Bulk Drag Research Articles

Physical modelling study on wave damping induced by an idealized floating kelp farm

A physical modelling study was carried out to investigate random wave damping promoted by an idealized floating kelp farm. The experimental conditions spanned intermediate water depths and both linear and nonlinear water waves. Unlike previous studies of wave damping promoted by vegetation, the floating kelp farm was placed close to the water surface with a ratio between vegetation height and water depth close to 0.25. The wave transmission coefficient induced by the floating kelp farm ranged between 0.56 and 0.96. This coefficient decreased for longer floating kelp farms and it was a function of the ratio between kelp farm length and incident wavelength and of the relative wave depth. Spectral analysis showed that wave damping was not frequency-dependent for wave frequencies close to the peak frequency. The wave transmission coefficients of a floating kelp farm with about 100 culture lines and with an extension of approximately 200 m were similar to those of submerged detached breakwaters with a relative crest freeboard smaller than -0.4. Furthermore, the bulk drag coefficient of near-surface idealized floating kelp farms can be modelled as a function of the Keulegan-Carpenter number. This study highlights the potential viability of nature-based solutions such as floating kelp farms for coastal protection.

Numerical modeling of bamboo fences with various infill porosities deployed for mangrove restoration

As part of mangrove restoration initiatives eco-friendly fence has been implemented in eroded coastal areas in recent years. These fences provide the capacity to mitigate incoming wave energy and facilitate sediment deposition, thereby promoting the establishment and maintenance of mangrove habitats. Nevertheless, it is crucial to investigate the influence of the infill porosity on the wave dissipation performance of these fences, as the infill porosity can vary considerably across different restoration projects. The aim of this research is to explore the relationship between the infill porosity and wave dissipation effectiveness to identify more efficient designs for these eco-friendly restoration measures. The experiments involving wave interactions with fence models were conducted in a wave flume measuring 0.8 m in width and 25 m in length. Four wooden fences with distinct infill porosities ranging from 0.60 to 0.90 were strategically positioned to assess wave transmission, reflection, and dissipation phenomena under 18 distinct wave conditions. Additionally, the simulating waves till shore (SWASH)model was employed to calibrate critical bulk drag coefficient parameters and simulate the flow velocity distribution surrounding the fences under the experimental wave conditions. The findings indicated that a fence with a reduced infill porosity exhibits a higher wave transmission coefficient. However, this is accompanied by a higher reflection coefficient and lower wave energy dissipation within the fence. Both the infill porosity and incident wave conditions influence the flow velocity distribution characteristics in the vicinity of the fences. The area where the interaction between waves and fences is the most prominent is concentrated in the upper water layer immediately adjacent to the frontal section of the fences. Understanding the velocity distribution and hydrodynamic characteristics of the fence area aids in better determining the suitable porosity of fill materials for engineering applications.

A multi-faceted methodology for calibration of coastal vegetation drag coefficient

The accurate prediction of wave height attenuation due to vegetation is crucial for designing effective and efficient natural and nature-based solutions for flood mitigation, shoreline protection, and coastal ecosystem preservation. Central to these predictions is the estimation of the vegetation drag coefficient (Cd). The present study undertakes a comprehensive evaluation of three distinct methodologies for estimating the drag coefficient: traditional manual calibration, calibration using a novel application of state-of-the-art metaheuristic optimization algorithms, and the integration of an empirical bulk drag coefficient formula (Tanino and Nepf, 2008) into the XBeach non-hydrostatic wave model. These methodologies were tested using a series of existing laboratory experiments involving nearshore vegetation on a sloping beach. A key innovation of the study is the first application of metaheuristic optimization algorithms for calibrating the drag coefficient, which enables efficient automated searches to identify optimal values aligning with measurements. We found that the optimization algorithms rapidly converge to precise drag coefficients, enhancing accuracy and overcoming limitations in manual calibration which can be laborious and inconsistent. While the integrated empirical formula also demonstrates reasonable performance, the optimization approach exemplifies the potential of computational techniques to transform traditional practices of model calibration. Comparing these strategies provides a framework to determine effective methodology based on constraints in determining the vegetation drag coefficient.

