Threshold conditions for sand movement on a rippled bed

Flume experiments have been carried out to determine the threshold of grain movement on a rippled bed. The results indicate a form drag component of between 5 and 12 times the skin friction. The threshold of motion on the rippled sand bed can be represented by = 70D ^0.3 in whichD > 0.09 cm.     

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.     

Experimental investigations on developments of velocity field near above a sandy bed during regular wave-induced fluidized responses

Regular waves were applied in a laboratory flume to investigate the evolutions of the velocity fields near above a fine sandy bed (d₅₀=0.073 mm) during fluidized responses. Measurements of 2D velocity components and suspended sediment concentration (SSC) at 1 cm above the bed in addition to water surface displacements and sub-soil pore pressures were carried out with an acoustic Doppler velocimeter and an optical probe. The results have shown similar three typical soil responses including one unfluidized and two fluidized responses to previous report in other fine-grained soil beds. In the post- and pre-fluidized stages of a resonantly fluidized response, amplitudes of horizontal velocity component can be decreased by a maxima value of 50% while vertical components can be amplified up to 5 times larger. The developments of near-bed velocity field become less significant in consecutive non-resonantly fluidized responses. Particularly, the evolutions of the velocity field are closely dependent on the deepening of fluidized surface soil layers d_f and the characteristics of soil fluidization responses. The amplified vertical velocity components are clearly contradictory to the dissipated overloading waves near above a fluidized bed but are critical to much drastic sediment suspensions by interactions between overloading waves and fluidized bed soils.     

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.     

Propagation of water waves over permeable rippled beds

Unsteady two-dimensional Navier-Stokes equations and Navier-Stokes type model equations for porous flow were solved numerically to simulate the propagation of water waves over a permeable rippled bed. A boundary-fitted coordinate system was adopted to make the computational meshes consistent with the rippled bed. The accuracy of the numerical scheme was confirmed by comparing the numerical results concerning the spatial distribution of wave amplitudes over impermeable and permeable rippled beds with the analytical solutions. For periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. The trajectories of the fluid particles that are initially located close to the ripples were also determined. One of the main results herein is that under the action of periodic water waves, fluid particles on an impermeable rippled bed initially moved back and forth around the ripple crest, with increasing vertical distance from the rippled wall. After one or two wave periods, they are then lifted towards the next ripple crest. All of the marked particles on a permeable rippled bed were shifted onshore with a much larger displacement than those on an impermeable bed. Finally, the flow fields and the particle motions close to impermeable and permeable beds induced by a solitary wave are elucidated.     

Fundamental study for morphodynamic modelling: Sand mounds in oscillatory flows

Experiments on sand mounds in oscillatory flow, undertaken in controlled, large-scale laboratory conditions, have produced well-defined data sets for model comparison. Three bathymetries with different levels of submergence, including a surface-piercing case, were tested. The maximum slope was about 1:5.5. Sediment transport is due to bed load with ripple formation. The principal time-dependent bulk parameters are the vertical distance of the centre of gravity above the base and the volume of the mound. A semi-implicit finite-volume depth-averaged hydrodynamic model is used to drive morphodynamics, using van Rijn's sediment flux model generalized to take account of bed slope, and some justification is given for depth-averaged modeling in these conditions. Starting the model runs with the conditions at the end of the first cycle avoided initial atypical physical behaviour. In general good predictions were obtained with an angle of repose reduced from the standard value of about 30° for stationary beds to 15°. For these situations, morphodynamics was largely unaffected by a hydrodynamic roughness height in the range 2.5D₅₀ to 51D₅₀, with larger values accounting for ripple roughness. The reduced angle of repose may be physically expected with mobile beds but this specific value is only expected to be suited to this form of bed motion. In one case an exaggerated ripple formed near the top of the mound reducing agreement with experiment. For the submerged case with normal ripple structure excellent predictions were obtained. For the initially surface-piercing mound, the time of submergence was better predicted with a 30° angle of repose, presumably due to the prominent influence of the near stationary bed near the wet/dry interface, although long term predictions were better predicted with 15°. The occurrence of vortex shedding in the first cycle modeled was in agreement with experimental observation.     

Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method

In this paper, a well-developed numerical model based on the immersed boundary (IB) method is used to study oscillatory flows over a bed with large-amplitude ripples in a systematic manner. The work shows that the complex flow over the rippled bed can be numerically dealt with in Cartesian coordinate by the IB method and that the IB method is able to provide main features of the flows near the ripples. An accurate simulation of vortices generation as a result of flow separation at the rippled bed is obtained. It is found that the oscillatory flows start to separate during the flow deceleration when the Keulegan–Carpenter (KC) number is small. The steady streaming for various ripple steepness is simulated and the criterion for separating the single and double structure streaming is also discussed. Moreover, a new type of steady streaming which consists of a pair of embedded recirculations in the vicinity of the ripple trough is obtained for relatively steep ripples in this work. The numerical results, including the steady streaming in particular, may be helpful to improve the understanding of the sediment transport and the seabed evolution with natural ripples under sea waves.     

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.     

Surface layer mixing during the SAGE ocean fertilization experiment

Vessel-based observations of the oceanic surface layer during the 14-day 2004 SAGE ocean fertilization experiment were conducted using ADCP, CTD and temperature microstructure in a frame of reference moving with a patch of injected SF₆ tracer. During the experiment the mixed layer depth z_mld ranged between 50 and 80 m, with several re-stratifying events that brought z_mld up to less than 40 m. These re-stratifying events were not directly attributable to local surface-down development of stratification and were more likely associated with horizontal variation in density structure. Comparison between the CTD and a one-dimensional model confirmed that the SAGE experiment was governed by 3-d processes. A new method for estimating z_mld was developed that incorporates a component that is proportional to density gradient. This highlighted the need for well-conditioned near-surface data which are not always available from vessel-based survey CTD profiles. A centred-displacement scale, L_c, equivalent to the Thorpe lengthscale, reached a maximum of 20 m, with the eddy-centroid located at around 40 m depth. Temperature gradient microstructure-derived estimates of the vertical turbulent eddy diffusivity of scalar (temperature) material yielded bin-averaged values around 10⁻³ m² s⁻¹ in the pycnocline rising to over 10⁻² m² s⁻¹ higher in the surface layer. This suggests transport rates of nitrate and silicate at the base of the surface layer generate mixed layer increases of the order of 38 and 13 mmol/m²/day, respectively, during SAGE. However, the variability in measured vertical transport processes highlights the importance of transient events like wind mixing and horizontal intrusions.     

A quasi-similarity between wind waves and solid surfaces in their roughness characteristics

A formulation for the aerodynamic roughness length of air flow over wind waves $$z_0 = \gamma {\text{ }}u_* /\sigma p$$ which was proposed by Toba (1979) and Toba and Koga (1986) from dimensional considerations with some data analysis, is shown to correspond with a formulation for irregular solid surfaces $$(z_0 /h) = a(h/l)^{1 + \beta } $$ which resulted from work by Woodinget al. (1973) and Kustas and Brutsaert (1986);u _* is the friction velocity,σ _p the spectral peak frequency of wind waves,h the mean height of the solid obstacles,l the mean distance between their crests, andα,Β, andγ are constants. This correspondence is reached by the existence of a statistical 3/2-power law and an effective dispersion relationship for wind waves. Because both approaches of parameterizingz ₀ were arrived at independently, they provide each other mutual reinforcement.     

An ichnological-assemblage approach to reservoir heterogeneity assessment in bioturbated strata: Insights from the Lower Cretaceous Viking Formation,Alberta, Canada

