Unit Width Research Articles

Energy Efficiency Analysis of a Deformable Wave Energy Converter Using Fully Coupled Dynamic Simulations

Deformable wave energy converters have significant potential for application as flexible material that can mitigate structural issues, while how to design the dimensions and choose an optimal deployment location remain unclear. In this paper, fully coupled computational fluid dynamics and computational solid mechanics were used to simulate the dynamic interactions between ocean waves and a deformable wave energy converter. The simulation results showed that the relative length to wave, deployment depth and aspect ratio of the device have significant effects on the energy conversion efficiency. By calculating the energy captured per unit width of the device, the energy efficiency was found to be up to 138%. The optimal energy conversion efficiencies were achieved when the structure length was 0.25, 0.5 or 0.75 of the dominating wavelength and submerged at a corresponding suitable depth. The aspect ratio and maximum stress inside the wave energy converter showed a nonlinear trend, with potential optimal points revealed. The simulation approach and results support the future design and optimisation of flexiable wave energy converters or other marine structures with notable deformations.

Dynamics of axially moving viscoelastic panels immersed in fluid

The vibration of axially moving panels immersed in fluid are widely concerned in engineering problems. In this paper, free vibration characteristics and dynamic stabilities of an axially moving viscoelastic panel immersed in fluid are investigated. The governing equation is given by applying the generalized extended Hamilton principle. The axial tension per unit width is related to the axial speed and the axial acceleration, changing continuously in the axial direction, which is the innovation point and key problem of this paper. However, they were independent of each other in most previous studies. The fluid is assumed to be an ideal liquid, that is, inviscid, homogeneous and incompressible. By using the velocity potential function, the Bernoulli equation, the dynamic pressure and the boundary conditions of the fluid are derived and incorporated into the governing equation in the form of an additional mass. The Galerkin method is used to discretize the governing equation and convert it into a matrix form. The influences of the truncation order numbers and the immersion depths on the first four natural frequencies are analyzed. We found an interesting phenomenon that the fluid has an effect on both the inertia term and the damping term of the system and the effect of damping force generated by fluid is greater than that of inertia. Another innovation is that the immersion depth has little effect on the natural frequency. Moreover, the subharmonic resonance and the combination resonance are analyzed by using the averaging method. The influences of system parameters including truncation order numbers, axially supported stiffness parameters, viscoelasticity coefficients, mean axial speeds, fluids and immersion depth on the stability boundaries are considered. The stability boundaries of three models, namely the vacuum model, the material derivative model, and the partial derivative model, are compared. The results show that the material derivative model is more reasonable. The results are verified by the Runge-Kutta algorithm. The results of the analytical and numerical methods of the subharmonic and combination resonances are in good agreement with each other. In this paper, the dynamic stability of an axially moving viscoelastic panel immersed in fluid is studied by means of the average method. It extends the application range of the averaging method and provides a reference for the study of axially moving structures immersed in fluid.

A Strange Result Regarding Some MHD Motions of Generalized Burgers’ Fluids with a Differential Expression of Shear Stress on the Boundary

In this work, we investigate isothermal MHD motions of a large class of rate type fluids through a porous medium between two infinite horizontal parallel plates when a differential expression of the non-trivial shear stress is prescribed on the boundary. Exact expressions are provided for the dimensionless steady state velocities, shear stresses and Darcy’s resistances. Obtained solutions can be used to find the necessary time to touch the steady state or to bring to light certain characteristics of the fluid motion. Graphical representations showed the fluid moves slower in presence of a magnetic field or porous medium. In addition, contrary to our expectations, the volume flux across a plane orthogonal to the velocity vector per unit width of this plane is zero. Finally, based on a simple remark regarding the governing equations of velocity and shear stress for MHD motions of incompressible generalized Burgers’ fluids between infinite parallel plates, provided were the first exact solutions for MHD motions of these fluids when the two plates apply oscillatory or constant shear stresses to the fluid. This important remark offers the possibility to solve any isothermal MHD motion of these fluids between infinite parallel plates or over an infinite plate when the non-trivial shear stress is prescribed on the boundary. As an application, steady state solutions for MHD motions of same fluids have been developed when a differential expression of the fluid velocity is prescribed on the boundary.