Integrated drag coefficient formula for estimating the wave attenuation capacity of Rhizophora sp. mangrove forests

Recently, bulk drag coefficient (C˜D) formulations used to quantify wave energy dissipation by Rhizophora mangroves were developed from laboratory data; however, these formulations have not yet been validated with field data. Additionally, due to the complex geometry of mangrove trees within forests and spatial variability, common criteria for determining the adequate geometric characteristics of mangrove forests are lacking and are required to obtain accurate definitions for C˜D. This paper addresses these knowledge gaps by proposing a newly integrated C˜D formulation based on the comprehensive characterization of a Rhizophora mangle forest combined with wave measurements in field, and by using numerical modeling for the calibration process. The field campaign consisted of 23 continuous days of recorded wave data and spatial distribution observations of the geometric characteristics of the mangrove forest. The variation in frontal area per unit height per square meter (Ahm) along the mangrove forest was reported for three zones with different densities identified along the study transect, with decreasing root density from the vegetation edge to the forest interior. On average, the incident wave height decreased by 34% at 63 m in mangrove forests, and the wave attenuation ratios (r) varied between 0.001 and 0.01 m-1. To estimate the C˜D values associated with these wave height attenuation ratios, the Simulating Waves Nearshore (SWAN) numerical model was used to calibrate the model results with the field observations. The variation in the tree frontal area along the mangrove forest and the wave conditions at the site are considered during the calibration process. To further characterize C˜D for this type of mangrove species, the C˜D values acquired from the calibration together with the values reported in the literature from laboratory experiments are presented as a function of the Keulegan-Carpenter number (KC). Root diameter is defined as the characteristic length according to the inherent geometric characteristics of a Rhizophora sp. forest. The new formulation allows us to predictably estimate C˜D values that can be used as inputs in drag force-based models to estimate the attenuation of wave energy produced by Rhizophora sp. forests.

Urban-canopy airflow dynamics: A numerical investigation of drag forces and distribution for generic neighborhoods, and their relationships with breathability

Thorough investigations of urban-canopy drag primarily stemming from pressure drag on building surfaces are necessary given the turbulent flows within complex urban areas. Moreover, a gap persists regarding the relationships between canopy drag and breathability. Therefore, this work delves into the canopy-layer airflow dynamics for generic urban neighborhoods by performing three-dimensional Reynolds-Averaged Navier-Stokes simulations. A total of 32 subcases are examined, encompassing uniform- and varying-height and diverse plan area densities (λp, categorized into groups of sparse: 0.0625/0.067, medium: 0.23/0.25, and dense: 0.53/0.56). Results for the drag distribution highlight the windward-row shelter effect for the medium and the dense, local shelter by taller buildings, and distinct shapes of sectional drag forces (F⁎Z). Local velocity and mean age of air are found strongly positively and negatively correlated to F⁎Z, respectively, with distinct slopes in relation to λp. For the uniform-height, the normalized bulk drag (F⁎bulk, referred to as drag coefficient in literature) peaks for the medium with wake-interference regime; F⁎bulk demonstrates a maximum increase of over two times with height variation; moreover, F⁎bulk for varying-height groups exhibits a marked increase from the sparse to the medium, while remaining comparable values for the dense. The frontal area averaged drag (FAf,ave) exhibits a decreasing trend against λp across all cases. Further, FAf,ave exhibits strong correlations with λp and porosity, and with bulk ventilation indices such as spatially averaged velocity, air change rate, and normalized net escape velocity. Throughout the ‘suburban-urban-suburban’ canopy, medium neighborhoods exerting larger drag cause greater streamwise outdoor pressure drops and flow reductions compared to the sparse. However, dense neighborhoods with lower drag exhibit even larger pressure losses, which should be carefully scrutinized. The findings can inform urban planners in designing more aerodynamically efficient neighborhoods and guide strategies for improving air quality within urban environments.

