This study presents an analytical model to estimate the vertical distribution of streamwise velocity in double-layered flexible vegetation. The model divides the flow into distinct zones based on force balance conditions. Validation was conducted using experimental data from previous studies, demonstrating strong agreement between model predictions and observed velocity profiles. The influence of vegetation bending angles on velocity distribution was examined, revealing minimal impact in the lower vegetation zone for a fixed vegetation density. The model also incorporates wave effects using Keulegan–Carpenter (KC) numbers and evaluates both linear and nonlinear Stokes wave theories. The findings highlight the role of vegetation flexibility in modifying flow resistance, contributing to improved predictions of flood mitigation, erosion control, and wetland hydrodynamics.

In recent days, emerging nations have needed new and enhanced infrastructure projects to support their growing populations. There is a daily rise in the demand for residential land as the population expands. In addition to flat land, sloping land in hilly areas must be considered to satisfy the demand for housing land. Moreover, vertical development in the form of multi-storey buildings is the only solution to the problem. In this context the effects of various forms of bracing on the seismic performance of two hill building configurations, such as stepback and stepback-setback, were investigated and compared to a building standing on level ground. A time history dynamic analysis was performed to assess structural responses in terms of seismic parameters such as fundamental time period, top storey lateral displacement, storey drift, base shear, and torsion. The building standing on leveled and sloping ground have been modelled with bracings placed at three different locations, namely at the corners, the mid-edge, and the centre of the building. Buildings standing on sloping land are found to be extremely vulnerable to earthquakes due to irregularities in elevation. X-braced frames, V braced frames, and inverted V braced frames have all been examined in order to identify the best bracing system that significantly improved the seismic resilience of building frames. The Stepback-setback X-braced frame, positioned at the center of the building model, demonstrated the highest percentage decrease in lateral displacement compared to the control model during the El Centro earthquake: 16.27% along and 15.55% across the slope line, respectively. Similar trends were observed for the Northridge and Loma Prieta earthquakes. This highlights the effectiveness of the setback-stepback model with a centrally placed X-bracing system as the preferred choice for buildings on sloping ground due to its superior seismic resilience.

Flood risk is usually defined as the combination of the probability of occurrence of events and the potential consequences on people, environment and anthropic structures (Renato et al., 2018).

The present work describes the development of a mathematical model for the evaluation of the equilibrium scour depth around a single cylindrical pier under the influence of co-existing waves and current. The presented equation includes the effect of the Keulegan-Carpenter number and Froude number on the formation of scour hole. The principle of energy balance is used to form a nonlinear equation of scour, where the energy of incoming flow when collided with the pier is equated with the weight of the sediments moving away from the vicinity of the pier to establish an equilibrium scour depth. An effort has been made to capture the nature of the flow along x-, y-, and z-directions when the current is inclined at an angle θ with the direction of progress of the wave. Further, the scour profile chosen can incorporate any shape and size of the scour hole. The model has been tested against published experimental data pertaining to two cases, namely when the waves are following the current and when the waves are traveling normal to the current. Here, only linear wave is considered while deriving the equation.

An analysis of forces for flow around an elliptic cylinder at low Reynolds number has been presented in this work. The finite-volume based open source code OpenFOAM is used for the numerical simulations. pimpleFoam solver is used to solve Navier- Stokes equations for incompressible flow. The combined effects of aspect ratios (AR = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0), domain sizes (Ds = 30Dh, 40Dh, 50Dh and 60Dh) and Reynolds numbers (Re = 40, 100) on flow fields and various aerodynamic parameters are presented. Here, Dh represents characteristic length, which is two times the semi-major axis. It is found that at Re= 40 , the value of CD,avg decreases with the increase of aspect ratio. While, at Re= 100 , the value of CD,avg first decreases up to AR= 0.5 and then increases for all domain sizes. The contribution of the pressure and viscous force in the flow is studied in detail for both the Reynolds number. The contribution of pressure in lift force at Re= 40 is found to be one to two times higher than that of viscous force. Whereas, at Re= 100 the contribution of viscous force in producing lift force is insignificant. The value of Strouhal number at Re= 100 is non-decreasing for increase in aspect ratio at a given value of domain size.

