Rippled Bed Research Articles

An adaptation of the immersed boundary method for turbulent flows over three-dimensional coastal/fluvial beds

A modification of the immersed boundary method is presented, using the discrete-forcing concept, for the large-eddy simulation of turbulent flows over coastal/fluvial beds. The method was adapted to be compatible with the usual surveying practice to obtain the bathymetry of coastal/fluvial beds, i.e., point measurements of water depth. An efficient fluid/solid point identification process and an improved trilinear interpolation algorithm were implemented for more accurate boundary forcing expressions and easier algorithm implementation. The temporal and spatial discretizations of the filtered Navier–Stokes equations were based on a time-splitting projection scheme and second-order finite-differences, respectively. The method was applied to the simulation of an oscillatory flow over bed ripples and a unidirectional flow over bed dunes. The accuracy of the computational results was verified by comparison to existing numerical and experimental results in the literature.

Large‐Eddy Simulation of Turbulent Oscillatory Flow Over Three‐Dimensional Transient Vortex Ripple Geometries in Quasi‐Equilibrium

AbstractVortex ripples induced by oscillatory flow display straight crests at equilibrium, but they develop transient three‐dimensional (3‐D) bedform geometries when transitioning from one equilibrium state to another due to changes in the oscillatory flow. Large‐eddy simulations were performed of oscillatory flow over 3‐D bedform defects associated with an increase of the orbital motion amplitude, similar to what might happen during the waxing phase of a storm. The objective is to determine the intercorrelation between flow processes and evolution of 3‐D bedform defects toward an equilibrium two‐dimensional (2‐D) state of vortex ripples. Results are presented for oscillatory flows over fixed ripples with sinusoidal crests in the spanwise direction, which introduce slope asymmetries on opposite sides of the crests, during different transient states. It was found that steep‐sloped regions of the bedforms are associated with thicker recirculation areas, whereas in more gently sloped regions thinner recirculation vortices exist. Furthermore, streamwise vortical structures and significant secondary flow develop in the vicinity of sinusoidal crests, relative to straight crests. These flow structures might be responsible for the gradual reformation of the rippled bed, as they induce higher bed shear stresses, that is, increasing bed sediment transport, and they diffuse turbulent kinetic energy to higher levels above crests, that is, increasing suspended sediment transport, relative to equilibrium 2‐D ripples. Finally, the period‐averaged currents around the sinusoidal crests exhibit higher velocities on the steep‐sloped side than on the mild‐sloped one, also likely contributing to sediment transport and bed reformation toward a 2‐D configuration.

Sediment suspension and bed morphology in a mean shear free turbulent boundary layer

We experimentally characterize turbulence in boundary layers generated by different levels of nearly isotropic homogeneous turbulence over flat impervious boundaries and over non-cohesive sediment beds with and without ripples. We use randomly actuated synthetic jet arrays (RASJA – Variano & Cowen, J. Fluid Mech., vol. 604, 2008, pp. 1–32) to generate high Reynolds number ( ) turbulence with negligible secondary mean flows or mean bed shear. The isotropic region and the boundary layer connecting this isotropic region to the bed are investigated using particle image velocimetry measurements. Surprisingly, we observe the development of ripples on the sediment bed ( ). We draw comparisons between the mean shear free turbulent boundary layer formed above a flat stationary solid boundary (Johnson & Cowen, J. Fluid Mech., vol. 835, 2018, pp. 217–251) and its sediment counterpart by considering statistical metrics including root mean square velocity fluctuations, turbulent kinetic energy, dissipation rates, production, integral scales, Reynolds stresses and spatial spectra. Using an 8 × 8 RASJA, we find the damping of turbulence and dissipation rates at flat and rippled sediment beds with low levels of suspended sediments relative to an impermeable glass bed, whereas with a 16 × 16 RASJA we find the enhancement of turbulence and dissipation rates of a resuspending sediment bed relative to an impermeable glass bed. We hypothesize that this may be a result of a change in direction of the bed-normal mean flows at the porous boundary. We explore a relationship between the integral length scale of the turbulence with the resulting sediment ripple spacing by varying the mean on-time of the RASJA algorithm.

Evaluation of Stage–Discharge Relationships in Alluvial Rivers (Case Study: Shahroud River, Qazvin province, Iran)