Computational analysis of magnetized Casson liquid stretching flow adjacent to a porous medium with Joule heating, stratification, multiple slip and chemical reaction aspects

This article aims to investigate the characteristics of thermo-solutal magnetohydrodynamic (MHD) non-Newtonian smart coating boundary layer flow of a stretching substrate adjacent to a porous medium, considering the influence of chemical reactions and thermal radiation subject to a transverse static magnetic field. A non-Darcy drag force model is deployed to capture both Darcy bulk drag and inertial Forchheimer (quadratic) drag effects. A diffusion flux model is deployed for radiative heat transfer. The Casson viscoplastic model has been utilized to simulate rheological characteristics. Due to polymeric slip effects, three slip phenomena are included at the wall (hydrodynamic, thermal and concentration) in the formulation. Furthermore, viscous dissipation and Ohmic heating (Joule dissipation) are also included. Robust scaling similarity variables are deployed to transform the governing partial differential equations into ordinary differential equations. Subsequently, the emerging dimensionless coupled nonlinear boundary value problem is solved utilizing the Bvp4c method in MATLAB version 2022. This numerical approach allows for a logical parametric examination of all key control parameters on the transport phenomena, enabling a comprehensive understanding of the system behavior. Validation with previous studies is included. Detailed graphical and tabular computations are included for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number, for the influence of Darcian parameter, Forchheimer inertial parameter, mixed convection, velocity (momentum) slip, magnetic number, Casson parameter, nonlinear thermal convection parameter, nonlinear concentration convection parameter, radiation parameter, thermal stratification parameter, Prandtl number, heat source/sink parameter, Eckert number, thermal slip parameter, Schmidt number, chemical reaction, solutal stratification parameter and solutal slip parameter. Detailed interpretation of the physics associated with these multiple effects is included. The simulations provide further insight into the transport characteristics of electromagnetic viscoplastic coating material manufacturing.

Derivation and stability analysis of two-fluid model equations for bubbly flow with bubble oscillations and thermal damping

The two-fluid model with bubble oscillations, proposed by Egashira et al. (2004), can explain the properties of cavitating bubbly flow and pressure wave propagation in the bubbly liquid. However, the viscous effect as well as energy conservation leading to temperature changes inside the bubble with bubble oscillations have not yet been considered. Hence, this study aimed to incorporate the viscous (bulk viscosity and drag) and thermal effects to the previously proposed two-fluid model with bubble oscillations. Bulk viscosity was considered by averaging the shear stress term in the single-phase momentum conservation for a Newtonian fluid, and the drag was introduced by transforming the interfacial shear stress. We derived the averaged energy conservation for a general two-phase flow with a thermal conduction inside bubbles and heat transfer between the two phases, and limited this equation to that for a bubbly flow by closing the interfacial temperature gradient term via constitutive equations for a single bubble. Furthermore, we investigated the stability of our proposed one-dimensional model equations using the dispersion analysis. This analysis provided the following insight: (i) The difference in the temperature gradient models had a slight effect on the stability of the proposed model equations; (ii) the thermal conduction inside the bubbles was dominant in the thermal damping in bubbly flows rather than the heat transfer between the two phases; (iii) incorporating both the bulk viscosity and drag stabilized the proposed model equations. Our results provide insights into the development of mathematical models to investigate the thermal effects in bubbly flow with bubble oscillations, such as cavitating bubbly flow and wave propagation in bubbly liquids.

Experimental and Artificial Neural Network (ANN) Modeling of Instream Vegetation Hydrodynamic Resistance

