Bottom Friction Coefficient Research Articles

Update to Friction Factor Formulations That Impact Rocky Shores and Coral Reefs

AbstractThe bottom friction factor, , estimates for computing wave bottom frictional dissipation in Gon et al. (2020, https://doi.org/10.1029/2019jc015963), titled Wave Dissipation by Bottom Friction on the Inner Shelf of a Rocky Shore, are too large by a factor of 2 due to an error in the formulations by Thornton and Guza (1983, https://doi.org/10.1029/jc088ic10p05925), titled Transformation of Wave Height Distribution. Corrected formulations reduce the prior overestimation of the bottom friction coefficient, , which is more significant for rougher bottom surfaces, such as coral reefs and rocky shores, than for sandy beaches.

Three-dimensional numerical study of the deep western boundary current in the South China Sea

This study utilized a three-dimensional ocean general circulation model to investigate the intensity, thickness, and width of the three-dimensional deep western boundary current (DWBC) in the South China Sea (SCS). The numerical results show that the DWBC begins near the inlet of the Luzon overflow, flows westward along the northern boundary, proceeds southward along the western boundary, and ultimately terminates at the southern boundary. The mean DWBC’s velocity, thickness, and width is 4.78 cm/s, 1645 m, and 140 km, respectively. Combined with the dynamic results, it is evident that the three-dimensional structure of the DWBC appears to have been visibly weakened after the closure of the deep Luzon overflow. Strong deep mixing has a significantly stronger, thicker, and wider effect on the intensity, thickness, and width of the DWBC. Both the bottom and lateral friction coefficients negatively impact the DWBC in the SCS.

Coupling numerical models of deltaic wetlands with AirSWOT, UAVSAR, and AVIRIS-NG remote sensing data

Abstract. Coastal marsh survival relies on the ability to increase elevation and offset sea level rise. It is therefore important to realistically model sediment fluxes between marshes, tidal channels, and bays as sediment availability controls accretion. Traditionally, numerical models have been calibrated and validated using in situ measurements at a few locations within the domain of interest. These datasets typically provide temporal information but lack spatial variability. This paper explores the potential of coupling numerical models with high-resolution remote sensing imagery. Products from three sensors from the NASA Delta-X airborne mission are used. Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) provides vertical water level change on the marshland and was used to adjust the bathymetry and calibrate water fluxes over the marsh. AirSWOT yields water surface elevation within bays, lakes, and channels, and was used to calibrate the Chezy bottom friction coefficient. Finally, imagery from AVIRIS-NG provides maps of total suspended solids (TSS) concentration that were used to calibrate sediment parameters of settling velocity and critical shear stress for erosion. Three numerical models were developed at different locations along coastal Louisiana using Delft3D. The coupling enabled a spatial evaluation of model performance that was not possible using simple point measurements. Overall, the study shows that calibration of numerical models and their general performance will greatly benefit from remote sensing.

Hydraulic Bottom Friction and Aerodynamic Roughness Coefficients for Mangroves in Southwest Florida, USA

Mangroves are a natural feature that enhance the resilience of natural and built coastal environments worldwide. They mitigate the impacts of hurricanes by dissipating energy from storm surges and waves, as well as reducing wind speeds. To incorporate mangroves into storm surge simulations, surface roughness parameters that accurately capture mangrove effects are required. These effects are typically parameterized using Manning’s n bottom friction coefficient for overland flow and aerodynamic roughness length (z0) for wind speed reduction. This paper presents the suggested values for these surface roughness parameters based on field observation and a novel voxel-based processing method for laser scanning point clouds. The recommended Manning’s n and z0 values for mangroves in southwest Florida are 0.138 and 2.34 m, respectively. The data were also used to retrain a previously developed random forest model to predict these surface roughness parameters based on point cloud statistics. The addition of the mangrove sites to the training data produced mixed results, improving the predictions of z0 while weakening the predictions of Manning’s n. The paper concludes that machine learning models developed to predict environmental attributes using small datasets with predictor features containing subjective estimates are sensitive to the uncertainty in the field observations.