A comparative study of the flow hydrodynamics around two cylinders, simulated using Reynolds Averaged Navier Stokes (RANS) and Large Eddy Simulation (LES), is investigated in this paper. Numerical simulation results of the flow field around tandem cylinders have been carried out using OpenFOAM toolbox for circular cylinders. The computational flow domain of 26D × 20D × 3D in streamwise, spanwise and vertical directions is considered, respectively. Simulations are performed for Reynolds numbers, Re = 253, 12,674, 25,348 and 12,674 (representing the change of the flow from laminar to turbulent) and for three different gap ratios between the cylinders, S/D = 2, 3 and 4. Grid convergence studies are carried out for the concerned geometry. Effect of Reynolds number and gap ratios on horseshoe vortex, wake vortex, and streamlines are explored. At low Reynolds number and low gap ratio, flow regimes around a single cylinder are noticed different from tandem cylinders, because of the interaction of the flow with two cylinders. However, at higher Reynolds numbers and gap ratios, the flow pattern is observed to be independent of the spacing between the cylinders. The LES model exhibited better accuracy when compared to the RANS in describing the flow hydrodynamics. The OpenFOAM results are validated against the existing data available in the scientific literature.

A steady-state analytical solution is proposed for computing three-dimensional seepage into a partially penetrating ditch drainage system receiving water from an uneven ponding field of finite size. The draining soil is assumed to be saturated, homogeneous, and anisotropic, resting on an impervious stratum. The correctness of the proposed model was checked with the analytical and experimental results for a simplified case. A numerical comparison was also carried out between the proposed analytical model and the corresponding finite-difference model for a given flow condition. The study highlights the significance of drain width, penetration depth, ponding distribution, and anisotropic ratio on the discharge distribution from the side and bottom face of the drains. In ditches of shallow depth, a significant rise in the percentage of bottom flow was found in soil with a low anisotropic ratio. With the introduction of the uneven ponding field, considerable enhancement in the contribution of flow discharge from the bottom face of the drain was observed. Travel time and orientation of flow paths were found sensitive to the point of release at the soil surface. Moreover, partially penetrating ditches promote a highly curved flow path from the surface to the recipient drain which in turn increases the travel time of the water particle.

A comprehensive review of the local scour due to vortical flow around a cylindrical bridge pier under steady current is presented in this paper. The mechanism of the formation of vortices, the size, velocity and strength of horseshoe vortex (HSV), formation of the HSV by the separation of laminar and turbulent boundary layer and the scour around a cylindrical pier due to vortices have been presented. The complexity involved in the scour-related calculations, and the scope for future research are discussed in the last section.

This paper sheds light on the formulation of a new equilibrium local scour depth equation around a pier. The total bed materials removed from the scour hole due to the force exerted by the flowing fluid after colliding with the pier in the flow field are estimated. At the equilibrium condition, the shape of the scour hole around the pier may take any form, viz. linear, circular, parabolic, triangular, or combination of different shapes. To consider that, two functions are assumed at the stoss and the lee sides of the pier. The total volume of bed materials removed from the scour hole of an arbitrary shape at the stoss and the lee sides of the pier is obtained by integrating the two functions. The equilibrium scour depth is formed by applying the energy balance theorem. An example problem is illustrated and the results are compared with the equations presented by Melville and Coleman (Bridge scour. Water Resources Publication, Colorado, 2000) and HEC-18 (Richardson and Davis in Evaluating scour at bridges, HEC-18. Technical report no. FHWA NHI, 2001).

In this paper, a mathematical equation is developed for the equilibrium scour depth considering an arbitrary shape of the scour hole around a pier under the action of collinear waves and current. A power-law current velocity profile is assumed for the purpose of the analysis. The equilibrium scour depth is obtained by equating the work done by the flowing fluid while interacting with the pier under the action of the collinear waves and the current and the work done by the total volume of the sediment particles removed from the scour hole, respectively. The equilibrium scour depths predicted by the model show good agreement with the experimental and numerical results available in the literature.

In this review article, the current status of research on pier scour under waves is presented. This includes a summary of different bridge failure events due to scour, scour mechanism, scour depth predictors under waves, influence of pier shape on scour depth formation, shape of scour hole around piers, and many others. Further, this article describes the scour process, development of scour depth predictors, and the complexity involved in the scour related calculations. Finally, the future scope of research is delineated.