A Framework for Quantifying Reach-Scale Hydraulic Roughness in Mountain Headwater Streams

The presence of macroroughness elements directly affects the flow velocity in mountain headwater streams. Hydraulic roughness is the dominant resistance to flow caused by objects protruding into the water, but it is not measurable in the field. This study quantified the reach-average hydraulic roughness based on the channel morphology in two mountain streams. The average flow velocities of the reaches were measured using the dye-tracing method. The magnitude of the hydraulic roughness was derived from the grain size of the streambed materials (D50 and D84) and the cross-sectional/longitudinal bed roughness. The observations for low flows (0.04–0.43 m2/s discharge per unit width) indicated that the longitudinal 90% inter-percentile range (IPR90L) seemed to have considerable merit in examining the influences of large roughness elements on flow conveyance. A dimensionless hydraulic geometry relation that can reflect the field measurements over a limited range of hydraulic characteristics was also developed for estimating the reach-average flow velocity in steep and rough streams. Thus, the research framework used appears to provide a reliable method of quantifying reach-average hydraulic roughness from local data in mountain headwater streams.

Impact of Levee-Breach Width on the Channel–Levee–Floodplain: A Case Study in the Huaihe River Basin, China

Breach geometry is one essential feature for flood modelling in the channel–levee–floodplain system. It is hard to accurately predict the breach geometry because of its high uncertainty. However, due to the fact that breach geometry direct impacts the flow through the breach, the water surface profile in the channel and the flood hazard factors within the floodplain are changed with the breach geometry. To explore the impacts of breach width (one feature of the breach geometry) on the channel–levee–floodplain system, we took the Cinan Feiyou Flood Control Protection Area (CNFY-FCPA) in the middle reach of the Huaihe River Basin as the study area. We constructed a coupled 1D-2D hydrodynamic model to simulate the flooding with a series of breach-width scenarios. According to the simulation results of the models, we quantitatively analyzed the impacts of breach width on the inflow through the breach, fluvial flood process, and flood hazard factors in the CNFY-FCPA. The results indicate that (i) the relationship between the peak discharge (and inflow volume) and breach width was approximate to an S-shaped curve, while the peak discharge, inflow volume, and duration per unit width decreased with the wider breach; (ii) the breach caused a decrease in the water surface profile along the entire river sections; and (iii) while the breach width exceeded a certain width, the inundation area was nearly stable without changing with wider breach. The certain width was not the same in different rivers of 300 m in the Yinghe River and of 500 m in the Huaihe River. The research results can provide a scientific basis for flood-control and disaster-reduction decision making.

Cascaded Thinning in Upscale and Downscale Representation for EEG Signal Processing.

Smoothing filters are widely used in EEG signal processing for noise removal while preserving signals' features. Inspired by our recent work on Upscale and Downscale Representation (UDR), this paper proposes a cascade arrangement of some effective image-processing techniques for signal filtering in the image domain. The UDR concept is to visualize EEG signals at an appropriate line width and convert it to a binary image. The smoothing process is then conducted by skeletonizing the signal object to a unit width and projecting it back to the time domain. Two successive UDRs could result in a better-smoothing performance, but their binary image conversion should be restricted. The process is computationally ineffective, especially at higher line width values. Cascaded Thinning UDR (CTUDR) is proposed, exploiting morphological operations to perform a two-stage upscale and downscale within one binary image representation. CTUDR is verified on a signal smoothing and classification task and compared with conventional techniques, such as the Moving Average, the Binomial, the Median, and the Savitzky Golay filters. Simulated EEG data with added white Gaussian noise is employed in the former, while cognitive conflict data obtained from a 3D object selection task is utilized in the latter. CTUDR outperforms its counterparts, scoring the best fitting error and correlation coefficient in signal smoothing while achieving the highest gain in Accuracy (0.7640%) and F-measure (0.7607%) when used as a smoothing filter for training data of EEGNet.

