The natural protection offered by saltmarsh and mangrove wetlands is increasingly recognised and there is widespread interest in understanding this phenomenon to assist nature-based coastal interventions. Roughness plays a fundamental role in shallow-water hydrodynamic process and hence is a critical parameter for simulating flow over coastal vegetation and the resulting dynamics of surge and wave attenuation. This study provides a comprehensive review of our understanding of the Manning’s coefficient (T/L 1/3 ) in saltmarsh and mangroves. The literature was screened using a rigorous selection procedure to identify studies relevant to saltmarsh and mangrove hydrodynamics and bed roughness. Considering all the numerical, laboratory and field studies that used Manning’s coefficient in saltmarsh and mangrove ecosystems, 36 papers were identified and assessed. The results indicate an interquartile range of Manning’s coefficient (s/m 1/3 ) from 0.04 to 0.08 for saltmarshes and 0.10 to 0.14 for mangroves, providing indicative ‘global’ estimates for these two coastal wetland types. Geographic location, tidal range and temperature showed no statistical relationship, supporting the use of global indicative values. However, statistical testing reveals that the Manning’s coefficient for saltmarshes and mangroves do show significant cross-shore variability with increasing values from the seaward to landward direction. This should be considered and further assessed, especially in more detailed studies. Hence, this analysis provides an indicative ‘global’ constant estimate of Manning’s coefficient for saltmarshes and mangroves, as well as suggestions for more systematic future research on wetland roughness. • A global review of Manning’s number in saltmarsh and mangrove wetlands is presented. • Global assessment of supporting nature based solutions restoring coastal wetlands • Indicative Manning’s values: 0.04–0.08 for saltmarsh and 0.10–0.14 for mangroves. • No statistical link found between Manning’s number and location, tide or temperature. • Cross-shore variability of roughness is significant and needs further investigation.

Numerical study of swash dynamics: Development of a porous layer boundary treatment for rough surfaces modelling

Eddy-resolving numerical simulations are used to investigate the fully developed open-channel flow over an array of large-scale bed roughness elements placed on a rough or on a smooth surface that mimics freshwater mussels partially buried in a gravel or in a sand bed, respectively. The rough surface corresponds to the scanned surface of a gravel bed with uniformly distributed bed roughness. In this paper we analyse how the surface mussel coverage density, BC , the roughness of the bed surface on which the mussels are placed and the filtering activity of the mussels (i.e. the local mass exchange occurring through the mussels’ syphons) affect the double-averaged profiles of the streamwise velocity, turbulent kinetic energy, Reynolds and dispersive shear stresses, and the equivalent bed roughness height, $ K_{S} $ . Results show that similar to rough-bed boundary layers forming over sparse roughness elements in a deep environment (uniform free-stream velocity) and to those developing in a depth-limited environment (e.g. open channel), a multilayer analytical model can be used to approximate the double-averaged profile of the streamwise velocity over the flow depth, D , in the case of fully developed flow over a mussel bed. For similar values of BC and height of the protruding mussels, h , the scaling coefficient of the law-of-the-wake component supplementing the law-of-the-wall inside the inertial layer ( $h \lt z \lt D$ ) is found to be lower than values estimated for developing boundary layers over mussel beds. Results show that the equivalent roughness height increases monotonically with the surface mussel coverage density until BC ≈ 0.8, when the average distance between the mussels becomes sufficiently low for a skimming flow regime to develop over the top of the mussels. Bed roughness effects on the double-averaged variables are significant only for cases with $ \textit{BC} \lt 0.3$ . Results also show that mussel-induced velocity streaks are generated over the top of the mussels and the average transverse spacing of the streaks, λ , decays with increasing BC for constant h . The variation of $ \lambda / K_{S} $ with the non-dimensional distance from the bed surface is similar to that observed for fully developed flow over a rough bed with distributed roughness except for very low surface mussel coverage densities (i.e. $ \textit{BC} \lt 0.02 $ ) when λ remains constant (i.e. $ \lambda / K_{S} $ ≈ 10).

