Laboratory flume studies on monochromatic wave-fine sandy bed interactions Part 2. Sediment suspensions

As reported in preceding paper (Part 1. Soil Fluidization), the observed phenomena of sediment suspensions above a fluidized sandy bed of Sand II (d₅₀ = 0.092 mm) under monochromatic wave actions are quantitatively investigated. The suspended sediment concentration (SSC) at a single point within 5 cm above the bed was synchronously measured with water waves and bed soil's pore pressures with an intrusive optical sediment-concentration probe. The measurements show that SSC initiates several wave cycles after initiation of bed soil's fluidized response and grows to a peak value mainly in the post-fluidization phase. Under similar wave loadings in the same test series, SSC is usually higher over a resonantly fluidized (RF) bed than over a non-resonantly fluidized (NRF) bed. On the contrary, only relatively low SCC can be identified above an unfluidized bed. The analyses illustrate that to certain extent, peak values of SSC are directly proportional to the thickness of fluidized soil layer d_f. Values of d_f usually decrease with repeated fluidized response, longer consolidation periods, and in deeper water depths. Once the fluidized responses initiate, pore pressures are generally much significantly amplified in both shallow fluidized soil layers and near below the fluidized layer, especially during the resonance event. The resulting depth gradients of dynamic pore pressure amplitudes in shallow layers are likely to have caused higher initial rises of SSC in a RF bed than in the subsequent NRF bed. Those in deeper layer should have contributed to sustain the fluidization state for further SSC increments. Immediately after termination of wave loading, re-deposited suspended sediments always result in a typical flat bed form. For a pre-fluidized bed, wave-induced drastic sediment suspensions are still obtainable very near above the bed with even a rather thin fluidized surface soil layer.     

Unfluidized soil responses of a silty seabed to monochromatic waves

A flume experimental study on unfluidized responses of a silty bed (d₅₀=0.05 mm) to monochromatic water waves had shown that pore pressure variations were generally poro-elastic in the bulk body and displayed two other characteristic features not found in previous laboratory sand tests. They were an immediately fluidized thin surface layer induced by wave stresses inside the seabed's boundary layer and a porous skeleton with internally suspended sediments due to channeled flow motions. The analyses verified that on soils beneath the measurement points, both features resulted in relatively small-step pore pressure build-ups, while the former played a primary role. Besides, laboratory observations confirmed that there were some near-bed sediment suspensions during wave actions resulting in a flat bed form over a silty bed compared to small-scaled ripples over a sandy bed with no clearly identified suspended sediments. These characteristic silt responses suggest that sediment transport is critically associated with the internal soil responses and some field-observed sediment suspensions near above sandy beaches can further be approached in the laboratory by utilizing fine-grained soils.     

Laboratory flume studies on monochromatic wave-fine sandy bed interactions: Part 1. Soil fluidization

Tests on two fine sandy soils (d₅₀ = 0.134 mm and 0.092 mm) under monochromatic wave actions were conducted in a wave flume of 37 m (L) by 1.2 m (H) by 1 m (W) to investigate characteristics of fluidized responses. The pore pressure measurements demonstrate only an unfluidized response in the coarser sandy bed, while in the finer one, two more feature fluidized responses. Fluidized responses are similarly classified into resonantly and non-resonantly fluidized according to Foda and Tzang [Foda, M.A., Tzang, S.-Y., 1994. Resonant fluidization of silty soil by water waves. J. Geophys. Res., 99-C10: 20463–20475.]. At a given depth, they are in principle defined by magnitude of fluidization ratio between excess pore pressure and static soil stresses and by the occurrence of a resonance event in the same test series. Inside the sandy bed, the excess pore pressures of a fluidized response are almost initiated simultaneously. Their magnitudes are essentially in static balance to the integrated weight of overlaying fluidized soil layers. Comparisons with previously reported data from a silty bed (d₅₀ = 0.05 mm) by Foda and Tzang have immediately indicated the importance of grain fraction. With less fine constituents, surface layers of the two sandy soils are less susceptible to fluidization. Resonance mechanism is evidently diminishing in a resonantly fluidized response, and re-fluidization becomes less potential in the subsequent tests. In a resonantly fluidized response, pore pressures at a given depth would start to resonantly grow from a fluidization ratio of 7–14%. In a few wave cycles, resonant growth subsides at a fluidization ratio of greater than 50%, which value increases with depth. The analyses clearly illustrate that fluidization tends to be initiated in surface layers and fast spreads into lower layers. Fluidization is dependent on finer constituting grains, smaller shear modulus G and permeability k and thinner boundary layers in bed soils. Measurements of previous silt tests are analyzed to show that lower limits of wave steepness on resonantly fluidizing a soil bed increase linearly with relative water depth ranging from 0.13 to 0.23. Data of present fine sand tests have preliminarily confirmed the linear trend. Over a fluidized sandy bed, similar vivid sediment suspensions were observed during wave generations as had been reported in silt tests.     