Multi-Objective Finned-Tube Heat Exchanger Optimization Using a Genetic Algorithm

Heat exchangers are a significant component in many industries, particularly in energy conversion systems. The design of heat exchangers itself is a complex process because it involves experience-based decisions, numerous variables and parameters, and some of them are competing with each other. Genetic Algorithms (GAs) are one of the first evolutionary algorithms which remains one of the most extensively used non-linear optimization methods today. This study explores the implementation of Non-Dominated Sorting Genetic Algorithm II (NSGA-II) for thermal design and optimization of a finned-tube heat exchanger. The chosen objective functions were minimizing the heat exchanger volume and minimizing the air side pressure drop. The decision variables for the design were tube outer diameter, number of tube rows, fin pitch, unit height, and unit width. The calculated parameters and estimated cost of both preliminary design and optimized design were also compared. The optimized design offered a bigger alternative design while meeting all the constraints according to standards and industrial needs. The optimization reduced annualized operational and maintenance costs by 228% and lowered air pressure drop by 413% with bigger heat exchanger volume of 12% compared to the preliminary design.

Geomorphic adjustments of channel bars in the braided reach of the lower Yellow river from 1986 to 2018

Channel bars are an important aspect of braided river morphology, and have a significant effect on flood control, waterway navigation and the aquatic ecological environment. In this study, the number, area and shape index of channel bars in the braided reach of the Lower Yellow River (LYR) were determined based on remote sensing images from 1986 to 2018, and the evolution characteristics of channel bars were investigated temporally and spatially. The effects of flow regime, sediment supply and bank erosion were also investigated as part of geomorphic adjustments of channel bars in the braided reach. The findings of this study indicate that the number and area ratio of channel bars were lower in the pre-dam period when water levels were higher and higher in the post-dam period when water levels were lower. More variance in the peak discharge may lead to more variance in channel bars indices in the braided reach. The number of channel bars per unit width is closely related to the specific stream power in the braided reach, and a larger specific stream power leads to more channel bars. The total area of channel bars increased with an increase in the reach-scale bankfull width, which indicates that bank erosion was closely associated with the adjustments of channel bars in the braided reach of the LYR.

The trend of groundwater recharge in the secondary perched reaches of the Yellow River in the past 50 years

Precipitation infiltrates into the soil or river and then percolates downward through the deeper mineral soil to the groundwater. Understanding the interactions between surface water and groundwater in the river ecosystem is crucial for supporting decision-making in eco-construction and the efficient use of water resources. In our study, the secondary perched reach of the lower Yellow River was taken as the research area. The trend analysis and correlation relationship were evaluated using the M–K significance test and gray correlation; furthermore, the groundwater recharge was quantified by Darcy‘s law and the water balance method based on 50 years of hydrological data. The results showed that 1) from 1972 to 2020, the runoff and water level of the Huayuankou hydrological station and the Jiahetan hydrological station showed a significant downward trend. 2) The calculation of the gray correlation degree method shows that the groundwater level is mainly affected by the Yellow River. The river water and groundwater levels show a significant downward trend using the M–K significance test. 3) The unit width recharge values of the secondary perched river to the groundwater in the dry year were calculated to be 566.79 and 374.13 m3/m·d, using Darcy‘s law and the water balance method, respectively, indicating that the results of the two methods are basically the same. Our findings highlight the storage capacity of groundwater and can provide support for regulation and sustainable management of water resources in the ecosystem.