This study examines the impact of upstream structures on the bulk drag coefficient of vegetation through experimental means, which has not been previously conducted. An embankment model was placed upstream of the vegetation, both with and without a moat/depression. The results showed that the presence of an upstream structure reduced the bulk drag coefficient of vegetation as the structure shared the drag. When only the embankment was placed upstream, a maximum decrease of 11% in the bulk drag coefficient was observed. However, when both the embankment and moat models were placed upstream, a 20% decrease in the bulk drag coefficient was observed. Regression models and artificial neural network (ANN) models were developed to predict the bulk drag coefficient based on the variables affecting it. Five ANN models with different training functions were compared to find the best possible training function, with performance indicators such as coefficient of determination (R2), root mean square error (RMSE), Nash–Sutcliffe efficiency (NSE), sum of square error (SSE), mean absolute error (MAE), and Taylor’s diagrams used to evaluate the model performance. The ANN model with nine neurons in each hidden layer performed the best, achieving the highest R2 and NSE values and the lowest RMSE, SSE, and MAE values. Finally, the comparison between the regression model and the ANN model showed that the best ANN model outperformed the regression models, achieving R2 values of 0.99 and 0.98 for the training and validation subsets, respectively.

Visualization of thermo-magnetic natural convective heat flow in a square enclosure partially filled with a porous medium using bejan heatlines and Hooman energy flux vectors: Hybrid fuel cell simulation

The aim of the article is to study the magneto-convective laminar incompressible flow within a differentially heated square enclosure partly filled with porous medium saturated with ionized helium gas in the presence of a transverse magnetic flux, as a model for emerging fuel cell designs. A Darcy model is utilized for porous medium bulk drag effects. Visualization of heat line and energy flux vectors is computed via Bejan's heat line approach and the Hooman energy flux vector method. The horizontal (i.e., bottom and top) wall boundaries are considered adiabatic and impermeable, while the side walls (cold and hot walls) are maintained at different but constant temperatures. The nonlinear coupled conservation equations under prescribed boundary conditions are solved with a finite difference-based vorticity-stream function approach. Appropriate convergence criteria factors are deployed. Furthermore, validation with earlier studies for the purely fluid, non-magnetic case i. e. in the absence of porous medium (Da) and Hartmann number (Ha) effects, is included. A parametric examination of the impact of Rayleigh number (Ra), Darcy number (Da) and Hartmann number (Ha) on temperature contours, heat lines, energy flux vectors and streamline patterns for ionized helium gas (Prandtl number, Pr = 0.71) is conducted. An increment in Hartmann magnetic number decreases the magnitudes of heat lines, suppresses heat transmission in the enclosure and curtails flow circulation. Enhancing the magnetic parameter and Rayleigh number however boosts the average heat transfer rate. Average Nusselt number at the left hot wall is elevated with increasing permeability of the porous medium and Rayleigh number. Mid-section velocities are enhanced in the porous layer but depleted in the non-porous layer of the enclosure with greater Rayleigh number. The simulations find provide some insight into applications in emerging hybrid electromagnetic fuel cells enabling better visualization of the thermal/fluid characteristics via the novel heat flow visualization heat-function and energy flux vectors analogy.

Hydrodynamics affected by submerged vegetation with different flexibility under unidirectional flow

Submerged vegetation changes the hydrodynamic characteristics of rivers, lakes, wetlands, and coastal zones. However, only a few studies have focused on the effect of flexible submerged vegetation on hydrodynamic characteristics under unidirectional flow. Therefore, laboratory experiments were conducted to study the effects of submerged vegetation with different flexibility on the flow structure and turbulence characteristics under unidirectional flow. The results showed that the reconfiguration and coordination of wave motion of flexible submerged vegetation redistribute flow velocity, Reynolds stress, and turbulent kinetic energy inside and outside of the vegetation canopy. With a gradual decrease in the deflection height of vegetation, the differences in dimensionless velocity, dimensionless mixed layer thickness, bulk drag coefficient, averaged turbulent kinetic energy, and the averaged contribution rate of its shear production term for the vegetation canopy also decrease; the trend of the penetration depth of Reynolds stress is opposite. Based on the turbulent kinetic energy budget equation, a turbulent kinetic energy model (TKE model) was established, which can be used to predict the turbulent kinetic energy and its shear production term within the vegetation canopy. Here, the scaling factor was determined by the vegetation canopy Cauchy number. The TKE model can be applied under unidirectional flow conditions for submerged vegetation with different flexibilities with high accuracy. It is a simple method to predict vegetation-induced turbulence and the characteristics of sediment and material transport under the influence of submerged vegetation with different flexibility.