Effect of bed roughness on turbulent boundary layer and net sediment transport under asymmetric waves

This paper presents an investigation of the roughness effects in the turbulent boundary layer for asymmetric waves by using the baseline (BSL) k–ω model. This model is validated by a set of the experimental data with different wave non-linearity index, N_i (namely, N_i = 0.67, N_i = 0.60 and N_i = 0.58). It is further used to simulate asymmetric wave velocity flows with several values of the roughness parameter (a_m/k_s) which increase gradually, namely from a_m/k_s = 35 to a_m/k_s = 963. The effect of the roughness tends to increase the turbulent kinetic energy and to decrease the mean velocity distribution in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the turbulent kinetic energy and the mean velocity distribution is relatively unaffected. A new simple calculation method of bottom shear stress based on incorporating velocity and acceleration terms is proposed and applied into the calculation of the rate of bed-load transport induced by asymmetric waves. And further, the effect of bed roughness on the bottom shear stress and bed-load sediment transport under asymmetric waves is examined with the turbulent model, the newly proposed method, and the existing calculation method. It is found that the higher roughness elements increase the magnitude of bottom shear stress along a wave cycle and consequently, the potential net sediment transport rate. Moreover, the wave non-linearity also shows a big impact on the bottom shear stress and the net sediment transport.     

Variability of wave-induced ripple migration in wave-flume experiments and its implications for sediment transport

A thorough discussion of results from laboratory experiments with regular waves sheds light on the gap that lies between the sediment transport associated with ripple migration and the performance of a standard bedload transport formula in terms of bed shear concept. It is found that the extent of deviations of the bedload transport formula by Ribberink (1998) from the measured rate of sediment transport associated with ripple migration becomes systematically apparent under conditions of increasing settling time factor Ω_s (= η/(w₀T); η is the ripple height, w₀ the settling velocity and T the wave period). Re-examination of previous two field studies demonstrates a further reinforcement for phase-lag argument addressed in this paper.     

Suspended-sediment reference concentration under waves: field observations and critical analysis of two predictive models

Two commonly adopted but fundamentally different approaches for predicting time-averaged suspended-sediment reference concentration (C̄_REF) under waves are tested against field measurements and compared with each other. The first model relates C̄_REF to the cube of the non-dimensional skin friction, whereas the second model adopts a more complex function of excess skin friction incorporating the empirical constant γ₀. The dataset is from the zone of wave shoaling seaward of an open-coast surfzone and includes measurements of waves, currents, suspended sediment and bedforms. Estimates of C̄_REF are derived from acoustic backscatter data, and the seabed and suspension process are described from video footage. When waves were energetic, the bed was deformed into large hummocks; during less energetic conditions, the bed was rippled. The time-averaged concentration profiles over the ripples were consistent with settling flux balanced by pure gradient diffusion and a sediment diffusivity that is constant with elevation above the bed. C̄_REF in that case is shown to apply at z=0, where z is the elevation above the bed. Over the hummocks, there was a sheet flow at the base of the suspension and C̄_REF is shown to apply at z=1 cm. The concentration profiles over the hummocks implied sediment diffusivity that varied linearly with elevation within ∼10 cm of the bed and constant sediment diffusivity above that level. For both rippled and hummocky beds, γ₀ derived from the field data was found to be sensitive to the value assumed for critical stress for initiation of sediment motion, which could explain the range of values reported in the literature for γ₀. γ₀ was also found to vary in a complex way with skin friction, which suggests that the reference-concentration model based on excess skin friction is not correctly formulated. Nevertheless, two functions for γ₀ (one applying to rippled beds and the other to hummocky beds) were contrived to make the model fit the data. The model based on non-dimensional skin friction was found to be a good predictor of C̄_REF when a correction was made for flow contraction over ripples. The correction was not required for the hummocky bed, where sediment was being entrained in a thin sheet flow layer. The model based on non-dimensional skin friction correctly portrayed the relationship between flow and sediment response without contrivance and therefore should be the favoured approach in predicting reference concentration.     

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.     

