Direct bed shear stress measurements in bore-driven swash

Direct measurements of bed shear in the swash zone are presented. The data were obtained using a shear plate in medium and large-scale laboratory bore-driven swash and cover a wide range of bed roughness. Data were obtained across the full width of the swash zone and are contrasted with data from the inner surf zone. Estimates of the flow velocities through the full swash cycle were obtained through numerical modelling and calibrated against measured velocity data. The measured stresses and calculated flow velocities were subsequently used to back-calculate instantaneous local skin friction coefficients using the quadratic drag law. The data show rapid temporal variation of the bed shear stress through the leading edge of the uprush, which is typically two–four times greater than the backwash shear stresses at corresponding flow velocity. The measurements indicate strong temporal variation in the skin friction coefficient, particularly in the backwash. The general behaviour of the skin friction coefficient with Reynolds number is consistent with classical theory for certain stages of the swash cycle. A spatial variation in skin friction coefficient is also identified, which is greatest across the surf-swash boundary and likely related to variations in local turbulent intensities. Skin friction coefficients during the uprush are approximately twice those in the backwash at corresponding Reynolds number and cross-shore location. It is suggested that this is a result of the no-slip condition at the tip leading to a continually developing leading edge and boundary layer, into which high velocity fluid and momentum are constantly injected from the flow behind and above the tip region. Finally, the measured stress data are used to determine the asymmetry and cross-shore variation in potential sediment transport predicted by three forms of sediment transport formulae.     

Bed shear stress under skewed and asymmetric oscillatory flows

We present a new formulation to predict the bed shear stress under skewed/asymmetric oscillatory flows (with or without a co-linear mean current), extending the work of Nielsen (1992). The nonlinearity of the oscillatory flow is incorporated through the use of two parameters: the index of skewness or nonlinearity, and the waveform parameter. The new formulation is tested against the bed shear stress estimated from the log-fit and momentum-integral methods, using oscillatory data from oscillating water tunnel experiments. The new formulation and the momentum-integral method agree well, but differ from those with the log-fit method, possibly because both methodologies lead to different results for the phase lead between the bed shear stress and the free-stream velocity. The new bed shear stress formulation is incorporated in a quasi-steady bedload formula, and accurately reproduces net transport rates under non-linear, nonbreaking waves with and without an opposing current.     

Measurement and modeling of bed shear stress under solitary waves

Direct measurements of bed shear stresses (using a shear cell apparatus) generated by non-breaking solitary waves are presented. The measurements were carried out over a smooth bed in laminar and transitional flow regimes (~ 10⁴ < R_e < ~ 10⁵). Measurements were carried out where the wave height to water depth (h/d) ratio varied between 0.12 and 0.68; maximum near bed velocity varied between 0.16 m/s and 0.51 m/s and the maximum total shear stress (sum of skin shear stress and Froude–Krylov force) varied between 0.386 Pa and 2.06 Pa. The total stress is important in determining the stability of submarine sediment and in sheet flow regimes. Analytical modeling was carried out to predict total and skin shear stresses using convolution integration methods forced with the free stream velocity and incorporating a range of eddy viscosity models. Wave friction factors were estimated from skin shear stress at different instances over the wave (viz., time of maximum positive total shear stress, maximum skin shear stress and at the time of maximum velocity) using both the maximum velocity and the instantaneous velocity at that phase of the wave cycle. Similarly, force coefficients obtained from total stress were estimated at time of maximum positive and negative total stress and at maximum velocity. Maximum positive total shear stress was approximately 1.5 times larger than minimum negative total stress. Modeled and measured positive bed shear stresses are well correlated using the best convolution model, but the model underestimates the data by about 4%. Friction factors are dependent on the choice of normalizing using the maximum velocity, as is conventional, or the instantaneous velocity. These differ because the stress is not in phase with the velocity in general. Friction factors are consistent with previous data for monochromatic waves, and vary inversely with the square-root of the Reynolds number. The total shear stress leads the free stream fluid velocity by approximately 50°, whereas the skin friction shear stress leads by about 30°, which is similar to that reported by earlier researchers.     