Many rivers are classified in alluvial rivers. Stage–discharge curve of these rivers is reliable just in measured conditions and for the sections by the use of measured data. Most of the stage–discharge equations are not able to consider flow resistance, and it causes some errors in qualitative and quantitative modeling. Therefore, it seems necessary to determine the accuracy of stage–discharge curve methods in the river sections without hydrometric stations. In this study, Einstein and Barbarossa (Trans ASCE 117:1121–1132, 1952), Engelund and Hansen (A monograph on sediment transport in alluvial streams. Technical University of Denmark, Copenhagen, Denmark, 1967) and White et al. (A new general method for predicting the frictional characteristics of alluvial streams. Report No IT 187. Hydraulics Research Station, Wallingford, England, 1979) methods were investigated in four hydrometric stations in Shahroud River. To do so, after field data collection, the stage–discharge curve of studied hydrometric stations was obtained by the mentioned methods. Results revealed that effect of flow resistance factors increased in maximum discharge. Einstein and Barbarossa’s (1952) method enjoyed the most accuracy in the stations with ripple bed form and discharge less than 20 cms. By increasing discharge or changing the bed form, the accuracy of this method decreased, so in this condition Engelund and Hansen (1967) and White et al.’s (1979) methods showed reliable accuracy. In the rivers with anti-dune bed form, White et al.’s (1979) equation had the most accuracy. Additionally, evaluating the effect of bed form, discharge, bed slope and bed load sediment size indicated that all the methods are highly sensitive to discharge flow and river bed form; on the other hand, bed slope and bed load sediment size are not determining factors in choosing proper method for the development of stage–discharge curve in alluvial rivers.

Steady Streaming Induced by Asymmetric Oscillatory Flows over a Rippled Bed

The flow induced by progressive water waves propagating over a rippled bed is reproduced by means of the numerical solution of momentum and continuity equations to gain insights on the steady streaming induced in the bottom boundary layer. When the pressure gradient that drives the flow is given by the sum of two harmonic components an offshore steady streaming is generated within the boundary layer which persists in the irrotational region. This steady streaming depends on the Reynolds number and on the geometrical characteristics of the ripples. Nothwithstanding the presence of a steady velocity component, the time-average of the force on the ripples vanishes.

Modeling of net sediment transport rate due to wave-driven oscillatory flow over vortex ripples

A one-dimensional-vertical (1-DV) model is developed for predicting net ripple-averaged sediment transport rate over a rippled bed under wave-driven oscillatory boundary layer flows. This model is extended from a sheet-flow model developed by Yuan and Tan [52], which is able to account for the effect of wave nonlinearity (velocity skewness and asymmetry) together with a mild bottom slope. The rippled bed is conceptualized as a flat bed with a large bottom roughness accounting for the presence of ripples in modeling the boundary layer flow and sediment concentration. The vortex-shedding effect is incorporated into the model by adding a pick-up rate on top of the one induced by skin-friction turbulence. The model performance is good for 2-D ripples under periodic oscillatory flows, which are used for calibrating the model. We also showed that it is applicable for 3-D ripples and irregular oscillatory flows. In addition, this 1-DV model can capture some intermediate ripple- and period-averaged physical processes, e.g., cycle averages of velocity, sediment concentration and sediment flux, suggesting that the model correctly captures the underlying physics. The relative importance of vortex-shedding effect is shown to be controlled by ripple dimension, sediment grain size and the driving mechanisms for net sediment transport rates.

An experimental study of net sediment transport rate due to acceleration-skewed oscillatory flows over rippled seabeds

Wave-driven near-bed oscillatory flows can be acceleration-skewed due to the onshore leaning of shoaling waves in shallow coastal waters. A full-scale experimental study was conducted to investigate the acceleration-skewness-induced net sediment transport rate over coarse-sand rippled beds. A dataset of ripple geometry, migration and net sediment transport rate has been produced for oscillatory flows with different degrees of acceleration skewness. The steepness of equilibrium ripples decreases due to the effect of acceleration skewness and a consistent onshore ripple migration with a very low speed was observed for all the tests involving acceleration-skewed flows. The measured ripple-averaged net sediment transport rate is always in the direction of highest-acceleration (onshore) and increases with acceleration skewness. The magnitude of net transport rate is comparable to that due to velocity skewness, highlighting the necessity of considering acceleration skewness in modeling coastal sediment transport. The measurements can be well predicted by the formula of van der A et al. (2013), of which the calibration dataset does not cover such test conditions. The good model-data agreement suggests that sheet-flow and ripple-bed conditions share similar mechanisms by which acceleration skewness produces net transport rate.

Wave-Induced Oscillatory Flow Over a Sloping Rippled Bed

In this paper, the findings of an experimental analysis aimed at investigating the flow generated by waves propagating over a fixed rippled bed within a wave flume are reported. The bottom of the wave flume was constituted by horizontal part followed by a 1:10 sloping beach. Bedforms were generated in a previous campaign performed with loose sand, and then hardened by means of thin layers of concrete. The flow was acquired through a Vectrino Profiler along two different ripples, one located in the horizontal part of the bed and the second over the sloping beach. It was observed that, on the horizontal bed, near the bottom, ripple lee side triggered the appearance of an onshore directed steady streaming, whereas ripple stoss side gave rise to an offshore directed steady streaming. On the sloping bed, a strong return current appears at all positions, interacting with the rippled bottom. The turbulence is non-negligible within the investigated water depth, particularly when velocities were onshore directed, due to flow asymmetry. Turbulence caused a considerable flow stirring which, above a non-cohesive bed, could lift the sediment up in the water column and give rise to a strong sediment transport.