Comparison of ADCP and ECCOv4r4 Currents in the Pacific Equatorial Undercurrent

Abstract The Pacific Equatorial Undercurrent (EUC) flows eastward across the Pacific at the equator in the thermocline. Its variability is related to El Niño. Moored acoustic Doppler current profiler (ADCP) measurements recorded at four widely separated sites along the equator in the EUC were compared to currents generated by version 4 release 4 of the Estimating the Circulation and Climate of the Ocean (ECCOv4r4) global model–data synthesis product. We are interested to learn how well ECCOv4r4 currents could complement sparse in situ current measurements. ADCP measurements were not assimilated in ECCOv4r4. Comparisons occurred at 5-m depth intervals at 165°E, 170°W, 140°W, and 110°W over time intervals of 10–14 years from 1995 to 2010. Hourly values of ECCOv4r4 and ADCP EUC core speeds were strongly correlated, similar for the EUC transport per unit width (TPUW). Correlations were substantially weaker at 110°W. Although we expected means and standard deviations of ECCOv4r4 currents to be smaller than ADCP values because of ECCOv4r4’s grid representation error, the large differences were unforeseen. The appearance of ECCOv4r4 diurnal-period current oscillations was surprising. As the EUC moved eastward from 170° to 140°W, the ECCOv4r4 TPUW exhibited a much smaller increase compared to the ADCP TPUW. A consequence of smaller ECCOv4r4 EUC core speeds was significantly fewer instances of gradient Richardson number (Ri) less than 1/4 above and below the depth of the core speed compared to Ri computed with ADCP observations. We present linear regression analyses to use monthly-mean ECCOv4r4 EUC core speeds and TPUWs as proxies for ADCP measurements. Significance Statement Hundreds of scientific papers have used ECCO data products generated with a continually evolving state-of-the-art ocean-model–data synthesis system. We ask, How representative is the latest version of ECCO equatorial ocean currents? We use independent in situ current measurements as the reference dataset to establish the accuracy of ECCO currents in the tropical Pacific. Attention is focused on the Pacific Equatorial Undercurrent (EUC) because it contributes to the formation of El Niño and La Niña events. ECCO EUC core speeds were smaller in magnitude and less variable in time compared to observations. As a consequence, ECCO currents generated smaller vertical mixing in the EUC compared to that inferred from current measurements. We developed a linear regression model to improve representation of monthly-mean ECCO currents.

Cosmogenic Nuclide Tracking of Sediment Recycling From a Frontal Siwalik Range in the Northwestern Himalaya

AbstractThe Himalayan orogen exports millions of tons of sediment annually to the Indo‐Gangetic foreland basin, derived from both hinterland and foreland fold‐thrust belts (FTB). Although erosion rates in the hinterland are well‐constrained, erosion rates in the foreland FTB and, by extension, the sediment flux have remained poorly constrained. Here, we quantified erosion rates and sediment flux from the Mohand Range in the northwestern Himalaya by modeling and measuring the cosmogenic radionuclide (CRN) 10Be and 26Al concentrations in modern fluvial sediments. Our model uses local geological and geophysical constraints and accounts for CRN inheritance and sediment recycling, which enables us to determine the relative contributions of the hinterland and foreland FTB sources to the CRN budget of the proximal foreland deposits. Our model predictions closely match measured concentrations for a crustal shortening rate across the Mohand Range of 8.0 ± 0.5 mm yr−1 (i.e., approximately 50% of the total shortening across the Himalaya at this longitude) since Ma. This shortening implies a spatial gradient in erosion rates ranging from 0.42 ± 0.03 to 4.92 ± 0.34 mm yr−1, controlled by the geometry of the underlying structure. This erosion pattern corresponds to an annual sediment recycling of ∼2.0 megatons from the Mohand Range to the downstream Yamuna foreland. Converted to sediment fluxes per unit width along the Himalaya, the foreland FTB accounts for ∼21% ± 5% of the total flux entering the foreland. Because these sediments have lower 10Be concentrations than hinterland‐derived sediment, they would lead to ∼14% overestimation of 10Be‐derived erosion rates, based on Yamuna sediments in the proximal foreland.

A Hybrid Data-Driven Metaheuristic Framework to Optimize Strain of Lattice Structures Proceeded by Additive Manufacturing.