An experimental study of seabed responses around a marine pipeline under wave and current conditions

Experiments on three types of soil (d₅₀=0.287, 0.057 and 0.034 mm) with pipeline(D=4 cm) either half buried or resting on the seabed under regular wave or combined with current actions were conducted in a large wave flume to investigate characteristics of soil responses. The pore pressures were measured through the soil depth and across the pipeline. When pipeline is present the measured pore pressures in sandy soil nearby the pipeline deviate considerably from that predicted by the poro-elasticity theory. The buried pipeline seems to provide a degree of resistance to soil liquefaction in the two finer soil seabeds. In the silt bed, a negative power relationship was found between maximum values of excess pore pressure p_max and test intervals under the same wave conditions due to soil densification and dissipation of the pore pressure. In the case of wave combined with current, pore pressures in sandy soil show slightly decrease with time, whereas in silt soil, the current causes an increase in the excess pore pressure build-up, especially at the deeper depth. Comparing liquefaction depth with scour depth underneath the pipeline indicates that the occurrence of liquefaction is accompanied with larger scour depth under the same pipeline-bed configuration.     

An experimental investigation of the velocity field under cnoidal waves over the asymmetric rippled bed

1 IntroductionIn coastal areas a ubiquitous phenomenon is theformation of ripples in the seabed. It is now widelyaccepted that the flow and sediment transport overseabed are vital in relation to erosion, surface wavedissipation and pollution dispersion et…     

The inception of sheet flow in oscillatory flow

A simple model is developed to study the inception of sheet flow in oscillatory flow based on the available experimental data. The inception of sheet flow in oscillatory flow is well defined by the simple model: A/d=KA²ω/ν+B, where A is the semi-excursion of wave orbital motion near the bed, d is the grain size, ω is the angular frequency, ν is the kinematic viscosity of water, and K and B are the coefficients and dependent on sediment properties only. The inception velocity of sheet flow derived from the model is shown to be the function of grain size d, oscillatory period T and specific sediment density s. For a given sediment, the inception velocity is found to increase sharply initially with T and then approach a constant at T>6.0 s. The present model is quite simple and gives good agreement with the available experimental data.     

Prediction of berm geometry using a set of laboratory tests combined with teaching–learning-based optimization and artificial bee colony algorithms

Understanding sediment movement in coastal areas is crucial in planning the stability of coastal structures, the recovery of coastal areas, and the formation of new coast. Accretion or erosion profiles form as a result of sediment movement. The characteristics of these profiles depend on the bed slope, wave conditions, and sediment properties. Here, experimental studies were performed in a wave flume with regular waves, considering different values for the wave height (H₀), wave period (T), bed slope (m), and mean sediment diameter (d₅₀). Accretion profiles developed in these experiments, and the geometric parameters of the resulting berms were determined. Teaching–learning-based optimization (TLBO) and artificial bee colony (ABC) algorithms were applied to regression functions of the data from the physical model. Dimensional and dimensionless equations were found for each parameter. These equations were compared to data from the physical model, to determine the best equation for each parameter and to evaluate the performances of the TLBO and ABC algorithms in the estimation of the berm parameters. Compared to the ABC algorithm, the TLBO algorithm provided better accuracy in estimating the berm parameters. Overall, the equations successfully determined the berm parameters.     

On the response of a Coulomb‐damped poroelastic bed to water waves

Abstract

The problem of forced vibration of a slightly inelastic porous bed by water waves is treated analytically on the basis of a linearized expression of the nonlinear damping term for the grain‐to‐grain friction in bed soils and the linear theory by Biot (1962a [Jour. Appl. Physics, 33:1482–1498]) on the elastic wave propagation in porous media. A dispersion relation of water waves is obtained as a function of wave frequency, water depth, permeability, Poisson's ratio, rigidity, and specific loss of bed soil. Three types of elastic waves are induced in a bed by water waves: a shear wave and a compressional wave in the skeletal frame of soil, and a compressional wave in the pore fluid. The compressional wave, due to the motion of the pore fluid relative to the skeletal frame of soil, is highly damped by the viscosity of pore fluid and only a short range effect near the boundaries of discontinuity, such as a sea‐seabed interface. The seabed response to water waves is characterized by the two Mach numbers, i.e., the ratio of water‐wave speed to shear‐wave speed in soil and the ratio of water‐wave speed to compressional‐wave speed in soil. Most of the water‐wave propagation problems fall into the subsonic flow condition, where elastic waves in the bed travel faster than water waves.