Hydrodynamic Characteristics of Idealized Flexible Vegetation under Regular Waves: Experimental Investigations and Analysis

Wang, H.; Yin, Z.; Luan, Y.; Wang, Y., and Liu, D., 2022. Hydrodynamic characteristics of idealized flexible vegetation under regular waves: Experimental investigations and analysis. Journal of Coastal Research, 38(3), 673–680. Coconut Creek (Florida), ISSN 0749-0208. Salt marshes protect coastal communities from erosion and damage by damping incoming waves. A series of physical experiments were conducted to investigate the wave attenuation characteristics of idealized flexible vegetation, and the parameters of submergence, stem density, wave height, and wave length were considered. It was observed that the wave transmission coefficient decreased and the wave damping factor increased with increasing submergence ratio, relative wave height, and relative stem density and decreasing relative wave length. Moreover, the wave transmission coefficient decreased with increasing Ursell number. In addition, with an increase in the submergence ratio, relative wave height, Reynolds number, Keulegan-Carpenter number, and Ursell number, the bulk drag coefficient decreased. The bulk drag coefficient was more strongly related to the Ursell number than the other parameters. A simple equation for the wave transmission coefficient was constructed using the dimensional analysis method, the least squares method, and randomly selected experimental data, and it was effectively validated based on the other experimental data.

Quantifying Frontal-Surface Area of Woody Vegetation: A Crucial Parameter for Wave Attenuation

The last years, capacity of vegetation to reduce wave impact is receiving considerable attention. To predict wave attenuation processes within vegetation fields reliable estimates of vegetation parameters are needed. This proves to be difficult for woody vegetation as it consists of complex branch structures, characterized by varying branch densities, diameters and angles. State of the art physical and numerical models effectively use a single value for the diameter, bv and density, N of vegetation, which is unrepresentative for complex vegetation, such as trees. Trees can be better described by the projected frontal-surface area, Av. Hence, this work compares methods to quantify the Av in space for a pollard willow forest, and determines suitability of these methods for predicting wave attenuation using a spectral wave model (SWAN). We use data from manual measurements and Terrestrial Laser Scans (TLS), to estimate the vertical distribution of Av; and data from large-scale flume experiments performed on a willow forest to verify model sensitivity to Av inferences. As a baseline for comparison, tree models that describe the structure of the trees in various degrees of complexity are compiled. The most realistic tree model is used to quantify potential errors in TLS and basic manual measurements of N and bv. An initial comparison shows that the TLS data underestimates Av, which indicates that conducting manual measurements is more suitable to quantify a homogeneous forest. We found that the TLS suffers from shadowing effects (i.e., blockage of laser beams) and we recommend to apply a correction factor to improve its measurements. Furthermore, we identified the impact that the different methods to determine Av have on the estimation of wave attenuation using SWAN; in addition we verified the model results with data from large-scale flume experiments performed on the willow forest. The modeled sensitivity tests indicate large differences in wave attenuation and, consequently, a wide range (0.94–1.70) of bulk drag coefficients, C~D, for the various methods applied. This shows the variation of outcome between measuring methods and highlights the importance of stating the selected method for reliable frontal-surface area estimations, and consequently for reliable wave attenuation predictions.

Wave attenuation by flexible vegetation (and suspended kelp) with blade motion: Analytical solutions