An empirical formula of bottom friction coefficient with a dependence on the current speed for the tidal models

Tides are of great importance for ocean mixing and nearshore ocean engineering. Bottom friction is a major factor in tidal dissipation and is usually parameterized by the bottom friction coefficient (BFC). BFC is a critical parameter in numerical tidal models and is known to vary with time and space, as calculated with measured data. However, it is difficult to accurately adjust the spatially-temporally varying BFC in numerical tidal models. Based on the relationship between the spatially-temporally varying BFC estimated by adjoint data assimilation and the simultaneously simulated current speed, an empirical formula of BFC with a dependence on the current speed is proposed. This new empirical formula of BFC is compared with several traditional empirical formulas, including the constant BFC, the Chezy-Manning BFC, and two depth-dependent BFCs. When the four principal tidal constituents (M2, S2, K1, and O1) in the Bohai, Yellow and East China Seas (BYECS) are simulated, the mean vector error between the simulated results obtained using the current speed-dependent BFC and the TOPEX/Poseidon satellite altimetry data (the tidal gauge data) is 8.81 cm (10.62 cm), which is decreased by up to 8.1% (18.2%) compared with those using the several commonly used empirical formulas of BFC. Furthermore, in the sensitivity experiments where only the M2 tide in the BYECS, the M2, S2, K1, and O1 tides in the Bohai and Yellow Sea (BYS), and the M2, S2, K1, and O1 tides in the South China Sea (SCS) are simulated, the errors between the simulated results obtained by using current speed-dependent BFC and the tidal gauge data are less than those using the other empirical formulas of BFC, further demonstrating the superiority of the current speed-dependent BFC proposed in this study. From numerical model experiments, the current speed-dependent BFC can adequately reflect the spatial and temporal variations of BFC and improve the simulation accuracy of tides, thus having a broad application scope.

Wave forced vorticity and dissipation scaling on a rip channeled beach

Rip-currents, commonly observed on natural beaches, are vorticity induced and part of large scale near-shore circulations. The questions arise: how do bathymetric gradients magnitudes relate to rip velocities? how does rip current vorticity scale with wave characteristics and dissipation? What is the dynamics of the large scale 2D vorticity? To address these questions, we utilize a Non Linear Shallow Water model with a shock-capturing scheme. It is validated with preexisting experiments of wave induced rip-currents on uneven bathymetries generated by irregular waves. To do so the enstrophy (spatially averaged square of the vorticity) is shown to be a relevant metric to calibrate the bottom friction coefficient of the model. The numerical study based on a large number of simulations with monochromatic wave forcing shows that the more non-uniform the bathymetry is, the stronger the gradients in wave dissipation are and the stronger the enstrophy is. The rip current velocity is shown to linearly increase with the square root of the local enstrophy. The wave-averaged shallow water vorticity equation terms are evaluated. It is suggested that large scale 2D vorticity dynamics mainly result from an equilibrium between vorticity production, vorticity advection by the circulation and dissipation by bottom friction.

An optimization method of adjoint assimilation based on the cumulative gradient: An application for correction of the bottom friction coefficient in the tidal wave model

In this paper, we explored the optimization process in adjoint method. An optimization method based on the cumulative gradient is proposed to minimize the cost function. On the basis of the gradient descent method, the cumulative gradient is added and the information of first-order gradient is further utilized to update the control variable. Instead of focusing on the gradient in the current iteration only, the method combines the gradient information in the previous iterations. By weighting and cumulating the previous gradients, it can provide constructive guidance for the update direction and update stride of the control variable. To test the optimization performance in the practical problem, the method is applied to the correction of the bottom friction coefficient in the tidal wave model with adjoint method and the gradient descent method is set as the control. The results show that the method based on the cumulative gradient can optimize the cost function to a lower level than the gradient descent method under the same number of iterations. With our method, the model had more accurate simulation results. The simulation effect in areas without assimilation data is also tested, and the results prove that the method has great stability and can work for the entire simulation area. Moreover, the optimization efficiency of the method is much higher than that of the gradient descent method. It can reach the same effect while the optimization time is greatly shortened. In further experiments, we compare some other optimization methods with the method in the paper, and the optimization results of the cost function show that our method is still competitive. Our method is effective and simply implemented. It requires few computation and storage resources, which is of great significance for large-scale optimization problems. The method has shown satisfactory performance for optimization of the cost function in adjoint method. It can enhance the assimilation effect and improve optimization efficiency to a certain extent. The method has certain engineering significance for solving the optimization problems in the actual assimilation system. As a general method, it may provide a reference for the selection and innovation of optimization methods in data assimilation process.