This research is centered on optimizing the mechanical properties of additively manufactured (AM) lattice structures via strain optimization by controlling different design and process parameters such as stress, unit cell size, total height, width, and relative density. In this regard, numerous topologies, including sea urchin (open cell) structure, honeycomb, and Kelvin structures simple, round, and crossbar (2 × 2), were considered that were fabricated using different materials such as plastics (PLA, PA12), metal (316L stainless steel), and polymer (thiol-ene) via numerous AM technologies, including stereolithography (SLA), multijet fusion (MJF), fused deposition modeling (FDM), direct metal laser sintering (DMLS), and selective laser melting (SLM). The developed deep-learning-driven genetic metaheuristic algorithm was able to achieve a particular strain value for a considered topology of the lattice structure by controlling the considered input parameters. For instance, in order to achieve a strain value of 2.8 × 10-6 mm/mm for the sea urchin structure, the developed model suggests the optimal stress (11.9 MPa), unit cell size (11.4 mm), total height (42.5 mm), breadth (8.7 mm), width (17.29 mm), and relative density (6.67%). Similarly, these parameters were controlled to optimize the strain for other investigated lattice structures. This framework can be helpful in designing various AM lattice structures of desired mechanical qualities.

Performance of OWC device under Stokes second-order waves

The present work simulates the flow behavior in the system having oscillating water column (OWC) device for wave energy conversion using numerical modelling. To achieve this, the OWC device is structured inside the 2-dimensional numerical wave tank (NWT). Using the ANSYS Fluent software and the multiphase-based CFD technique, the issue is resolved. Unsteady, transient, and pressure-based solvers are included in this work. In this numerical model, the governing equations are based on Reynolds Averaged Navier-Stokes (RANS) equations with the Shear Stress Transport (SST) model, to capture the turbulence effect and the interface of 2-phases are implicitly captured by using volume of fluid (VOF) method. Using an open-channel wave generator, this study generates nonlinear “second-order Stokes waves”. In addition, the impact of nonlinearity on the “free surface description” at specific locations, the vertex average of total pressure near the air-duct, and the vertex average of y-velocity through the air-duct per unit width of the OWC device are investigated in detail. The outcomes indicate that the OWC device will consistently extract energy over an extended period of time.

Analysis of mandibular asymmetry in adolescent and adult patients with unilateral posterior crossbite on cone-beam computed tomography

This study aimed to evaluate mandibular asymmetry in unilateral posterior crossbite (UPXB) patients and compare the asymmetry between adolescents and adults with UPXB. This study included and analyzed cone-beam computed tomography scans of 125 subjects. The subjects were divided into a UPXB group and a control group according to the presence or absence of UPXB, and each group included adolescent patients (aged 10-15 years) and adult patients (aged 20-40 years). Linear, angular, and volumetric measurements were obtained to evaluate the asymmetries of the mandibles. Both adolescent and adult patients in the UPXB group presented asymmetries in condylar unit length, ramal height, body length, and mediolateral ramal inclination (P<0.05). Adult patients with UPXB showed greater asymmetries than adolescents. Differences with condylar unit length, condylar unit width, ramal height, condylar unit volume, and hemimandibular volume were significantly greater in adult UPXB patients than adolescent UPXB patients (P<0.05). The worsening of mandibular asymmetries in UPXB adults suggests that asymmetry in UPXB patients may progress over time; therefore, early treatment should be considered for UPXB adolescent patients. Further studies are still needed to evaluate the effectiveness of early treatment.

Antisymmetric Lamb Wave Simulation Study Based on Electromagnetic Acoustic Transducer with Periodic Permanent Magnets.