For sandy beds, generally the speeds of compressional and shear waves are much higher than the phase velocity of the water wave. For this case, the solution of the Coulomb‐damped poroelastic bed response presented in this paper approaches the solution of the massless poroelastic bed response in Yamamoto et al. (1978 [Jour. Fluid Mech., 87(1): 193–206]). The damping of water waves due to internal grain‐to‐grain friction is equally or more significant than the damping due to percolation in sand beds.

For clay beds, the speed of the shear wave in soil becomes low and comparable to the phase speed of the water wave. The bed motion for this case is considerably amplified due to the near‐resonance vibration of shear mode of bed vibration. The water wavelength on a clay bed is significantly shortened compared to the water wavelength over a rigid bed. The water wave damping due to internal grain‐to‐grain friction in soil becomes much larger compared to the water wave damping due to percolation in clay beds. Long water waves over a soft clayey bed attenuate within several wavelengths of travel distance.     

Stability of submerged rock berms exposed to motion of liquefied soil in waves

The paper describes the results of an experimental study on the behaviour of a submerged rock berm in liquefied backfill soil. The soil is liquefied by waves, and the rock berm is subject to the orbital motion of the liquefied soil. The soil used in the experiments was silt with d₅₀=0.075 mm. Various berm materials were used, stones of size 0.74-2.5 cm, plastic balls of size 3.6 cm, brass of size 2.5 cm and steel of size 1.0 cm. The experiments show that rock berms that are stable under very large waves can be unstable when they are exposed to the motion of liquefied soil. The limited data obtained in the study were plotted as a function of the mobility number versus the Keulegan-Carpenter number for the range of the Reynolds number of the tests. The critical mobility number corresponding to the incipient motion of the berm stones is determined. Recommendations are made as to how the present findings can be implemented in practice.     

Cover stones on liquefiable soil bed under waves

The paper describes the results of an experimental study on the behavior of cover stones on a liquefiable soil bed exposed to a progressive wave. The soil was silt with d₅₀ = 0.098 mm. Stones, the size of 4 cm, were used as cover material. The effect of packing density of stones, and that of number of stone layers (including the effect of an intermediate filter layer) were investigated. Pore pressure was measured across the soil depth. The experiments show that the soil liquefaction depended mainly on two parameters: the packing density of stones, and the number of stone layers. When the liquefaction occurs, stones sink in the soil. Mechanisms of liquefaction and sinking are described, and practical guidelines are recommended.     

底床粉质土液化下波动水体含沙量垂向L型分布特征试验研究

根据现场大风浪条件下的实测资料,粉质土海岸水体中的含沙量沿垂向具有上部均匀、近底突增的分布特点,即呈L型分布特征。利用黄河三角洲粉质土作为试验底床开展波浪水槽试验研究,揭示了底床粉质土在波浪作用下产生液化情况的水体含沙量沿垂向存在L型分布特征。根据试验现象以及悬沙粒度变化,分析认为底部高含沙层的形成主要受粉质土液化后细颗粒析出的影响,上部水体中悬沙由湍流脉动维持。对粉质土海岸大风天气期间水体含沙量剧烈增加采用波致粉质土液化的观点进行了初步解释。     

Direct numerical simulations of flow over two-dimensional and three-dimensional ripples and implication to sediment transport: Steady flow

A well resolved and highly accurate direct numerical simulation (DNS) solver has been developed to understand the implication of hydrodynamics to sediment transport. In the first part of the study we focus on steady flow over two-dimensional and three-dimensional ripples at two Reynolds numbers Re_τ = 180 and 400 (defined by channel half-height and wall-friction velocity) in a channel geometry. The DNS scheme is based on a fourth-order vertical velocity and second-order vertical vorticity formulation, which resolves the difficulties in pressure boundary condition encountered when solving the Navier–Stokes equations. The complex boundary introduced due to the ripples has been imposed in the Cartesian domain using an elegant immersed boundary method. Detailed hydrodynamic analysis has revealed turbulence statistics (in particular, the higher order) and henceforth, the flow structures are sensitive — whether the ripples are two-dimensional or three-dimensional. The importance of fluctuating component of the bottom stress in addition to its mean component; and its significance to sediment transport and ripple migration speed have been investigated.     