This study examines the effect of roughness spacing on the characteristics of hydraulic jumps in open-channel flows, based on experimental results in a rectangular flume with a smooth bottom and three different sets of discrete roughness (spacingsS = 12 cm, 24 cm, and 46 cm; fixed heightK = 2 cm). Tests were conducted with supercritical incoming flows at discharges of 15, 20, and 25 L/s. Flow visualization revealed regime transitions from skimming-like flow at close spacing (S/K = 6) to wake-interference at intermediate spacing, and wake-type hydraulic jumps at the largest spacing (S/K = 23), with increasing discharge promoting unsteady wake-jump interactions, surface rolling, and enhanced turbulence. Results show that increasing roughness spacing significantly reduces relative jump length (Lj/y₁) from 20 to 35 (S = 12 cm) to 10-17 (S = 46 cm), while relative energy dissipation (ΔE/E1) decreases with larger spacing due to reduced flow-roughness interaction density; optimal dissipation occurs at smaller spacings. Velocity profiles, pressure distributions, and roller lengths were also affected, with closer spacings yielding more compact jumps and higher turbulence near the bed. Empirical predictive relationships were developed for relative jump length and a modified conjugate depth ratio incorporating a roughness correction factor, showing good agreement with measurements. These findings highlight the critical role of roughness spacing in optimizing energy dissipation and jump control in stilling basins and hydraulic structures.

Bed roughness plays an important role in controlling flow resistance, turbulence and energy dissipation in open-channel flows, particularly in high-velocity hydraulic structures such as spillways. The influence of wart-type roughness elements on supercritical open-channel flow dynamics was investigated through controlled flume experiments, comparing smooth and rough ( S = 20 cm spacing) bed conditions. Velocity profiles, shear stress, and specific energy distributions were measured along the channel using point velocity measurements in a 7 m long, 0.5 m wide Plexiglas flume with a 2% slope at the Ujigawa Hydraulic Laboratory, Kyoto University. Results show that the rough configuration significantly reduces mean velocities compared to the smooth bed, with pronounced velocity deficits near the bed. Wall shear stress ( τ ) in the smooth case ranged from 2.92 to 3.04 Pa, showing a slight Reynolds number (Re) dependence, while the rough case exhibited lower τ (1.88–2.28 Pa) with greater variability, suggesting reduced drag due to flow separation. Non-dimensional shear stress ( τ/(ρv 2 )) was nearly constant for the smooth bed and fully constant for the rough bed, indicating a transition to a fully rough regime. The logarithmic law of the wall was validated, with a consistent von Kármán constant ( κ = 0.41) and reduced intercept ( A = 5.09 vs. 5.5) for the rough bed. Specific energy distributions revealed enhanced dissipation near the rough bed, impacting hydraulic efficiency. These findings are limited to S/K = 5.71 and Fr > 1.8, but highlight the potential of this specific wart-type roughness for energy dissipation and erosion protection in high-velocity structures.

Bed roughness plays a critical role in shaping flow structures, especially in large width-to-depth ratio channels. River confluences, characterized by complex flow dynamics, are further modulated by variations in bed roughness. However, the effect of roughness on confluence hydrodynamics remains unclear. Through flume experiments with three width-to-depth ratios, this study compared hydrodynamic responses between smooth and gravel beds, analyzing velocity fields, secondary current intensity, water depth, streamline curvature, and Reynolds stress. Unexpectedly, the introduction of bed roughness was found to enhance, rather than weaken, the secondary current. This is primarily attributed to the decreased separation zone (especially near the bed), which led to an increase in the curvature of the secondary current. The rise in local water levels further limited the effect of roughness in reducing the secondary current. The reduction of the separation zone caused a decrease in the primary velocity of the nearby tributary flow and also resulted in a more immediate recovery of downstream flow velocity.