Estimation of the Manning’s n coefficient in multi-constituent tidal models by assimilating satellite observations with the adjoint data assimilation

The bottom friction is critical for the dissipation of the global tidal energy. The bottom friction coefficient is traditionally determined using the Manning’s n formulation in tidal models. The Manning’s n coefficient in the Manning’s n formulation is vital for the accurate simulation and prediction of the tide in coastal shallow waters, but it cannot be directly measured and contains large amounts of uncertainties. Based on a two-dimensional multi-constituent tidal model with the adjoint data assimilation, the estimation of the Manning’s n coefficient is investigated by assimilating satellite observations in the Bohai, Yellow and East China Seas with the simulation of four principal tidal constituents M2, S2, K1 and O1. In the twin experiments, the Manning’s n coefficient is assumed to be constant, and it is estimated by assimilating the synthetic observations at the spatial locations of the satellite tracks. Regardless the inclusion of artificial random observational errors associated with synthetic observations, the model performance is improved as evaluated by the independent synthetic observations. The prescribed ‘real’ Manning’s n coefficient is reasonably estimated, indicating that the adjoint data assimilation is an effective method to estimate the Manning’s n coefficient in multi-constituent tidal models. In the practical experiments, the errors between the independent observations at the tidal gauge stations and the corresponding simulated results of the four principal tidal constituents are substantially decreased under both scenarios of the constant and spatially-temporally varying Manning’s n coefficient estimated by assimilating the satellite observations with the adjoint data assimilation. In addition, the estimated spatial and temporal variation trend is robust and not affected by the model settings. The spatially-temporally varying Manning’s n coefficient is negatively correlated with the current speed and shows significant spatial variation in the shallow water areas. This study demonstrates that the Manning’s n coefficient can be reasonably estimated by the adjoint data assimilation, which allows significant improvement in accurate simulation of the ocean tide.

Effects of spatial bottom friction parameterization scheme on the tidal dynamics in the macrotidal East China Seas

In this study, the effects of different bottom friction coefficient (BFC) parameterization schemes on the modelling of four principal tidal constituents (M2, S2, K1, O1 tides) in the macrotidal East China Seas were investigated by using a high-resolution model based on FVCOM (Finite Volume Community Ocean Model). The applied BFC schemes include: the empirical constant (EC-BFC), sediment-dependent form (SD-BFC), and spatial varying BFC obtained from adjoint data assimilation (SV-BFC). The comparisons between the simulated results and the observations from satellite altimeters and tidal gauge stations indicated that the SV-BFC scheme is superior to others. The locations of amphidromic points calculated with EC-BFC and SD-BFC were in the northwest of those from SV-BFC. The variations in tidal dynamics between different BFC schemes were closely related to the spatial distributions of BFCs, especially in high-valued BFC areas, e.g., the West Korea Bay, the South Yellow Sea, and the eastern coasts of Jiangsu, Zhejiang and Fujian provinces. The tidal energy flux transporting into Bohai and Yellow Seas increased under the SV-BFC scheme, while smaller tidal energy flux transporting from the Korea Strait was generated by SV-BFC as compared to those from EC-BFC and SD-BFC. The high-valued BFC areas in the SV-BFC scheme dissipated larger amounts of tidal energy, and the average values of Simpson-Hunter numbers were lower than those with the other two schemes. However, the values of Simpson-Hunter numbers increased in the West Korea Bay and Jianghua Bay with high-valued BFCs because of the decreasing current velocity under the headland-shaped topography.

