Bijoy Singha Mazumder

The current research investigates, for the first time, the multidimensional transport process of solute in a hydromagnetic, viscous, incompressible, unidirectional, steady, fully developed, third-grade fluid flowing through a channel saturated by a porous medium under the influence of a constant pressure gradient. First-order heterogeneous boundary reactions are applied at both channel walls. A regular perturbation method is applied to derive an approximate steady velocity profile for the third-grade fluid. Aris's method of moments is employed on the governing time-dependent advection–diffusion equation, followed by an implicit finite-difference scheme to study the dispersion process of solute through the channel. The first four central moments are used on the Hermite polynomial representation to ascertain the axial distribution of the solute's mean concentration. The concentration profiles of the solute in both longitudinal and transverse directions are obtained using Aris's method of moments, extending beyond one-dimensional axial dispersion. The study demonstrates how solute dispersion in a third-grade fluid is influenced by Darcy number, Hartmann number, magnetic field inclination, and absorption parameter. It is observed that the flow velocity significantly drops across the channel as the third-grade parameter, Hartmann number, and angle of inclination of the magnetic field increase. However, the fluid velocity increases as the Darcy number rises. The dispersion coefficient decreases with lower values of the third-grade parameter and Darcy number, but the opposite scenario is observed for the increment of the Hartmann number, inclination angle of the magnetic field, and reaction parameter. It is evident that the dispersion of solute enhances by 177.89% when the Darcy number rises from 0.1 to 0.2, and by 54.93% when it increases from 0.2 to 0.3. The dispersion of solute decreases by 1.15% when the third-grade parameter increases from 0.1 to 0.5. As Darcy number and absorption parameter raise, the amplitude of the mean concentration distribution of the solute sharply declines. On the other hand, when Hartmann number, angle of inclination of the magnetic field, and the third-grade parameter enhance, the peak of the tracer's mean concentration distribution increases. It is also seen that the mean concentration distribution of solute decreases by 63.91% when the Darcy number rises from 0.1 to 0.2, and by 24.44% when it increases from 0.2 to 0.3. Also, the mean concentration distribution of solute increases by 0.019% when third-grade parameter advances from 0.1 to 0.5, and by 0.19% when it improves from 0.5 to 1. The results provide insights into complex transport mechanisms relevant to petrochemical engineering, pharmaceutical processes, lubricant manufacturing, and food industries.

In this study, flow fields and higher-order turbulence around submerged cylinders with different spacing configurations and submergence levels are investigated under steady flow conditions. The criticality of various spacing and submergence ratios is assessed using the flow hydrodynamic parameters such as streamlines, mean velocities, Reynolds shear stress, and turbulent kinetic energy (TKE). In addition, higher-order statistics, including third-order moments, TKE fluxes, TKE budget, and turbulent length scales, are evaluated. From the results, reverse flow appears downstream up to x/H ≤ 0.3, indicating shear layer formation and wake vortices, for a single cylinder, irrespective of cylinder submergence. TKE decreases near the rear cylinder due to the sheltering effect, while high skewness near the bed in low-spacing cases suggests intense turbulence. Near the bed, high skewness coefficient values are observed for moderate spacing configuration, indicating strong turbulence. Turbulence dissipation rate increases with spacing, but for spacing beyond three times the cylinder diameter, flow behavior resembles that of a single cylinder. Turbulent kinetic energy budget is transported through turbulent motion into the outer flow and directed toward the bottom due to pressure gradient effects, and energy exchanges in the co-shedding flow regime is provided for different spacing configurations. Kolmogorov length scales are lower for twin cylinders than single cylinders. These findings provide valuable insights into the impacts of cylinder spacing and submergence influence turbulence, aiding in the optimization of tandem cylinder designs.

This study explores the effect of waves on sediment beds of known grain size distribution through controlled experiments for simulating coastal environments based on laboratory experiments. The experimental setup replicates flat and adversely sloping bed conditions, comprising sediments of bimodal grain-size distribution to assess changes in distribution under surface waves of different frequencies. The results demonstrate a significant modulation from an initial bimodal to an unimodal grain size distribution in the sloping bed. In contrast, the original size distribution is retained in the flatbed. Statistical analyses revealed a noticeable shift towards finer grains in the sloping area, driven by wave-induced sorting mechanisms. An interesting result is that the observed grain-size distribution follows the Gaussian distribution around the junction because both coefficients of skewness and kurtosis show zero, irrespective of studied wave frequencies. These outcomes align with previous research, contributing to a deeper understanding of sediment transport and grain size distribution in coastal zones. In addition, prototype field photographs of bed form due to low tidal waves show immense similarities with the ripple morphology along the upward slope generated in the laboratory flume. Moreover, the concentration of heavier coarse fractions of grains occasionally dropped at the trough regions of the fine-grained ripples of lunate shapes. The study insights are valuable for improving coastal management strategies, particularly in areas vulnerable to sediment redistribution and erosion.

Turbulence characteristics in the region of wave-blocking over a submerged forward-facing obstacle is explored, and the results are compared with those of base-flow over the obstacle. Wave-blocking over obstacle is setup, adjusting the strong incoming flow with counter-propagating waves, and confirmed by linear dispersion relation. A variation in the flow is detected in three distinct segments: flow from the upstream, wave-blocking over the obstacle and the waves propagating from the downstream. The instantaneous velocity is recorded using a three-dimensional micro-acoustic Doppler velocimeter along the flow. Turbulence properties such as the mean velocity, Reynolds stress, turbulent kinetic energy, and associated coherent structures around the wave-blocking are discussed. Moreover, power spectral density, kinetic energy budget, and turbulence length- and time-scales are examined. The stress fractions to the total shear stress contribute higher for only flow than those of wave-blocking over obstacle. The power-spectral peaks at a fixed frequency for wave-blocking along lee side are greater than those of base-flow over obstacle. Kinetic energy budget for only flow over the obstacle is much higher than that of wave-blocking, indicating loss of energy due to wave-blocking. In the near-bed region, length-scale increases indicating the higher momentum and energy transfer. Increase in anisotropy plays significant role in the production. Results are valuable to ship sailing, design of coastal structures, and sediment transport.