Estimating in a stream’s cross-section the depth-averaged velocity, V, from the free-surface velocity, vsurf, is an efficient, non-invasive hydrometric method. The ratio fv = V/vsurf is typically assumed constant at fv = 0.86 in field applications, despite observations to the contrary. Guidance is, therefore, needed in estimating actual fv-ratios when velocity profile data are absent. This work provides field-verified guidance based on the hydromechanics of the logarithmic velocity law, which shows that fv depends on the scaled resistance measure ‘friction length/depth’, yo/h, with the yo(k) function of the equivalent sand grain roughness, k. The mean-to-surface-velocity ratio in rough-bed streams is estimated from the bed roughness and stream morphology by modifying Nikuradze’s equation, yo = k/30, to yo = ck, with c(h/k) ≥ 1/30, and k ≈ D84—data fit: c ≈ 8.61(h/k)−1.821, ~5 ≤ h/k < ~30. Field-verification of the ratio’s modified hydromechanics, fv = fh/yo, with yo(h/k) evaluated from bed roughness estimated by inspection or sieve analysis shows this ratio holding within ~|10|% error for shallow streamflow over a coarse bed of gravels and rocks, giving submergences of ~5 ≤ h/D84 ≤ ~30; yo = k/30 suits large streams with smooth beds (h/k ≥ ~30, fv ≥ ~0.86). Variable roughness-estimated fv-ratios appear to be more reliable than the fixed default, fv(h/yo ≈ 1000) = 0.86. This flow-gauging concept is based on observable physical characteristics of a monitoring cross-section and facilitates the rating of hard-to-access streams draining small basins in ragged upland terrain.

Kelp forests play a crucial role in marine ecosystems, providing habitat, food, and shelter for a variety of marine organisms. However, these ecosystems are facing significant threats, prompting the need for effective restoration strategies. One promising method is the use of "Green Gravel",where kelp spores are cultivated on small stones for subsequent deployment in the ocean. The success of this method strongly depends on the kelp attaching firmly to the ground before the kelp-stone systems get displaced to unsuitable locations by hydrodynamic forcing. Here we systematically quantified the hydrodynamic and bed conditions leading to initiation of motion of kelp-stone systems in the laboratory. For full control on kelp dimensions, surrogates were used. Critical shear stress negatively correlated with kelp size, and bed roughness had a stronger influence on the initiation of motion than stone dimensions or bed slope. We introduce the Shields parameter with a stability correction, highlighting its strong correlation with kelp frontal area and stone diameter, and providing a powerful unifying metric for predicting the onset of movement under diverse conditions. Additionally, subtle movement of the kelp-stone systems prior to displacement was observed, potentially preventing attachment even at hydrodynamic conditions below the thresholds for initiation of motion. Understanding the mechanistic processes leading to motion of kelp-stone systems helps to improve restoration methods and thus contributes to the broader objectives of marine habitat conservation.

Bed shear stress is a key parameter governing sediment transport and fluxes at the sediment–water interface. In vegetated channels, predicting bed shear stress, especially for rough beds, remains a challenge. This study developed a unified theoretical model for bed shear stress that smoothly spans conditions from bare bed to vegetated bed for both smooth and rough beds. Building on phenomenological turbulence theory, the model relates bed shear stress to the characteristic velocities of the larger energy-containing eddies and the smaller, near-bed eddies, with the new assumption that the bottom boundary layer (BBL) thickness controls the larger, energy-containing eddy length scale. The BBL was defined as the region within which the bed shear stress contributed significantly, compared to vegetation drag, and a force balance predicted that the BBL thickness scales with the ratio of bed shear stress to vegetation drag. In the limit of zero vegetation density, the BBL thickness equals the water depth, and the bed shear stress model reduces to the classical bare bed formulation. With increasing vegetation density (drag), the thickness of the boundary layer decreases, and the bed friction coefficient increases, which is consistent with previous observations. For rough beds, the bed friction coefficient increases with bed roughness, but is not dependent on the mean velocity. In contrast, for smooth beds, the bed friction coefficient decreases with increasing mean velocity. The coupled models for bed shear stress and BBL thickness were compared against 114 physical and numerical experiments from multiple previous studies.