Modelling the Effects of Oyster Tables on Estuarine Tidal Flow

Oyster farming may impact the estuarine tidal circulation with a series of effects on environmental conditions and cultures’ growth. Hydrodynamic numerical models set up in estuaries integrated the presence of oyster structures by simply increasing the bottom friction coefficient over farming areas. However, for elevated oyster tables in tidal environments, such default calibration ignored the temporal variations of the friction coefficient between the conditions of submerged or unsubmerged structures. Thus, an original formulation of the Chézy coefficient was here proposed to integrate these modulations. Assessed against measured and predicted vertical velocity profiles on a 1/2 scaled model, this formulation was implemented in a simulation of the tidal circulation within the Aber Wrac’h estuary (Brittany, France). Particular attention was dedicated to the changes induced on the current magnitudes and sediment transport. Oyster tables were found to impact current magnitudes in the vicinity of elevated structures, with major differences at times of local peak flood and ebb. These modifications were characterised by (i) a reduction of current magnitudes over oyster farming areas and (ii) a tidal-flow acceleration on both sides of these structures. Increased sediment transport was, therefore, expected in the vicinity of these cultures, with potential implications on seabed morphology and water quality.

An operational improvement of A-4DEnVar and its application to the estimation of the spatially varying bottom friction coefficients of the M2 constituent in the Bohai and Yellow seas

The analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation scheme inherits the advantages of the conventional four-dimensional variational (4D-Var) data assimilation scheme and removes the adjoint model. However, compatible operational improvements such as the reduction of the computational costs and the localization method should be considered when it is used in realistic systems. In this paper, the computational complexity of calculating the inverse of background error covariance (the B matrix) is decreased by a precondition transform method, i.e., introducing a new state variable whose product with the B matrix is the original state variable to be optimized in the cost function. Furthermore, an independent point (IP) scheme is combined to construct an implicit localization method and further decreases the computational cost. Based on the Princeton Ocean Model with the generalized coordinate system (POMgcs), the operational improved A-4DEnVar is applied to optimize the spatially varying bottom friction coefficients (BFCs) of the M2 constituent in the Bohai and Yellow seas. A twin experiment with idealized observations is designed to validate the effectiveness of the proposed method. In practical experiments, with no more than 10 IPs, the algorithm can assimilate observations from the National Astronomical Observatory (NAO) dataset and obtain a good simulation. The experimental performances increase with the increase of either the IPs or observations, which indicates the efficacy of the proposed algorithm.

Ultimate Bearing Capacity Analysis of Pile Caps with New Socket Connections

Socket connection need a groove reserved in the cap to accommodate a bridge pier, which greatly weaken the vertical bearing capacity of the cap. The conventional treatment measure is to increase the thickness of the cap, and the corresponding cost will increase. The measures to enhance the vertical bearing capacity of socket caps without increasing the thickness of the cap were discussed in this paper, including a rough interface at the bottom of the pier, additional hanging bars, high-strength grouting material in the seam, and large-diameter metal corrugated pipes, etc. Based on a previous test, the finite element analysis of the vertical bearing capacity of pile caps with new socket connections was carried out. The analysis parameters included the construction method, steel bar diameter in the bottom of the cap, socket depth, thickness of the bottom plate, pile length, and friction coefficient, etc. The bearing capacity M–N relation of the full-scale model was also analyzed. Research indicated the vertical bearing capacity of the cap is mainly provided by rough interfaces, the bottom plate, and the additional hanging bars, and the contribution of the three parts was about 40%, 34%, and 26%; the vertical bearing capacity was proportional to the areas of steel bars on the cap and the thickness of the bottom plate, and was inversely proportional to the length of the pile. To obtain the vertical bearing capacity of the overall cast-in-place plan for the socket cap, the thickness of the cap needs to be increased by 27%. At last, a design formula for the calculation of the vertical bearing capacity was proposed.

Profile of a two-dimensional vortex condensate beyond the universal limit.