Vegetation is one of the most important components of nature-based coastal protection due to its ability to dissipate wave energy. To quantify the wave attenuation by vegetation, traditional analytical models assume rigid vegetation and use bulk drag coefficient (CD) or effective blade length (le) techniques to consider the effects of blade motion, where CD and le are conventionally fitted as a function of KC (the Keulegan–Carpenter number) and CaL (with Ca the Cauchy number and L the ratio of the blade length to wave excursion), respectively. These parameters do not include the full blade dynamics and so the empirical formulas of CD and le are different for varying vegetation with blade dynamics. To obtain analytical solutions for CD and le, an analytical wave attenuation model for flexible vegetation (and kelp) was developed in this study by simplifying and linearizing the blade motion. Compared with a wide range of experiments for both submerged vegetation and suspended kelp canopies, the simplified analytical model underestimated the wave decay coefficient (kD) by 27%, but with a small NRMSE (normalized root mean square error by the range of the measured data) of 0.054. In comparison, the numerical model with full nonlinearity underestimated the wave decay coefficient by 11.7% with NRMSE=0.063. To reduce the underestimation of the analytical model due to the simplification and linearization, a modification factor defined as the ratio of the numerically calculated kD and the analytically calculated kD was fitted. With the modification factor, the underestimation of the analytical model was reduced to 10.1%. Based on the analytical model, analytical solutions for CD and le were derived, which showed a similar precision with the experimentally fitted CD and le based on KC and CaL, respectively. Thus, the analytical solutions for CD and le could be a reliable alternative when the experimentally calibrated CD and le are not available. Using the analytical wave attenuation model, a case study showed the wave attenuation by cultivated Saccharina latissima changes seasonally with the kelp growth. When the kelp blade reaches 2.4 m long after 7 months of growth, the kelp farms with 50 longlines (over a distance of 200 m in the direction of wave propagation) in 8 m-deep water may attenuate wave energy by 29% for 1 m-high waves with the period of 6 s. The wave attenuation can be enhanced to 43% when the farms are located in 5 m-deep water. To provide considerable wave attenuation of kelp with adequate long blades around the year, biennial and multiple partial harvesting techniques are recommended.

Experimental investigation of wave attenuation and bulk drag coefficient in mangrove forest with complex root morphology

Mangrove forests play a crucial role in coastal protection. Numerous experimental studies have been performed to examine the interaction between wave flows and mangrove forests, while the mangrove forests are commonly modeled as cylinder arrays, and the effect of the complex root system on wave attenuation is still unclear. A series of physical experiments were conducted to study the hydrodynamic characteristics induced by a 10-m-long mangrove forest model, which was built to reproduce a mature Rhizophora forest. Wave-attenuation analysis was performed to highlight the importance of considering the wave damping produced by mangrove roots under different water depths. In addition, the wave-attenuation coefficient β increases linearly with an increase in the relative wave height and wave steepness to varying degrees. In addition, the bulk drag coefficient (CD), a key parameter for quantifying the mean vegetation resistance, was obtained based on the classical model proposed by Dalrymple et al. (1984). The influences of several dimensionless hydrodynamic parameters on the CD are discussed in detail. The results show that the Ursell number and Keulegan–Carpenter number (KCd) have stronger correlations with CD for vegetation models without roots. The KCLe number calculated using effective characteristic length Le is suitable for describing the CD of the mangrove model for given water depth. Then, a new parameter, KCrv, was defined using the average pore velocity and vegetation-related hydraulic radius by considering the bulk characteristics of the wave and vegetation. Finally, a generic empirical formula was proposed for the CD to reveal the drag coefficient characteristics of vegetation with a relatively high correlation.

Wave attenuation by suspended canopies with cultivated kelp (Saccharina latissima)