Impact of bed roughness and submergence on velocity profiles and flow structures in hydraulic jumps.

Abstract Granular flows are central to geophysical and industrial processes, yet their internal properties remain difficult to quantify. Understanding how energy and momentum are exchanged at the flow–substrate boundary is key to predicting their erosion and mobility. Here, we assess the accuracy of particle image velocimetry (PIV) in resolving velocity and granular temperature () in analog granular flows using like‐for‐like comparisons with discrete element method simulations. Synthetic image sequences from simulations reveal that PIV systematically underestimates by ∼34% owing to Eulerian spatial averaging. Applying this correction factor enables accurate quantification of within stated uncertainties. This calibrated approach integrates laboratory, numerical, and field perspectives, offering new constraints on granular rheology and flow–bed coupling. Applying this calibrated workflow to analog flows over fixed and erodible beds reveals fundamental behavioral contrasts. Fixed rough beds exhibit basal spikes caused by intense shear and grain interlocking, whereas erodible substrates transmit momentum and into the substrate, producing velocity profiles that rise exponentially within the substrate. The flow–substrate interface is dynamic, oscillating and alternating erosion and deposition. These results identify as a key link between local and non‐local rheology: agitation within the flow can propagate, weaken the substrate, and control entrainment. Frame‐by‐frame velocity‐based boundary tracking reveals that standard erosion–deposition laws in depth‐averaged models fail to reproduce even simple experiments, highlighting the need for revision, especially for steep, mobile beds. Findings allow the observation and tracking of the fluctuating flow‐substrate interface observed in the deposits of many geophysical flows.

The three-dimensional heterogeneous flow over rough beds plays a significant role in fluvial geomorphology and river management. This article deals with the problem of understanding the turbulent flow properties over rough beds as encountered in open-channel flows. Literature suggests that the time-averaged turbulence characteristics are inadequate to characterize the three-dimensional heterogeneity within the roughness influenced flow zones over rough beds. The present study particularly focuses on the changes in double-averaged (DA) (time and space) turbulence characteristics governed by the double-averaged Navier–Stokes equations. In this review article, the characterization of turbulence parameters for different rough beds is presented. Moreover, several studies that have examined the mechanisms behind the changes in DA turbulence flow characteristics, focusing on both natural rough beds and artificial rough bed in laboratory flume experiments under controlled conditions, are compared. These investigations highlight how changes in DA turbulence parameters influence the roughness elements and assesses the usefulness of various turbulence properties for describing three-dimensional flow physics in different flow layers owing to the flow-roughness interaction. The review also points out limitations in current approaches, stressing the importance of standardizing methods to allow meaningful comparisons between studies. Furthermore, the study proposes recommendations for future inquiries and adds important perspectives to the overall understanding of three-dimensional flow physics. Finally, it outlines possible future research directions and aims to explore how turbulence parameters can be effectively characterized at the roughness boundary layer.

This experimental investigation examines the relative roller length (Lr/h1) of hydraulic jumps taking place in composite rectangular channel featuring positive inclinations and roughened minor beds, aiming to address gaps in understanding the effects of channel geometry, slope, and bed roughness. Experiments were conducted in a laboratory flume with a main channel width of 25 cm and a minor bed width of 14.4 cm. The experimental variables included channel slope (tan (α) = 0 to 0.015), bed roughness (ε = 0 to 12 mm), sill height (hs = 2.5 to 21 cm), and inlet flow depths (h1 = 2.5–4 cm), producing Froude number ranging from 1.5 to 9 and Reynolds number between approximately 24500 and 1025000. Results demonstrate that increasing bed roughness reduces the relative roller length by 21–29%, thereby enhancing turbulence and energy dissipation, while positive slopes stabilize hydraulic jumps by promoting smoother flow transitions. A novel dimensionless empirical model relating Lr/h1 to F1, tan (α), and relative roughness (ε/b) was developed and validated, exhibiting high accuracy (R² = 0.99) with predictions within ±5% of experimental values. This model provides a robust predictive tool for hydraulic structure design, enabling reductions in stilling basin dimensions by 23–28% while maintaining equivalent energy dissipation, yielding significant cost (17–22%) and space savings. These findings address critical gaps in understanding hydraulic jump dynamics in complex channel geometries and offer practical insights for designing energy dissipators, spillways, and flood control infrastructure to enhance flow stability, efficiency, and sustainable water management.