Exploring German Bight coastal morphodynamics based on modelled bed shear stress

The prediction of large-scale coastal and estuarine morphodynamics requires a sound understanding of the relevant driving processes and forcing factors. Data- and process-based methods and models suffer from limitations when applied individually to investigate these systems and, therefore, a combined approach is needed. The morphodynamics of coastal environments can be assessed in terms of a mean bed elevation range (BER), which is the difference of the lowest to highest seabed elevation occurring within a defined time interval. In this study of the coastal sector of the German Bight, North Sea, the highly variable distribution of observed BER for the period 1984–2006 is correlated to local bed shear stresses based on hindcast simulations with a well-validated high-resolution (typically 1,000 m in coastal settings) process-based numerical model of the North Sea. A significant correlation of the 95th percentile of bed shear stress and BER was found, explaining between 49 % and 60 % of the observed variance of the BER under realistic forcing conditions. The model then was applied to differentiate the effects of three main hydrodynamic drivers, i.e. tides, wind-induced currents, and waves. Large-scale mapping of these model results quantify previous qualitative suggestions: tides act as main drivers of the East Frisian coast, whereas waves are more relevant for the morphodynamics of the German west coast. Tidal currents are the main driver of the very high morphological activity of the tidal channels of the Ems, Weser and Elbe estuaries, the Jade Bay, and tidal inlets between the islands. This also holds for the backbarrier tidal flats of the North Frisian Wadden Sea. The morphodynamics of the foreshore areas of the barrier island systems are mainly wave-driven; in the deeper areas tides, waves and wind-driven currents have a combined effect. The open tidal flats (outer Ems, Neuwerker Watt, Dithmarschen Bight) are affected by a combination of tides, wind-driven currents and waves. Model performance should be measurably improved by integrating the roles of other key drivers, notably sediment dynamics and salt marsh stabilisation.     

Estimation of the wave-related ripple characteristics and induced bed shear stress

A large data set on ripples was collected and examined. A set of new formulas for the prediction of the ripple characteristics is proposed with an emphasis on the disappearance of the ripples. The ripple wavelength was observed to be proportional to the bottom wave excursion but also to be a function of the grain-related Shields parameter and wave period parameter introduced by Mogridge et al. (1994). The ripple steepness was found to be nearly constant for orbital ripples, and with a sharp decrease for suborbital ripples. Two empirical functions are added including the effects of the critical Shields parameters (inception of transport and inception of sheet flow), i.e. giving the boundaries for the ripple existence's domain. The proposed formulas yield better prediction capabilities compared to the previously published formulas, especially when ripples are washed out. The effect of the ripple characteristics on the roughness height and the calculation of the bed shear stress is also discussed. It appeared that the bed shear stress calculation is more sensitive to the empirical coefficient a_r introduced in the estimation of the ripple-induced roughness height or to the limits of existence of the ripples than the ripple characteristics themselves.     

植被对波浪作用下床面切应力影响的数值模拟分析

本文基于OpenFOAM建立三维波浪数值水槽,模拟计算植被水域波浪作用下的床面切应力,分析了入射波高、植被密度、植被淹没高度、水流对植被水域波浪作用下床面切应力的影响。结果表明：纯波时,由于植被的阻水作用,植被水域床面切应力沿程衰减,其衰减程度与入射波高、植被密度及植被淹没高度呈现正相关;与纯波时相比,在波浪和同向流共同作用下正向床面切应力幅值增大,负向床面切应力幅值减小;弱水流对植被水域床面切应力的大小及分布无明显影响;强水流时,床面切应力在植被水域先增大后逐渐减小并在植被水域后显著降低。     

A Lagrangian model for boundary layer growth and bed shear stress in the swash zone

A new model for the boundary layer development and associated skin friction coefficients and shear stress within the swash zone is presented. The model is developed within a Lagrangian reference frame, following fluid trajectories, and can be applied to both laminar flow and smooth turbulent flow. The model is based on the momentum integral approach for steady, flat-plate boundary layers, with appropriate modifications to account for the unsteady flow regime and flow history. The model results are consistent with previous measurements of bed shear stress and skin friction coefficients within the swash zone. These indicate strong temporal and spatial variation throughout the swash cycle, and a clear distinction between the uprush and backwash phase. This variation has been previously attributed the unsteady flow regime and flow history effects, both of which are accounted for in the new model. Fluid particle trajectories and velocity are computed using the non-linear shallow water wave equations and the boundary layer growth across the entire swash zone is estimated. Predictions of the bed shear stress and skin friction coefficients agree reasonably well with direct bed shear stress measurements reported by Barnes et al. (Barnes, M.P., O’Donaghue, T., Alsina, J.M., Baldock, T.E., 2009. Direct bed shear stress measurements in bore-driven swash. Coastal Engineering 56 (8), 853–867) and, for a given flow velocity, give stresses which are consistent with the bias toward uprush sediment transport which has consistently been observed in measurements. The data and modelling suggest that the backwash boundary layer is initially laminar, which results in the late development of significant bed shear during the backwash, with a transition to a turbulent boundary layer later in the backwash. A new conceptual model for the boundary layer structure at the leading edge of the swash is proposed, which accounts for both the no-slip condition at the bed and the moving wet–dry interface. However, further development of the Lagrangian Boundary Layer Model is required in order to include bore-generated turbulence and to account for variable roughness and mobile beds.     