Many kelp aquaculture farms consist of moored arrays of long horizontal lines that grow kelp near the water surface. Most kelp farms are deployed in the same direction of wave propagation. However, with numerous longlines of densely grown kelp, these farms may have the potential to attenuate waves if installed perpendicular to the direction of wave propagation. In this application, the kelp farm may serve as a form of nature-based coastal protection. To assess this potential, a set of 1:10 scale physical model experiments were conducted to measure the wave attenuation of a suspended kelp model. The model was scaled based on the morphological and mechanical properties of the cultivated Saccharina latissima (sugar kelp) from Saco Bay, Maine, USA. Experimental results demonstrated that suspended blades have asymmetric oscillatory motions with more bending in the opposite direction of wave propagation. Due to severe asymmetric blade motion in large waves, the suspended blade could roll over the attached line following the wave orbital motion. The results also showed that suspended kelp farms in the designed configuration with 20 longlines of 1-m-long blades and 100 blades/m have the potential attenuating wave energy by up to 33.7% under the experimental wave conditions. Based on the experimental data, empirical formulas were developed for the bulk drag coefficient (CDB) and effective blade length (le) of suspended kelp canopies for wave attenuation. To predict wave attenuation under a wider range of conditions and to identify the key parameters affecting wave attenuation, a numerical model was developed that could resolve blade motion. The benefits of resolving blade motion were to improve the model accuracy and reduce the number of experiments needed for obtaining CDB or le, which is required in the conventional wave attenuation models based on the rigid blade assumption. The results indicate that (i) the wave energy dissipation ratio (EDR defined as the ratio of the dissipated wave energy to the incident wave energy) of suspended kelp farms decreases with increased water depth, (ii) EDR is not sensitive to wave height, (iii) EDR first increases and then decreases with wavelength, and (iv) EDR increases with blade size, kelp vertical position, plant density, and the number of longlines. Therefore, the technique to improve the wave attenuation capacity of suspended kelp farms for nature-based coastal defense is to install the kelp farms in shallower water, expand the farm size by adding more longlines, locate the kelp in a higher position of the water column, grow the kelp more densely, and choose the kelp species with more rigid, wider, and longer blades/biomass.

Mapping the aerodynamic roughness of the Greenland Ice Sheet surface using ICESat-2: evaluation over the K-transect

Abstract. The aerodynamic roughness of heat, moisture, and momentum of a natural surface are important parameters in atmospheric models, as they co-determine the intensity of turbulent transfer between the atmosphere and the surface. Unfortunately this parameter is often poorly known, especially in remote areas where neither high-resolution elevation models nor eddy-covariance measurements are available. In this study we adapt a bulk drag partitioning model to estimate the aerodynamic roughness length (z0m) such that it can be applied to 1D (i.e. unidirectional) elevation profiles, typically measured by laser altimeters. We apply the model to a rough ice surface on the K-transect (west Greenland Ice Sheet) using UAV photogrammetry, and we evaluate the modelled roughness against in situ eddy-covariance observations. We then present a method to estimate the topography at 1 m horizontal resolution using the ICESat-2 satellite laser altimeter, and we demonstrate the high precision of the satellite elevation profiles against UAV photogrammetry. The currently available satellite profiles are used to map the aerodynamic roughness during different time periods along the K-transect, that is compared to an extensive dataset of in situ observations. We find a considerable spatio-temporal variability in z0m, ranging between 10−4 m for a smooth snow surface and 10−1 m for rough crevassed areas, which confirms the need to incorporate a variable aerodynamic roughness in atmospheric models over ice sheets.

Bulk Drag Predictions of Riparian Arundo donax Stands through UAV-Acquired Multispectral Images

Estimating the main hydrodynamic features of real vegetated water bodies is crucial to assure a balance between their hydraulic conveyance and environmental quality. Riparian vegetation stands have a high impact on vegetated channels. The present work has the aim to integrate riparian vegetation’s reflectance indices and hydrodynamics of real vegetated water flows to assess the impact of riparian vegetation morphometry on bulk drag coefficients distribution along an abandoned vegetated drainage channel fully covered by 9–10 m high Arundo donax (commonly known as giant reed) stands, starting from flow average velocities measurements at 30 cross-sections identified along the channel. A map of riparian vegetation cover was obtained through digital processing of Unnamed Aerial Vehicle (UAV)-acquired multispectral images, which represent a fast way to observe riparian plants’ traits in hardly accessible areas such as vegetated water bodies in natural conditions. In this study, the portion of riparian plants effectively interacting with flow was expressed in terms of ground-based Leaf Area Index measurements (LAI), which easily related to UAV-based Normalized Difference Vegetation Index (NDVI). The comparative analysis between Arundo donax stands NDVI and LAI map enabled the analysis of the impact of UAV-acquired multispectral imagery on bulk drag predictions along the vegetated drainage channel.