Due to its multi-mode and dispersion characteristics, Lamb waves cause interference to signal processing, which profoundly limits their application in nondestructive testing. To resolve this issue, firstly, based on the traditional EMAT, a horizontal polarization periodic permanent magnet electromagnetic acoustic transducer (HP-PPM-EMAT) was proposed. A 2-D finite element model was then developed to compare magnetic flux density, Lorentz force, and signal strength between the traditional EMAT and the HP-PPM-EMAT. The simulation results show that the HP-PPM-EMAT enhances the A0 mode Lamb wave (A0 wave) and suppresses the S0 mode Lamb wave (S0 wave). Finally, the influence of structural parameters of the HP-PPM-EMAT on the total displacement amplitude ratio of A0 and S0 was investigated using orthogonal test theory, and the width of magnet units was improved based on the orthogonal test. The results show that the total displacement amplitude ratio of A0 to S0 of the improved HP-PPM-EMAT can be improved by a factor of 7.74 compared with that of the traditional Lamb wave EMAT, which can produce higher-purity A0 mode Lamb waves.

Assessing the water conservation potential of optimized surface irrigation management in Northern Italy

The effects of climate change on water availability affect the performance of surface irrigation, which is the oldest and most common method of water application to row crops worldwide. A paradigm shift towards strategies aimed at increasing flexibility of irrigation scheduling and improving the design and management of field layouts and irrigation practices should be explored to promote water conservation at the farm scale. In this study, we investigate how by adopting a more flexible irrigation scheduling and optimizing irrigation management variables and field layout it is possible to increase the efficiency of border irrigation and thus achieve water conservations and improve quality of crop production. The analysis of the actual performance of border irrigation was carried out on two maize fields located in the Padana Plain (Northern Italy) in 2 years characterized by different rainfall patterns (i.e. 2021 and 2022). Based on this information, continuous monitoring of soil moisture status combined with the AquaCrop-OS agro-hydrological model was used to manage flexible irrigation scheduling over the experimental fields, while the optimization of irrigation management (flowrate per unit width and cutoff time) and field geometries (border width and slope) was studied using WinSRFR 5.1 USDA software, which was properly calibrated by measures of waterfront advance and recession. The results show that with flexible irrigation scheduling and proper irrigation management and field layout, significant water conservation can be achieved. Specifically, in the case study, seasonal water conservation of about 10% was obtained just by scheduling irrigation based on actual crop water needs in a very dry agricultural season, while water conservation reached up to 60% in a wetter season. On average, an additional 7% of water conservation was achieved over the agricultural season when the irrigation duration was correctly applied to each border of the experimental plots, while approximately 20% of water was conserved when the border width was correctly designed based on inflow availability. These results provide useful information for improving the management of border irrigation in practice, both under current conditions and in prospective of increasing freshwater scarcity in the future.

Determination of fracture toughness and yield strength of Inconel 718 by milling operation

This paper presents an analytical scheme to determine the fracture toughness and the yield strength of Inconel 718 by the widely used milling operation. It is noted that there exists material fracture at the tool tip and the removed layer of material undergoes plastic deformation along the primary shear plane. The fracture toughness is considered at the tool tip and the yield strength is applied on the primary shear plane. Subsequently, the modified Williams’ model and the modified Williams-minimization model are both proposed on the basis of the geometries and mechanics in the oblique cutting process. The modelling framework indicates that milling can be developed as an alternative method to determine the fracture toughness and the yield strength from the serrated chip thicknesses combined with the corresponding cutting forces. This is because the experimental method by milling is a convenient scheme as it only requires the cutting forces per unit width of cut with respect to a series of uncut chip thicknesses. In addition, the normal shear angle is predicted by applying the principle of energy minimization. Finally, milling experiments are conducted to validate the two proposed methods. Results show that the two analytical methods return similar values of fracture toughness and yield strength, respectively. Besides, it is noted that high values of yield strength are achieved based on Tresca criterion, which would indicate work hardening in the primary shear zone during the serrated chip formation. The proposed methods exhibit advantages of convenience and generality to derive the fracture toughness and the yield strength, since it is still a challenge for the traditional standard mechanical tests for Inconel 718 due to its toughness and ductility.