High Frequency Current Fluctuations and Cross-shelf Flows around the Pycnocline near the Shelf Break in the East China Sea

Relation between internal waves with short time scale and density distribution near the shelf break in the East China Sea is studied utilizing moored current meters, thermometers and conductivity-temperature-depth (CTD) casts. A well developed pycnocline was frequently observed around 150–200 m depth near the shelf break accompanied with the development of internal waves with short time scale. During the cruise in May 1998, the intensified internal wave motion with short time scale and the distinct offshore flow were observed just below the lower pycnocline, which shoaled and extended above the shelf area. It is suggested that vertical mixing generated by amplified internal waves would produce cross-shelf ageostophic density current around the pycnocline. During the cruise in May 1999, on the other hand, the lower pycnocline was located offshore below the shelf break, and the internal wave motion was amplified just above the lower pycnocline. In this case, the offshore flow should be generated above the lower pycnocline, but vertical profiles of current velocity were not obtained because acoustic Doppler current profiler (ADCP) data were not available around the lower pycnocline.     

Wave damping over artificial Posidonia oceanica meadow: A large-scale experimental study

An experimental study, conducted in the large wave flume of CIEM in Barcelona, is presented to evaluate the effects of Posidonia oceanica meadows on the wave height damping and on the wave induced velocities. The experiments were performed for irregular waves from intermediate to shallow waters with the dispersion parameter h/λ ranging from 0.09 to 0.29. Various configurations of the artificial P. oceanica meadow were tested for two stem density patterns (360 and 180 stems/m²) and for plant's height ranging from 1/3 to 1/2 of the water depth.The results for wave height attenuation are in good agreement with the analytical expressions found in literature, based on the assumption that the energy loss over the vegetated field is due to the drag forces. Based on this hypothesis, an empirical relationship for the drag coefficient related to the Reynolds number, Re, is proposed. The Reynolds number, calculated using the artificial P. oceanica leaf width as the length scale and the maximum orbital velocity over the meadow edge as the characteristic velocity scale, ranges from 1000 to 3500 and the drag coefficient C_d ranges from 0.75 to 2.0.The calculated wave heights, using the analytical expression from literature and the proposed relationship for the estimation of C_d, are in satisfactory agreement with those measured. Wave orbital velocities are shown to be significantly attenuated inside the meadow and just above the flume bed as indicated by the calculation of an attenuation parameter. Near the meadow edge, energy transfer is found in spectral wave velocities from the longer to the shorter wave period components. From the analysis it is shown that the submerged vegetation attenuates mostly longer waves.     

Megacusps on rip channel bathymetry: Observations and modeling

The formation of beach megacusps along the shoreline of southern Monterey Bay, CA, is investigated using time-averaged video and simulated with XBeach, a recently developed coastal sediment transport model. Investigations focus on the hydrodynamic role played by the bay's ever-present rip channels. A review of four years of video and wave data from Sand City, CA, indicates that megacusps most often form shoreward of rip channels under larger waves (significant wave height (H_s) = 1.5–2.0 m). However, they also occasionally appear shoreward of shoals when waves are smaller (H_s ~ 1 m) and the mean water level is higher on the beach. After calibration to the Sand City site, XBeach is shown to hindcast measured shoreline change moderately well (skill = 0.41) but to overpredict the erosion of the swash region and beach face. Simulations with small to moderate waves (H_s = 0.5–1.2 m) suggest, similar to field data, that megacusps will form shoreward of either rip channels or shoals, depending on mean daily water level and pre-existing beach shape. A frequency-based analysis of sediment transport forcing is performed, decomposing transport processes to the mean, infragravity, and very-low-frequency (VLF) contributions for two highlighted cases. Results indicate that the mean flow plays the dominant role in both types of megacusp formation, but that VLF oscillations in sediment concentration and advective flow are also significant.     

Drag and Sediment Dispersion Over Sand Waves

Estimates of the drag coefficient over sand waves during calm weather in the southern North Sea have been obtained from measurements of the water slope and currents at different heights (z) above the sea-bed using the log profile and momentum balance methods. An observed phase difference between principal terms in the momentum balance equation is examined theoretically. Drag coefficient estimates are found to agree broadly with previous studies. Owing to bedform asymmetry, average drag coefficient values obtained atz=1 m (C₁₀₀) are found to be 0·0021 and 0·0029 for flood and ebb tides, respectively. Systematic changes in bed roughness are not detected. Using a momentum balance approach, the average drag coefficient value (C_d) atz=10 m is found to be 0·0056. Changes in 10-min averageC_dvalues over sand waves during the tidal cycle are found to be small with bedform asymmetry having no detectable effect. Correlation betweenC_dandC₁₀₀is found to be poor and separation of skin friction and form drag terms is not possible with existing measurements. The inclusion of form drag inC₁₀₀values at the present site leads to over-estimation of the bed shear stress ({q) available to mobilize and transport sediment. Mobile sediment, detected through the use of tracers and a transmissometer, was not found to have any measurable effect on eitherC_dorC₁₀₀in calm weather conditions.