Drag variations, tidal asymmetry and tidal range changes in a mangrove creek system

AbstractAboveground root structures enhance drag on tidal currents in intertidal mangrove forests, whereas the creeks dissecting such forests provide low‐resistance conduits for tidal flows. Here, observations from an established mangrove forest in the Whitianga Estuary, Aotearoa New Zealand, are used to investigate the variability of the drag experienced by tidal flows in a mangrove creek system and subsequent effects on tidal asymmetries and ranges.Tidal flow speed maxima in the creek occurred at overbank water levels during the sheet flow stage on rising tides, but at water levels below the creek bank (the creek flow stage) on falling tides. Inferred bulk drag coefficients for the creek were greater during the sheet flow than the creek flow stage, and were linearly correlated with the bulk drag coefficients at stations in the adjacent forest. Although falling tides, associated with larger bulk drag coefficients, had an increasingly longer duration than rising tides towards the back of the forest, we observed ebb‐dominant flow speed asymmetry that declined inland in the creek. Conversely, flow speeds within the forest were consistently flood‐dominant, in accordance with smaller bulk drag coefficients during rising tides. Along the full length of the mangrove system, high‐water levels were lowered by up to 12 cm/km within the creek and 36 cm/km within the mangrove forest.Creek bed roughness associated with bulk drag coefficients observed in deeper parts of the creek was much greater than the hydraulic roughness of the sediment. For accurate simulations of landscape‐scale feedbacks between the creek and mangrove forest, incorporating both direct and indirect contributions of the vegetated forest platform to creek bed roughness is essential. These findings show that the interaction between creek flow and sheet flow in a mangrove creek system is a key driver of tidal asymmetries as well as the attenuation of high‐water conditions.

Dynamic Measurements with the Bicone Interfacial Shear Rheometer: The Effects of the Numerical Implementation of the Interfacial Boundary Condition

The increasing popularity of flow field-based data analysis (FFBDA) techniques has a paradigmatic example in the routines already developed for the rotational oscillating bicone bob interfacial shear rheometer. Such routines use a second order centered finite difference (SOCFD) discretization scheme, in both the vertical and radial coordinates, for the velocity field in the bulk fluid subphase and a first order forward finite difference (FOFFD) scheme in the vertical coordinate for the velocity field at the air/water interface. Such a mixture of schemes causes non-smooth flow fields at the interface that can be tackled by appropriately devising a SOCFD scheme for the vertical coordinate at the interface using a line of “phantom” nodes that merely serve to adequately merge the Navier–Stokes equations and the Boussinesq–Scriven boundary condition at the interface. Here we report on a detailed analysis of the quantitative improvements of such a scheme over the previous one by comparing the structure of the flow fields at and close to the interface, the differences in the interfacial and bulk drag torques on the bicone bob, and the differences in the torque/displacement complex amplitude ratio.

Predicting the bulk drag coefficient of flexible vegetation in wave flows based on a genetic programming algorithm

The prediction of the bulk drag coefficient (CD) for aquatic vegetation is of great significance for evaluating the influence of vegetation on the hydrodynamic processes in wave environments. Different CD empirical formulas have been mostly proposed as functions of either Reynolds (Re) number or Keulegan–Carpenter (KC) number in the literature, and the influences of other wave and vegetation parameters on CD were often ignored. The difference in formulas is largely attributable to inconsistent uses of characteristic velocity and length scales in the definitions of Re and KC. By considering the vegetation and hydrodynamic characteristics in this study, new Re and KC numbers were redefined using the mean pore velocity and vegetation-related hydraulic radius. Besides, a genetic programming algorithm was adopted to develop a robust relationship between CD and possible dimensionless variables based on extensive experimental data. Ultimately, a new CD predictor that has a similar form to that of the classical expression was obtained without any prespecified forms before searching. It turns out that the new predictor depends on not only the new KC number but also the submergence ratio and Ursell number. Compared with the existing predictors, the proposed CD predictor exhibits a considerable improvement in predictive ability for a wider parameter space.