The present study illustrates an experimental investigation of flow hydrodynamics in the vicinity of a submerged circular pier across various submergence levels under only current and wave–current combined flow conditions. The instantaneous velocity data are collected using particle image velocimetry for three distinct frequencies of waves to determine the influence of wave superimposition on the current-induced turbulence parameters. The distribution of phase averaged turbulence quantities, such as mean velocities, Reynolds shear stress, turbulent kinetic energy, flow patterns, and vorticity analysis by Q-criterion, are presented. The results provide insight into the impacts of wave frequency and submergence ratio on the formation of horseshoe vortices, trailing vortex, and reverse flow zones. From the results it is observed that a decrease in the submergence level of the structure causes the formation of strong horseshoe vortices and reverse flow zones in the absence of waves. Also, an increase in wave frequency intensifies the turbulence kinetic energy at the upstream of the pier and eddy generation behind the pier. The present findings highlight the effects of pier submergence and wave characteristics, such as frequency, wave height, and wave period, on flow patterns and turbulent flow characteristics and aid in the design of marine structures. Furthermore, experimental data serve as a valuable resource for validating theoretical or mathematical models related to combined wave–current environments.

The study of kinetic sorptive effects on the transport phenomena of reactive solute has numerous real-world applications, including in the industrial and environmental sectors. These kinds of investigations become more realistic when an oscillatory pressure gradient with both the reversible and irreversible reactions at the channel walls is considered in a magnetohydrodynamics flow. In the past, Ng and Yip [J. Fluid Mech. 446, 321–345 (2001)] studied the effect of sorptive phase exchange at boundaries on the solute transport phenomena in an open-channel flow using Mei's multiple-scale homogenization technique. They considered fluid flows without magnetic field and boundary absorption. This work uses the above-mentioned method to investigate the phase exchange kinetics of Taylor dispersion phenomena in a two-dimensional magnetohydrodynamics fluid flowing through a parallel channel. The paper discusses how various parameters and dimensionless numbers, such as the Hartmann, oscillatory Reynolds, and Damkohler, affect the flow velocity, transport coefficient, multi-dimensional concentration distributions, and transverse variation rate. Due to the strong magnetic field, the flow velocity and Taylor dispersivity are adversely affected and conspicuously reduced. Additionally, for large Damkohler numbers, the total dispersion coefficient and the Taylor dispersion coefficient both decrease. However, the longitudinal concentration distribution rises with the Hartmann number and partition coefficient. It is worth noting that in the presence of unequal boundary absorption, there is no occurrence of transverse symmetry in solute concentration at any given time. Controlling various processes of tracer dispersion in environmental systems, especially water purification and the chemical industry, may benefit from these intriguing findings.

In river engineering and fluvial hydraulics, bedform migration and erosion/scouring are very important as it may affect river regimes and stability of various man-made structures such as bridges across rivers. In alluvial rivers/channels, bedforms such as ripples and dunes generated from a flat sand bed interacting with the flow show significant changes in the flow conditions such as mean flow, resistance to flow, turbulence, bed load, and suspended load transport. Further in rivers with various structures such as bridges, the interactions between the flow and structure movable or non-movable on the sediment bed cause the sediment erosion around the structure due to vortex generation leading to scour or bed deformation. For the last one century, a number of experimental, theoretical, and field-level studies were carried out by various researchers related to bedform migration and scouring phenomena. In this chapter, resistance to flow, bedforms, and its migration, and flow and scour around the structures or bridge piers are discussed, as presented by many researchers.

The turbulent flow is irregular, random, and complex, which, in general, makes its appearance in fluids, gaseous or liquid, and hence is a challenge to scientists and engineers. Turbulent flow is characterized by irregular, chaotic motion of fluid particles. Though various theories related to turbulent flow are well developed over the past few decades, due to their complexity, it is impossible to get exact/analytical solutions. For turbulent flow analysis, we generally use experimental studies or approximate theories and solutions and numerical models. In this chapter, various theoretical developments in the areas of turbulent flows, approximate solutions, and analysis are deliberated in detail.

Turbulent flow is very complex and to understand its characteristics, various measurement techniques are developed in the last few decades. Extensive experimental works are carried out on the mean flows and turbulence characteristics in open-channel flow using sophisticated measuring gadgets, such as Ott-laboratory current meter, electromagnetic current meter, hot-wire anemometers (HWA), laser-Doppler anemometers (LDA), acoustic-Doppler velocimeters (ADV), particle image velocimetry (PIV), and various techniques of flow visualization such as the hydrogen-bubble and digital imaging technique. In this chapter, details of these equipment and measurement techniques are briefly discussed with some case studies.

In river engineering, channel hydrodynamics and fluvial hydraulics, the transport of sediment in terms of bed load transport is very important as it critically affects the stable regime of the channel or river concerned. The bed load transport depends on various aspects, such as flow conditions, nature, size and shape of sediment, and the ratio of the densities of sediment and fluids. The bed load transport can happen in terms of rolling, sliding, and saltation or jumping or lifting. The transported material by the flow above is generally known as suspended load. In this Chapter, the details of bed load, suspended load and the total load transport with respective methodologies and possible semi-empirical solutions are discussed.