Facies-scale trends in porosity and permeability are commonly mapped for reservoir models and flow simulation; however, these trends are too broad to capture bed and bed-set heterogeneity, and there is a need to up-scale detailed, bed-scale observations, especially in low-permeability reservoir intervals. Here we utilize sedimentology and ichnology at the bed- and bedset-scale to constrain the range of porosity and permeability that can be expected within facies of the Lower Cretaceous Viking Formation of south-central, Alberta, Canada.Three main facies were recognized, representing deposition from the middle shoreface to the upper offshore. Amalgamated, hummocky cross-stratified sandstone facies (Facies S_HCS) consist of alternations between intensely bioturbated beds and sparsely bioturbated/laminated beds. Trace fossil assemblages in bioturbated beds of Facies S_HCS are attributable to the archetypal Skolithos Ichnofacies, and are morphologically characterized by vertical, sand-filled shafts (VSS). Bioturbated beds show poor reservoir properties (max: 10% porosity, mean: 85.1 mD) compared to laminated beds (max 20% porosity, mean: 186 mD). Bioturbated muddy sandstone facies (Facies S_B) represent trace fossil assemblages primarily attributable to the proximal expression of the Cruziana Ichnofacies. Four ichnological assemblages occur in varying proportions, namely sediment-churning assemblages (SC), horizontal sand-filled tube assemblages (HSF), VSS assemblages, and mud-filled, lined, or with spreiten (MLS) assemblages. Ichnological assemblages containing horizontal (max: 30% porosity, mean: 1.28 mD) or vertical sand-filled burrows (max: 10% porosity, mean: 2.2 mD) generally have better reservoir properties than laminated beds (max: 20% porosity, mean: 0.98 mD). Conversely, ichnological assemblages that consist of muddy trace fossils have lower porosity and permeability (max 10% porosity, mean: 0.89 mD). Highly bioturbated, sediment churned fabrics have only slightly higher porosity and permeability overall (max: 15% porosity, mean: 1.29 mD). Bioturbated sandy mudstone facies (Facies M_B) contain ichnofossils representing an archetypal expression of the Cruziana Ichnofacies. Four ichnological assemblages occur throughout Facies M_B that are similar to Facies S_B; SC, HSF, VSS, and MLS assemblages. The SC (max: 15% porosity, mean: 21.67 mD), HSF (max: 20% porosity, mean: 3.79 mD), and VSS (max: 25% porosity, mean: 7.35 mD) ichnological assemblages have similar or slightly lower values than the laminated beds (max: 20% porosity, mean: 10.7 mD). However, MLS assemblages have substantially lower reservoir quality (max: 10% porosity, mean: 0.66 mD).Our results indicate that the most likely occurrence of good reservoir characteristics in bioturbated strata exists in sand-filled ichnological assemblages. This is especially true within the muddy upper offshore to lower shoreface, where vertically-oriented trace fossils can interconnect otherwise hydraulically isolated laminated sandstone beds; this improves vertical fluid transmission. The results of this work largely corroborate previous findings about ichnological impacts on reservoir properties. Unlike previous studies, however, we demonstrate that the characteristics of the ichnological assemblage, such as burrow form and the nature of burrow fill, also play an important role in determining reservoir characteristics. It follows that not all bioturbated intervals (attributed to the same facies) should be treated equally. When upscaling bed-scale observations to the reservoir, a range of possible permeability-porosity values can be tested for model sensitivity and to help determine an appropriate representative elementary volume.     

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.     

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.     

Phase-lag effects in sheet flow transport

The inception of the sheet flow regime as well as the effects of the phase lag when the sheet flow regime is established were investigated for oscillatory flows and combined steady and oscillatory flows. A new criterion for the inception of sheet flow is proposed based on around 300 oscillatory flow cases from experiments. This criterion was introduced in the Camenen and Larson [Camenen, B., Larson, M., 2005. A bedload sediment transport formula for the nearshore. Estuarine, Coastal and Shelf Science 63, 249–260.] bed load formula in order to take into account phase-lag effects in the sheet flow regime. The modification of the Camenen and Larson formula significantly improves the overall agreement with data and yields a correct behavior in relation to some of the main governing parameters, which are the median grain size d₅₀, the orbital wave velocity U_w, and the wave period T_w. The calibration of the new formula was based on more than 200 experimental data values on the net sediment transport rate for a full wave cycle. A conceptual model was also proposed to estimate the ratio between sediment transport rate with and without phase lag, (r_pl = q_s,net / q_s,net,ϕ=0). This simple model provides accurate results and may be used together with any quasi-steady model for bed load transport.     

The influence of seagrass beds on carbonate sediments in the Bahamas

Chemical variables were measured in calcium-carbonate-rich sediments inhabited by the dominant tropical seagrass, Thalassia testudinum, and in adjacent seagrass-free sediments at several locations in the Bahamas Islands. Pore-water alkalinity and p_CO2 were consistently greater, while pH was consistently lower in sediment-pore waters within seagrass beds. The ammonium and molybdate-reactive phosphate concentrations in sediment-pore water were variable for vegetated, compared with unvegetated, sample locations.Thalassia testudinum can generate very large amounts of organic matter within calcium-carbonate-rich sediments. However, little of the organic matter is retained in the sediment and the effect of that organic matter on pore water chemical factors appears to be surprisingly small. These observations are markedly different from those for seagrass beds in high latitude clastic sediments and in Syringodium filiforme seagrass beds near San Salvador Island, where major influences of the seagrass beds on sediment chemistry have been observed. The generally coarser grain size of the carbonate sediments may be a primary factor contributing to these differences.     

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.     

A method for evaluating statistical errors associated with logarithmic velocity profiles

A logarithmic velocity profile is often fitted to velocity data in order to calculate the friction velocity (u _*) and typify the surface texture by a roughness length (z _o ). A method is given for estimating the errors in these parameters as calculated by this method. An example is given in which the size of the error is compared with the fluctuations that typically occur in the time seriesu _*(t) andz _o (t).     

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.