Bed friction and dissipation in a combined current and wave motion

Two simple two-layer eddy viscosity models, which facilitate analytical solutions, are presented in order to describe the velocity field and associated shear stress in a combined current wave motion. The models, which have the same eddy viscosity in the current boundary layer, but different eddy viscosities in the wave boundary layer, cover together the whole rough turbulent regime. Straightforward definitions are made for the wave friction factor and the current friction factor for the combined motion, which are in accordance with the results for pure waves and pure currents. In this way one avoids the fictitious reference velocities and elliptic integrals which e.g. Grant and Madsen (1978, 1979) experienced. The two friction factors turn out to be functions of four dimensionless parameters. A detailed calculation procedure is presented. Comparison with laboratory experiments yields promising results. A new relation connecting dissipation and bed shear stress is also developed.     

Wave boundary layer over a stone-covered bed

This paper summarizes the results of an experimental investigation on wave boundary layers over a bed with large roughness, simulating stone/rock/armour block cover on the sea bottom. The roughness elements used in the experiments were stones the size of 1.4cm and 3.85cm in one group of experiments and regular ping-pong balls the size 3.6cm in the other. The orbital-motion-amplitude-to-roughness ratio at the bed was rather small, in the range a/k_s = 0.6–3. The mean and turbulence properties of the boundary-layer flow were measured. Various configurations of the roughness elements were used in the ping-pong ball experiments to study the influence of packing pattern, packing density, number of layers and surface roughness of the roughness elements. The results show that the friction factor seems to be not extremely sensitive to these factors. The results also show that the friction factor for small values of the parameter a/k_s does not seem to tend to a constant value as a/k_s → 0 (contrary to the suggestion made by some previous investigators). The present friction-factor data indicates that the friction factor constantly increases with decreasing a/k_s. An empirical expression is given for the friction factor for small values of a/k_s. The results further show that the phase lead of the bed friction velocity over the surface elevation does not seem to change radically with a/k_s, and found to be in the range 12°–23°. Furthermore the results show that the boundary-layer turbulence also is not extremely sensitive to the packing pattern, the packing density, the number of layers and the surface roughness of the roughness elements. There exists a steady streaming near the bed in the direction of wave propagation, in agreement with the existing work. The present data indicate that the steady streaming is markedly smaller in the case where the ping-pong balls are aligned at 45° to the wave direction than in the case with 90° alignment. Likewise, it is found that the steady streaming is relatively smaller in the case of the one-layer ping-pong-ball roughness than in the case of the two-layer situation.     

Incipient motion on a horizontal granular bed in non-breaking water waves

A criterion for initiation of sediment movement on a horizontal bed under non-breaking waves is established. Bagnold's sediment transport model is used. The dissipation rate of energy has been related to the length and velocity scales of the large-scale turbulence. The proposed equation is compared with the available laboratory results for fine and coarse material 0.1 mm < D ? 45 mm over a wide range of particle sizes, density ratios and liquid viscosities and a reasonable agreement between the two is obtained. An incipient motion hypothesis based on the development of vorticity is proposed.     

Flow and bed shear stresses in scour protections around a pile in a current

Transport of bed sediment inside and beneath the scour protection may cause deformation and sinking of the scour protection for pile foundations. This may reduce the stability of the mono pile and change the natural frequency of the dynamic response of an offshore wind turbine installed on it in an unfavourable manner. Using physical models and 3D computational fluid dynamic (CFD) numerical simulations, the velocity and bed shear stresses are investigated in complex scour protections around mono piles in steady current. In the physical model the scour protections consisted of an upper cover layer with uniformly distributed coarse stones and a lower filter layer with finer stones. For the numerical simulations, the Flow-3D software was used. The scour protection layers were simulated with different numerical approaches, namely regularly arranged spheres, porous media, or their combinations (hybrid models). Numerical simulations with one or four layers of cover stones without filter layer were first computed. Three additional simulations were then made for a scour protection with a cover layer and a single filter layer. Finally, a simulation of a full scale foundation and scour protection was made with porous media approach.Based on the physical and numerical results, a method to determine the critical stones size to prevent motion of the base sediment is established and compared to a full scale case with sinking of scour protection (Horns Rev I Offshore Wind Farm, Denmark). It is also found that the CFD simulations are capable of calculating the flow velocities when the scour protection is represented by regular arranged spheres, while the turbulence in general is underestimated. The velocity can also be calculated using porous media flow approach, but the accuracy is not as good as for spheres. The deviation is more severe for more complex scour protections. In general, computational models provide valuable information for the prediction and design of scour protections for offshore wind farms.     