It is well known that an inverse turbulent cascade in a finite (2π×2π) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length l_{f}=2π/k_{f} with k_{f} ranging from 100 to 12.5. Previously, it was found that in the asymptotic limit of small-scale forcing, the vorticity exhibits the power-law behavior Ω(r)=(3ε/α)^{1/2}r^{-1}, where r is the distance to the vortex center, α is the bottom friction coefficient, and ε is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite k_{f} the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behavior is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with r, and show that in this case the vorticity profile can be flatter than the asymptotic limit.

Coherent vortex versus chaotic state in two-dimensional turbulence

We examine analytically and numerically the state of a two-dimensional fluid in a finite box appearing as a result of the inverse cascade supported by a permanent pumping. We argue that there are two different states. One of the states is dominated by big coherent vortices with a well-defined mean profile. The other state is dominated by strong chaotic large-scale fluctuations. The character of the realized state depends on the ratio νkf2/α where ν is the kinematic viscosity coefficient, kf is the characteristic wave vector of the pumping force and α the bottom friction coefficient. If the ratio νkf2/α is large then one expects to observe the first state, whereas in the opposite state the second (chaotic) state is expected. To check the prediction we performed the direct numerical simulations of hydrodynamics of a weakly compressible two-dimensional fluid with no-slip boundary conditions. The pumping force is static and contains some spacial harmonics. The simulations are performed for different values of pumping and of the ratio νkf2/α. We introduce the criterion based on presence/absence of long time correlations to distinguish two above states. The numerical results confirm the analytical predictions.

Weather window and efficiency assessment of offshore wind power construction in China adjacent seas using the calibrated SWAN model

Waves simulated by a high-resolution calibrated SWAN model of China adjacent seas over a long-term period (from 1996 to 2020) are utilized to investigate the characteristics of offshore wind power construction efficiency. The model is forced by validated ERA5 wind data, which shows better agreement with ICOADS observations than CCMPv2 and CFSR&CFSv2. During the calibration process, we focused on wind input, whitecapping, and bottom friction terms and on whitecapping dissipation and bottom friction coefficients. Statistical error analysis of the calibration results demonstrates that the underestimation of significant wave height simulated with default settings has been corrected and the model performance has been improved in the study area. The assessment results revealed that construction efficiency has significant spatial and temporal variation characteristics. Annual and monthly averaged workloads of pile foundation construction and wind turbine installation are distinctly different since their specific weather restrictions and durations. Generally speaking, weather conditions from May to August are more favourable for offshore construction. In winter, offshore construction is strongly suggested to be stopped especially for sea areas of Fujian and Guangdong. For selected projects, the key environmental factors affecting offshore operation are different, which should be considered to improve construction efficiency and further decrease cost.

The relative merits of sediment transport formulas applied to the Nakdong Estuary, Korea using a coupled numerical modeling system

Three sediment transport formulas by Lund-CIRP (2012), van Rijn (1998), and Soulsby (1997) were applied for this study with field data by Yoon (2008) and several sedimentary variables of Nakdong Estuary in a coupled numerical modeling system, CMS. CMS is adopted to compare the measured depth change data and the calculated depth change data. As a result, the Lund-CIRP formula with mean grain size (0.25 mm) and multi-bottom friction coefficients based on the mean grain size distribution had higher accuracy (1.6 %) than the other formulas. The Soulsby formula has higher accuracy for multi-grain size and 0.06 of bottom friction coefficients. The van Rijn formula has high accuracy at shallow water areas such as a river. In this study, it is judged that the accuracy of the van Rijn cases was low because the water depth of the Nakdong Estuary and the nearby sea area rapidly deepens.

Data-assimilation-based parameter estimation of bathymetry and bottom friction coefficient to improve coastal accuracy in a global tide model

Abstract. Global tide and surge models play a major role in forecasting coastal flooding due to extreme events or climate change. The model performance is strongly affected by parameters such as bathymetry and bottom friction. In this study, we propose a method that estimates bathymetry globally and the bottom friction coefficient in shallow waters for a global tide and surge model (GTSMv4.1). However, the estimation effect is limited by the scarcity of available tide gauges. We propose complementing sparse tide gauges with tide time series generated using FES2014. The FES2014 dataset outperforms the GTSM in most areas and is used as observations for the deep ocean and some coastal areas, such as Hudson Bay and Labrador, where tide gauges are scarce but energy dissipation is large. The experiment is performed with a computation- and memory-efficient iterative parameter estimation scheme (time–POD-based coarse incremental parameter estimation; POD: proper orthogonal decomposition) applied to the Global Tide and Surge Model (GTSMv4.1). Estimation results show that model performance is significantly improved for the deep ocean and shallow waters, especially in the European shelf, directly using the CMEMS tide gauge data in the estimation. The GTSM is also validated by comparing to tide gauges from UHSLC, CMEMS, and some Arctic stations in the year 2014.

