asymmetric ripples having a steeper slope downstream face induced by the incoming current, followed by flat sand bars beneath the wave-blocking zone and more symmetric ripples below the wave-dominated region at the downstream. This phenomenon suggests that the sediment bed is segmented into three different regions of bed geometry along the flow. The deviations of mean flows, Reynolds stresses, turbulent kinetic energy, and power spectral density due to the wave-blocking phenomenon are presented along the non-uniform flow over sediment bed. The bottom shear stress, bed roughness and stochastic nature of the bed form features are also discussed. The results are of relevance to engineers and geoscientists concerned with contemporary process as well as those interested in the interpretation of palaeoenvironmental conditions from fossil bed forms., Comment: Accepted for publication in Earth Surface Processes and Landforms

This work presents a study of spatiotemporal changes of scour-holes around sand embedded submerged circular and non-circular cylinders with associated turbulence properties and aims at analyzing the contribution of each quadrant event to the Reynolds shear stress. Experiments were carried out using submerged circular, elliptical, square and triangular cylinders of same length having flow-facing sides as the cylinder diameter with a common submergence ratio of 0.6. It is evident that upstream scour depth was maximum for the circular cylinder and minimum for the elliptical one. Interestingly, side-wise scouring rate was significant for elliptical cylinder. The maximum deposition region was formed at the downstream of the triangular cylinder case; and for the square cylinder, interestingly quite largest sediment accumulations occurred at the two sides about the centerline. The bed elevation spectra for all cases in downstream scour and deposition region showed comparatively higher spectral slopes, where positive bed slopes were generated except for the square cylinder case. In the near-bed region of upstream scour hole, the occurrence of probabilities were higher for sweeping events and it was less for the elliptical cylinder, where the bed was minimum negatively sloped, compared to other cylinders. In the downstream scoured location of the elliptical cylinder, where comparatively lower bed elevation was formed and the bed was negatively sloped, mostly the ejections were the occurring events near the bed region. However, for the other three cases with positive bed slopes, sweeping events were the dominating in near-bed region.

The present paper explores the turbulent flow characteristics and overall drag over the trough region of a pair of adjacent 2-D forward-facing dune-shaped artificial structures with two different stoss-side slopes and aims to make a comparative study. Structures considered here were of equal base length ( λ ) with a common gentle slope of 6°at the downstream face. The stoss-side angles were respectively 50°and 90°. Experiments were conducted at the Fluvial Mechanics Laboratory (FML) of Indian Statistical Institute (ISI), Kolkata. The velocity data were collected using a 3-D Micro-Acoustic Doppler Velocimeter (ADV) at the flume centerline to analyze the mean flows, Reynolds stresses and the overall drag at a Reynolds number, R e h ≈ 1.44 × 10 5 . One-dimensional profiles of turbulent flow parameters demonstrate that the flow separation bubble and a thin perturbed shear layer between the negative velocity region and outer layer with high velocity are the main sources of turbulence production. A change in turbulence characteristics between the two crest positions is identified. A greater amount of flow resistance is observed in the case of the structure having higher stoss-side slope. The spectral analysis reveals that peak power spectral density generally occurs at 0.25–1 Hz for the stream-wise velocity component and at 0.9–3.0 Hz for the cross-stream and vertical velocity components. Power spectra showed better defined peaks near the shear layer in the separation cell where it reaches to maximum which is two to three times greater than its values in the upstream and further downstream region. Strouhal numbers are calculated using the frequencies of eddies and vortices with different sets of characteristic length and velocity scales; and compared with the previous results of other researchers.

