Dey, Subhasish

Turbulent stream approaching a cylinder embedded in an erodible bed triggers significant erosion to form a scour hole. We present a generalized scaling framework for the equilibrium scour depth at a circular cylinder by means of the similarity principle and discover that the similarity exponent can be uniquely determined through the turbulence phenomenology. We assess the veracity of our approach aided by the experimental and field data covering wide ranges of key parameters. The scaling law offers insight into how the dimensionless scour depth relates to the inertia, drag, shear, and threshold shear forces.

Bioroughness plays an important role in modifying the velocity and sediment flux near the riverbed. It is therefore pertinent to study the influence of benthic fauna on the bed forms. To this end, large-eddy simulations are performed to investigate the influence of the arrays of mounds and their density on the turbulence characteristics in an open-channel flow. The simulated distributions of the time-averaged streamwise velocity and the turbulence intensity are in good agreement with the experimental data. Four numerical simulations are performed with varying streamwise spacings of mounds. Details of the time-averaged and instantaneous flow velocities are analyzed by multiple visualization methods, and the effects of the bioroughness density on the equivalent roughness height and the Darcy-Weisbach friction factor are quantified. The time-averaged flow in the wake of the mounds is characterized by a symmetric pair of vortices. The mounds behave like bluff bodies, increasing the riverbed roughness and heterogeneity in the flow environment. An increase in mound density is to promote the development of secondary currents and to increase the dispersive stress near the bed. The peaks of the Reynolds shear stress distributions decrease in both the streamwise and vertical directions for the high-density case due to a blockage effect. The instantaneous flow features, in the form of various turbulence structures, are generated near the top edge and the wake zone of mounds. The spacing between low-speed streaks decreases with an increase in equivalent roughness height. Multifrequency behavior that is observed is a result of shear layer roll-up from the edges of mounds and the flapping of wake. Finally, two formulas for equivalent roughness height and Darcy-Weisbach friction factor are proposed involving the bioroughness density and height. The findings demonstrate the effects of the bioroughness on the near-bed turbulence characteristics and sediment stability.

Delving into a century of turbulence research, we have long concentrated on skin friction laws by Blasius and Strickler, especially for straight-tube flows. Yet, a persistent question remains: Does skin friction in curved-tube flows possess universality? Addressing this enduring challenge, we present a phenomenological model unveiling universal laws governing turbulent skin friction, applicable to both rough and smooth curved-tube flows. We find that the skin friction coefficients, denoted by f, follow the inverse three-fourths law, f/α1/2 ∼ k α − 3 / 4 , and the inverse four-fifths law, f/α1/2 ∼ I−4/5, for rough and smooth flows, respectively, beyond certain threshold values. Here, α ≡ D/(2Rc) is the curvature ratio, D is the tube diameter, Rc is the radius of curvature, kα ≡ [(ks/D)−2α3]1/6 is the roughness-curvature number, ks is the roughness height, I ≡ (Reα2)1/4 is the Ishigaki number, and Re is the flow Reynolds number. Below their respective threshold limits, they recover the familiar skin friction laws for rough and smooth straight-tube flows. Our findings are primarily validated with an extensive dataset for smooth flow because of the data scarcity in rough flow. Supported by compelling skin friction data from smooth flow across various geometries—plane curved tube, helical tube, and toroid—gathered through experiments and simulations, our model serves as a potential bridge, connecting the theoretical and experimental realms of curved-tube turbulence.

Understanding scour at bridge piers is crucial for safeguarding public safety, ensuring infrastructure resilience, and planning effective maintenance. Despite over six decades of extensive studies aiming to develop predictive formulas for the equilibrium scour depth at bridge piers, more than 20 000 highway bridges in the United States have been spotted “scour critical.” The traditional reliance on existing empirical formulas has posed a severe challenge for researchers, hindering to achieve a unified relation for the equilibrium scour depth from a fundamental scientific tenet. This perspective article presents a breakthrough—a universal law governing the equilibrium scour depth at a circular pier embedded in a sediment bed, specifically in clear-water scour condition. Derived from a phenomenological model, the universal law reveals that the equilibrium scour depth to pier diameter ratio obeys a consistent two-fifths scaling law with the introduction of a newly coined pier-scour number. This number accounts for all the key parameters involved in a local scour phenomenon, including the approach mean flow velocity, threshold shear velocity for sediment grain motion, approach flow depth, pier diameter, and sediment grain size. Importantly, the scaling law contains an additional term involving the drag coefficient raised to the power of 2/5, addressing the impact of the pier shape on the equilibrium scour depth. The derived universal law undergoes the validation through an extensive dataset of experimental measurements on circular pier scour.