Sedimentological data-driven bottom friction parameter estimation in modelling Bristol Channel tidal dynamics

Accurately representing the bottom friction effect is a significant challenge in numerical tidal models. Bottom friction effects are commonly defined via parameter estimation techniques. However, the bottom friction coefficient (BFC) can be related to the roughness of the sea bed. Therefore, sedimentological data can be beneficial in estimating BFCs. Taking the Bristol Channel and Severn Estuary as a case study, we perform a number of BFC parameter estimation experiments, utilising sedimentological data in a variety of ways. Model performance is explored through the results of each parameter estimation experiment, including applications to tidal range and tidal stream resource assessment. We find that theoretically derived sediment-based BFCs are in most cases detrimental to model performance. However, good performance is obtained by retaining the spatial information provided by the sedimentological data in the formulation of the parameter estimation experiment; the spatially varying BFC can be represented as a piecewise-constant field following the spatial distribution of the observed sediment types. By solving the resulting low-dimensional parameter estimation problem, we obtain good model performance as measured against tide gauge data. This approach appears well suited to modelling tidal range energy resource, which is of particular interest in the case study region. However, the applicability of this approach for tidal stream resource assessment is limited, since modelled tidal currents exhibit a strong localised response to the BFC; the use of piecewise-constant (and therefore discontinuous) BFCs is found to be detrimental to model performance for tidal currents.

Quality prediction of internal thread cold extrusion based on genetic algorithm optimized BP neural network

The extrusion process parameters have a great impact on the quality of the extrusion thread. In order to ensure the extrusion quality and the smooth progress of the extrusion process, a prediction model based on BP-GA neural network is established. The model takes the diameter of the bottom hole, extrusion speed, and friction coefficient as the input layer, and the extrusion torque, extrusion temperature, and tooth height as the output layer. After training the model with sample data, the extrusion internal thread quality prediction is carried out. The results show that the BP-GA neural network prediction model has a high accuracy in predicting the extrusion torque, extrusion temperature and tooth height rate during the cold extrusion of internal threads. The error between the experimental value and the predicted value of the extrusion torque is between 10% and 15%, the experimental value of the extrusion temperature is consistent with the predicted value, and the error between the experimental value and the predicted value of the tooth height rate is less than 5%. The BP-GA neural network prediction model can accurately predict the extrusion temperature, extrusion torque, and tooth height rate, providing a new way for the re-search of internal thread cold extrusion technology.

Integration of data-driven and physics-based modeling of wind waves in a shallow estuary

Numerical models solving the wave action balance equation have been widely used to simulate wind waves. In-situ measurements, albeit sparse, are crucial to the calibration and validation of numerical wave models. In this study, a novel hybrid approach was developed by integrating a physics-based Simulating WAves Nearshore (SWAN) model with machine learning algorithms to predict wind waves in a shallow estuary. Two machine learning methods, bagged regression tree (BRT) and artificial neural network (ANN), were employed. It was found that the hybrid approach (BRT–SWAN) could be an efficient tool for modelers to identify sources of error and calibrate parameters in physics-based models. In this study, the wind direction and bottom friction coefficient were determined as the main factors causing errors in SWAN-simulated significant wave height and peak wave period, respectively. Furthermore, it turned out that BRT–SWAN-ANN (ANN trained with BRT–SWAN results) could achieve a similar level of accuracy to OBS-ANN (ANN trained with field observations of wind waves). Thus, the hybrid approach can be applied to estimate wave parameters, removing the limitation of using scarce observations in developing a predictive ANN model.