The present paper explores the characteristics of turbulent flow and drag over two artificial 2-D forward-facing waveform structures with two different stoss side slopes of $$50^{\circ }$$ and $$90^{\circ },$$ respectively. Both structures possessed a common slanted lee side slope of $$6^{\circ }.$$ Flume experiments were conducted at the Fluvial Mechanics Laboratory of Indian Statistical Institute, Kolkata. The velocity data were analyzed to identify the spatial changes in turbulent flow addressing the flow separation region with recirculating eddy, the Reynolds stresses, the turbulent events associated with burst-sweep cycles and the drag over two upstream-facing bedforms for Reynolds number $$Re_h=1.44\times 10^5.$$ The divergence at the stoss side slope between the two structures revealed significant changes in the mean flow and turbulence. Comparison showed that during the flood-tide condition there was no flow separation region on the gentle lee side of the structure with smaller slope at the stoss side, while for the other structure with vertical stoss side slope a thick flow separation region with recirculating eddy was observed at the gentle lee side just downstream of the crest. The recirculating eddy induced on the lee-side had a strong influence on the resistance that the structure exerts to the flow due to loss of energy through turbulence. In contrast, a great amount of reduction in drag was observed in the case of smaller stoss side sloped structure as there was no flow separation. The quadrant analysis was also used to highlight the turbulent event evolution along the bed form structures under flood-tide conditions.

The purpose of this research paper is to investigate the third-order moments of velocity fluctuations, turbulent kinetic energy (TKE) fluxes, turbulence dissipation rate, turbulent length scales, and Reynolds stress anisotropy in the wake regions over two artificial upstream-facing bed forms. For the structure having a smaller flow-facing slope (slanting forward-facing structure, named as SFFS), the maximum flow intermittency is 0.6% with a maximum flow reversal frequency of 0.24 Hz, whereas for the greater flow-facing sloped structure (vertical forward-facing structure, named as VFFS), up to 70% flow intermittency is noticed just downstream of the corresponding crest location with a maximum of 28 Hz flow reversal frequency. A strong negative M-30 (stream-wise flux of stream-wise normal stress) and a strong positive M-03 (vertical flux of vertical normal stress), implying the occurrence of ejection events, take place above the flow separation region along the generated shear layer. However, near the lee-surface, positiveM(30) and negativeM(03) imply the presence of sweep events. For both the cases, maximum of normalized TKE (kappa) is generated in the vicinity of crest location, which spread over the retarding flow region near-bed of the trough and wake-flow region downstream of the crest. The production of turbulence is mainly concentrated at the interface of intense ejection and sweep dominated zones over the trough region for the VFFS case, and for the other bed form, i.e., SFFS case, maximum turbulence production is concentrated at the near-bed crest location. Near the bed, the length-scale of eddies in the inertial sub-range decreases substantially compared to that in the upstream. It is seen that in the region of negative kinetic energy production, local maximum anisotropy is found, especially for b(11,22,33)(S) and b(11,22,33)(V) components. Interestingly, at the corresponding crest points for SFFS and VFFS, maximum affinity toward the one-component isotropy is measured almost throughout the vertical height. However, a clear increasing trend in the affinity to a better isotropy; i.e., the three-dimensional isotropy is identified as the vertical height increases up to z approximate to 3 cm above the bed when a fair downstream location for the VFFS case is considered. A special look toward the investigation of possible connection of the flow region with negative TKE production with the stream anisotropy shows that a substantial increase in the degree of anisotropy (A(d)) in the anisotropy invariant maps of the negative TKE production takes place for both the cases, when compared to that for the positive TKE production region. Published by AIP Publishing.

The purpose of the present paper is to investigate the contributions of turbulent events to the total Reynolds shear stress over artificial waveforms and to make a comparative study of turbulence between two types of isolated wave geometries: the scalene triangular shape (STS) and the isosceles triangular shape (ITS). All three components of velocity with fluctuations have been measured using 3-D Micro- Acoustic Doppler Velocimeter (ADV) at the Indian Statistical Institute's (ISI) flume, Calcutta. The motivation of this study is to determine the spatial changes of flow and turbulent events, and to gain better understanding of the physics of flow, which are responsible for the transport of sediment.

Mathematical models have been developed to predict the vertical velocity and sediment concentration distributions in a sediment-laden turbulent open channel flow taking into account a modified mixing length based on sediment-induced stratification. The coupled non-linear differential equations for vertical velocity and concentration arising out of the problem have been solved numerically and the results have been compared with the comprehensive exiting data. Comparison shows good agreement with the observed data, which proves the validity of the present model.