Design of measuring instrument with whole direct method for bed shear stress under two-dimensional water-flow co-action

The present study aims at the design and making of measuring instrument of whole direct method for bed shear stress under two-dimensional water-flow co-action. The instrument combines the traditional strain gauge with a precise pressure gauge, and adopts the method directly measuring the difference between the lateral hydrodynamic pressure and different head pressures on both sides of the force plate. As a result, such an instrument solves a technical puzzle of the past strain gauge, i.e. the difficulty to set apart shear stress and lateral force. Static force test and sink test both prove that the instrument is precise, stable and applicable to the measurement of rough beds with different shear stresses.     

动、定砂床底部剪切力对比试验研究

在河口海岸工程中,常常会面临岸滩冲蚀、岸线演变、航道淤积、建筑物底部淘刷等涉及泥沙起动和输运的问题,而水流对底床的剪切力是研究泥沙起动与输运的重要参数。本文利用自行设计的底床剪切力测量装置,在不同流速的水流中,分别在固定砂床(定床)和可移动砂床(动床)上进行了底部剪切力的直接测量;同时,根据试验中声学多普勒流速仪(ADV)测得的流速信息,采用湍流动能法对底床剪切力进行了估算。结果显示:当比例系数取值0.19时,估算出的底床剪切力与测量值吻合较好。对测量结果进行分析后发现,流速较小、砂粒未起动时,动、定砂床上的底部剪切力大致相同;在有砂粒起动的情况下,动床上的底部剪切力比定床上的大,相对差值最大约20%。因此当涉及底床剪切力的问题时,需要先确认床面形式,然后再进行分析研究。     

波浪在Jarlan型开孔潜堤上的运动

The wave motion over a submerged Jarlan-type breakwater consisting of a perforated front wall and a solid rear wall was investigated analytically and experimentally. An analytical solution was developed using matched eigenfunction expansions. The analytical solution was confirmed by previously known solutions for single and double submerged solid vertical plates, a multidomain boundary element method solution, and experimental data. The calculated results by the analytical solution showed that compared with double submerged vertical plates, the submerged Jarlan-type perforated breakwater had better wave-absorbing performance and lower wave forces. For engineering designs, the optimum values of the front wall porosity, relative submerged depth of the breakwater, and relative chamber width between front and rear walls were 0.1–0.2, 0.1–0.2, and 0.3–0.4, respectively. Interchanging the perforated front wall and solid rear wall may have no effect on the transmission coefficient. However, the present breakwater with a seaside perforated wall had a lower reflection coefficient.     

Three-dimensional velocity measurements around bridge piers in gravel bed

The experimental results of time average velocity components measured around circular pier models during transient scour stage using acoustic Doppler velocimeter are shown for flow pattern and turbulence characteristics. Totally, four experiments were performed under clear water scour conditions in a model of gravel bed stream. Four circular pier models of diameter 6.6, 8.4, 11.5, and 13.5?cm were used for this study. Detailed controlled measurements on velocity components, and turbulence intensities near the pier and in scour hole at 0° and 180° plane are shown. Flow structure around a pier model in the presence of a scoured region was compared with the flow structure similarly noticed around all pier model runs by utilizing the observations taken at 0° and 180° plane from flow axis. Size of the primary vortex at 0° plane with largest diameter pier model in place (R4 run) is found to be maximum and was approximately 61% larger than that for smallest diameter pier model in place (R1 run). The time-averaged velocity components of turbulence intensities plots at 0° and 180° planes are also presented around each pier.     

A three-dimensional wave field over a bidirectionally periodic ripple bottom

For gravity wave trains propagating over an arbitrary wavy bottom, a perturbation expansion is developed to the second order so that the Bragg resonance effect of the ripple bottom on the free-surface wave can be analyzed. Both the resonant and non-resonant cases are treated and the singular behavior at resonance is avoided. This theory is successfully verified by reducing to simpler situations. Then, the analytical results for the special case of a unidirectional sinusoidal bottom are compared with experimental data for validation.