This study examines the instability of sand waves (dunes and antidunes) from both linear and weakly nonlinear perspectives. The linear and weakly nonlinear analyses use the standard linearization and the center manifold-projection technique, respectively. The mathematical framework includes the depth-averaged continuity and momentum equations, the advection–diffusion equation for suspended sediment concentration, and Exner’s equation for bed evolution. The streamline curvature is treated using the Boussinesq approximation. The model considers the departure of the pressure distribution from the hydrostatic law. Both modes of sediment transport, as bedload and as suspended load, are taken into consideration. The perturbations characterize the maximum growth rate for a selected wave number, called the resonant wave number, which is the most favorable wave number for the formation of sand waves. As the flow Froude number and the relative roughness number increase, the dimensionless resonant wave number decreases. The dimensionless amplitude of sand waves increases as the flow Froude number and the relative roughness number increase to achieve a maximum, and subsequently it decreases. The predicted wave number and amplitude of sand waves satisfactorily match the available experimental data.

This study presents a comprehensive dataset comprising multiple data packages derived from laboratory experiments on steady and unsteady hydraulic jumps interacting with a large-scale Gaussian-shaped bed obstacle in an open-channel flume. The primary objective was to accurately measure the impact of hydraulic jump on the free surface and the bed pressure along the obstacle, ensuring the transferability of the results. A multi-process method was followed: designed experiments were recorded, images were postprocessed, and water level data were digitalized. For steady conditions, the bed pressure along the obstacle were measured by piezometers. The repository data are organized and provided in a single package, supplemented by a second package containing panoramas for each experimental time instant and graphical representations of the data, facilitating rapid evaluation of the outcomes. This study provides versatile data that can be utilized in various ways, particularly for fluvial model validation and studying turbulence-driven phenomena in open-channel flows. The detailed methodology presented herein can contribute to the advancement of enhanced laboratory techniques to study similar flow problems. © The Author(s) 2024.

Quantifying turbulent friction holds significant importance, not only for understanding the fundamental flow physics but also for enriching system performance across a wide range of engineering applications. This vision article presents the state of the science of the turbulent friction in canonical flows, shedding light on its current status through a combination of theoretical developments and experimental observations. First, the article discusses the law of the wall, including the scaling behavior, the possible origin of the logarithmic law, and the effects of wall roughness. Then, it provides an overview of roughness height and its connection with the wall topography. The scaling behaviors of the logarithmic and power laws of turbulent friction are thoroughly appraised, offering insights into their implications. Additionally, the phenomenological models of turbulent friction based on the spectral and co-spectral budget theories are furnished. The behavior of turbulent friction for extremely large Reynolds number flows is examined, based on theoretical models and experimental data. The semiempirical finite Reynolds number model for turbulent friction is reviewed, emphasizing the pertinent scaling laws in various forms. The scaling laws of turbulent friction in curved-pipe and axisymmetric boundary layer flows are discussed. Finally, future research directions are outlined, highlighting the key challenges to be addressed.

Accurate flow models are crucial for simulating shallow water hydrodynamics, particularly in predicting and mitigating the impacts of extreme events involving free-surface flows. Many of these extreme scenarios in river environments involve fluid dynamics with significant dynamic pressures, invalidating the use of standard Saint-Venant-type models. This study presents a robust and accurate novel alternative based on the Reynolds-averaged Navier-Stokes (RANS) equations solved through variational methods. Despite their potential, variational methods have been underutilized in the literature, and their application has been limited to low-level expansions. Moreover, they are rarely validated against experiments that simulate complex flows. This study addresses both challenges. First, a general mathematical framework is developed for the variational RANS (VR) model of arbitrary high-level. The VR level III model is presented and is solved numerically using a robust finite volume-finite difference solver for turbulence flow modeling. Second, an extensive experimental program was conducted to validate this new flow modeling tool, focusing on two challenging flow scenarios. The first scenario involves the propagation of turbulent breaking waves over an irregular, uneven bathymetry—conditions similar to those observed during bedform development in riverine environments. This scenario involved the experimental characterization of unsteady surges over an array of obstacles in series. The second scenario investigated sill-controlled released discharges, similar to those occurring in estuary inlets with sediment bars. Comparisons between the new experimental data and the predictions from the VR level III model reveal the model's accuracy and robustness, making it a highly suitable tool for simulating free-surface flows.

A turbulent wall jet issuing tangentially over a loose sediment bed induces significant erosion, leading to the development of a scour hole. This perspective article presents a generalized scaling framework for determining the equilibrium scour depths caused by planar and circular wall jets. It applies the concept of similarity, including an incomplete similarity in the power-law asymptotic function of particle size to scour depth ratio. This framework demonstrates that the similarity exponent can be exclusively determined through the phenomenological theory of turbulence. The scaling laws reveal that the nondimensional scour depth obeys a linear-law with the respective planar and circular wall-jet scour numbers, which depend on issuing jet size, jet velocity, bed particle size, and threshold shear velocity. Moreover, the analysis reveals that for a given jet thickness equal to the jet diameter, the circular wall-jet scour number scales with the 3/5 power of the planar wall-jet scour number. The approach is extensively validated with the experimental data over a range of key parameters. The scaling laws provide valuable insights into the relationship between nondimensional scour depth and key hydrodynamic forces, including inertia, particle drag, shear, and threshold shear forces. © 2025 Author(s).