Resistance to sheet flow induced by raindrop impact on rough surfaces

Raindrops impact can affect the flow resistance to sheet flow by interfering with flow velocity profile. However, quantitative information regarding the flow resistance induced by raindrops impact to sheet flow (Δf) under the influence of different surface roughnesses is limited. In this study, multiple experimental simulations of rainfall and inflow were conducted on flumes with five unit width inflow discharges ranging from 0.02-0.1 m2 min−1, five rainfall intensities ranging from 40 to 120 mm h−1, and three levels of surface roughnesses ranging from 0.009 to 0.25 mm to identify flow resistance due to raindrop impact under different surfaces. Results showed that surface roughness was able to increase the total flow resistance without raindrop impact (fo) and with raindrop impact (fr), respectively. Under rainfall conditions, raindrop impact was able to increase fr on different surfaces. The surface roughness played a stronger role on contributing the fr than the raindrop impact. The major control of fr was the Reynolds number (Re), and fr decreased with the increasing Re. Δf were positively affected by surface roughness and rainfall intensity. Rough surface can increase the effects of raindrop impact on water flow by reducing the flow velocity of base flow or inflow, which leads to the increase in Δf. The major control of Δf was the Re, and Δf decreased with Re. Flow resistance induced by raindrop impact was larger for shallower and slower moving sheet flow with the low Re. In addition, a new equation has been developed to predict Δf under the conditions of Fr < 2.16 by using rainfall intensity, surface roughness, velocity, and water depth. This study helps to estimate the flow resistance induced by raindrops impact to sheet flow under surface roughness and provide the scientific insights for improving hydrologic and soil erosion models.

A new method for designing cube armours for low-crested and submerged breakwaters

Recently, coastal structures designers have paid more attention to low-crested/submerged breakwaters due to their significant inherent advantages. Although many formulae can be found in the literature for the design of breakwater armour layer, the majority of them are proposed for high-crested breakwaters. Currently, there is no comprehensive formula for the design of the cube armour layer for low-crested/submerged breakwaters. Among the important parameters affecting the armour layer stability of low-crested/submerged breakwaters, the most effective ones are crest width, packing density and placement pattern of the armour units. These parameters, however, are not directly included in the existing design formulae. In this article a comprehensive and complete formula for design of the armour layer for low-crested/submerged breakwaters based on the results of a large number of experimental investigations is presented. The proposed formula contains the most important parameters such as the crest width, armour units packing density and placement pattern, slope, freeboard, as well as the wave characteristics. The comparison between the armour layer's hydraulic stability number obtained from this formula and the corresponding values recorded at the laboratory reveals its favorable accuracy indicating the applicability of the proposed formula for safe design of the cubic armour layer for low-crested/submerged breakwaters.

Effect of Combined Subsurface Structures and Steps on Hyporheic Exchange

AbstractThe deployment of artificial structures in streambeds has been proposed as a way to enhance 21 hyporheic exchange, and numerical models can be used to quantify their effects. In this study, combinations of different structures—that is, boxes, steps and a new type of subsurface structure (L‐shaped structure)—were considered to evaluate their potential applicability on river restoration. Flow‐3D and COMSOL were applied to simulate surface and subsurface flow, respectively. The performance of the structures was evaluated on the basis of hyporheic flow and residence time distributions. For the structure sizes here considered, results showed for steps (single step, combination of two steps) and L‐shaped structures (single L‐shaped structure, combination of two L‐shaped structures) most hyporheic flowpaths return to the stream after 5 and 2.5 hr, respectively. Instead, shorter residence times (&lt;0.25 hr) were found for boxes (single box, combination of two boxes). For combinations of steps and permeable boxes, the values of hyporheic flow per unit width are higher (0.35 and 0.3 m2/hr, respectively) than for the combination of L‐shaped (0.06 m2/hr). As a result, the combinations of steps and boxes are more effective in increasing hyporheic flow. However, when subsurface structures are combined with steps the resulting hyporheic exchange is dominated by the steps. Therefore, the combined use of in‐stream and subsurface structures separately may increase their benefits for hyporheic exchange, but when steps are the other subsurface structures provide minor advantages.