The effect of channel meander on flow resistance with different aspect ratio, bed roughness, and sinuosity: fixed-flatbed cases

Numerical study of particle rolling entrainment in wall turbulence on rough bed

Bed roughness effects on horseshoe vortex dynamics and soil erosion mechanisms in vegetated overland flows

This issue of Smart and Green Materials Journal brings together a diverse yet coherent collection of studies that collectively advance sustainable materials and structural hydraulic performance for resilient infrastructure systems. The contributions span material innovation, performance optimization, and experimental validation across concrete technology, pavement engineering, masonry materials, timber structures, and open-channel hydraulics. Several articles address the sustainability and performance of cement-based systems through improved curing strategies, internal curing using super-absorbent polymers, optimized sand grading, and the incorporation of natural fibers as eco-friendly reinforcements. Complementing these efforts, the mechanical characterization of indigenous timber species and the reuse of reclaimed asphalt pavement as recycled aggregates highlight the role of locally sourced and recycled materials in reducing environmental burdens while maintaining structural reliability. Extending beyond material behavior, this issue also includes an experimental investigation into hydraulic jumps over rough and sloped beds, emphasizing the importance of boundary conditions in energy dissipation and flow stability. Together, these studies demonstrate how sustainable material choices and performance-oriented design can be synergistically applied to develop infrastructure systems that are both environmentally responsible and resilient to increasing operational demands.

In cold-region rivers, the formation of ice cover during winter markedly modifies the hydraulic conditions, leading to enhanced local scour around in-stream infrastructures such as bridge piers. To analyze the flow characteristics and maximum local scour depth around the pier under both open-channel and ice-covered conditions with varying roughness, both experimental methods and numerical simulations were employed in this study. The findings reveal that, under rough ice-covered flow conditions, the interaction of elevated bed shear stress and intensified turbulent kinetic energy contributes to an increased maximum scour depth around the pier. Under identical approaching flow conditions, when the ratio of ice cover roughness to bed roughness increases to 1.9, the increase in maximum local scour depth around the pier becomes less pronounced owing to the enhanced energy dissipation caused by the rough ice cover. A numerical model for local scour around the pier under open-channel flow and ice-covered flow conditions was developed by integrating the RNG k − ε turbulence model with the Meyer-Peter sediment transport equation. A new formula was developed to estimate the maximum local scour depth around bridge piers considering various ice cover roughness conditions. Comparison with existing formulas demonstrates that the proposed formula achieves the highest accuracy, offering a useful reference for the design of bridge foundations in ice-affected regions.

Bed roughness effect on flow separation beneath partially submerged simulated ice cover in a shallow channel

Observations in the field suggest that the existing guidelines for bed protection design may lead to overly conservative protections at berthing structures of inland vessels. In this study, physical scale model tests have been performed using particle image velocimetry to assess the near-bed velocity and the velocity decay of jets generated by transverse bow thrusters. The effect of the bed roughness, under-keel clearance (UKC) and quay wall clearance on the resulting near-bed velocities are discussed here. The results show that the maximum near-bed velocity occurs in the vicinity of the quay wall and results from an interplay between jet diffusion and the blockage effect of the nearby boundaries (e.g., quay wall, bed, and vessel), where the roughness of the confining boundary plays a role. The existing design guidelines predict fairly well the maximum near-bed velocity for smooth beds and for relatively large UKC’s. However, the guidelines tend to overestimate the maximum near-bed velocities for rough beds and for small UKC’s. This study proposes a new method based on measurement data to estimate the maximum near-bed velocity for confined bow thruster jets.