The mean suspended sediment concentration profile of silty sediments under wave-dominant conditions

Suspended sediment concentration (SSC) is one of the fundamental topics in sediment study. The parameterization of the SSC profile of silty sediments is still under-researched. This study focuses on the mean SSC profile for silty sediments under non-breaking wave-dominant conditions. First, inspired by a 1DV model, different types of the distribution of mean eddy viscosity were proposed, i.e., a toe-type distribution over flat bed and a constant-toe type distribution over rippled bed. Then, the time-averaged diffusion equation for suspended sediment transport was analytically solved, and expressions for the mean SSC profiles were derived. The expressions involve several basic physical processes, including the effects of bed forms, stratification, hindered settling and mobile bed. Verification using a number of experimental datasets showed that the proposed expressions can properly calculate the mean SSC for silt and are applicable for sand as well. In conclusion, this research provides an approach to estimate the mean SSC for silty sediments under wave-dominant conditions, which is expected to be applicable for engineering practice and numerical modelling.

Non-cohesive and cohesive sediment transport due to tidal currents and sea waves: A case study

A model is proposed to determine the sediment transport rate generated by the combined action of sea waves and tidal currents, the latter being modelled as a sequence of steady currents because of the large values of the Keulegan-Carpenter number of the tidal flows, which allow to neglect inertial effects in their modelling. The hydrodynamic module solves Reynolds-averaged momentum equations by introducing a two-equation turbulence model, which considers also the flow in the region closest to the sea bottom and enforces the no-slip condition and the vanishing of the turbulent kinetic energy at the bottom without the need to assume the existence of a logarithmic velocity profile and to fix the normal derivative of the turbulent kinetic energy close to the sea bed. Hence, the evaluation of the velocity profile in the near-bed region turns out to be accurate. The sediment transport module determines the sediment concentration and sediment transport for a mixture of non-cohesive and cohesive sediments. To validate the model, its predictions are compared with laboratory measurements and field data collected over rippled beds at two different tidal estuaries. Then, results are obtained for values of the parameters chosen to mimic a site close to Punta Umbría (Huelva, Spain) and considering different hydrodynamic conditions and different sediment mixtures. The influence of the waves on the suspended sediment concentration is lower for the cohesive fraction than for the non-cohesive fraction. For all the sediment mixtures, it turns out that the cohesive fraction is well mixed over the whole water depth, meanwhile the concentration of the non-cohesive fraction has significant values only near the bottom, thus showing that an accurate description of turbulence dynamics in the buffer layer and viscous sublayer (if it exists) is important to quantify the sediment transport rate.

A laboratory study of class III Bragg resonance of gravity surface waves by periodic beds

When moderately steep waves travel over a periodic rippled bed, class III Bragg resonance may occur due to the third-order quartet wave-bottom interaction among one bottom and three surface wave components. The theory, however, has not been experimentally confirmed. To verify the existence of class III Bragg resonance, we consider the simplest possible case involving a single incident wave and conduct a series of physical experiments. The experiments show that as the theory predicts, class III Bragg resonance could generate not only the reflected waves (from subharmonic resonance) but also the transmitted waves (from superharmonic resonance), and the reflection and transmission coefficients vary linearly along the rippled bottom patch. Furthermore, the experimental data of the reflected and transmitted waves (due to class III resonance) agree quantitatively well with the prediction by high-order spectral (HOS) method computations. To further understand the characteristics of class III resonance, we apply HOS simulations to study the more general cases including the presence of two incident waves of different frequencies as well as the presence of an incident wave group with Gaussian envelope. The results show that in addition to class I and class II Bragg resonances, class III Bragg resonance can significantly influence the evolution of surface wave fields passing over a rippled bottom, especially in the case of shallow water.

Bed configuration under sluice gate at Sandy–Loam Bed Channel

Sluice gate operation is necessary to keep the continuity the design discharge. The mis-operation of sluice gate occurs endanger stucture and destruct the bed irrigation channel. Investigation about sluice gate operation and bed configuration are needed to avoid the destruction of the structure bed irrigation channel. The changes in bed form result from interaction of the flow, fluid and bed material. The aim of this paper is to investigate the influence of different flow parameter, height of opening gate and types of bed material. Fourty five runs were executed at different discharge started from 1.0 l/s to 5.0 l/s with an increment of 0.5 where each discharge has five different opening gate to get all characteristics of bed configuration. The material used in the experiments were sandy loam. The experimental were conducted in an acrylic side flume with recirculating water at Applied Hydraulics Laboratory in Water Resources Engineering Faculty, Brawijaya University, Malang, Indonesia. The result of investigation showed that the bed configuration of sandy loam is ripple for most of the condition. At the same opening gate and various discharge the configuration is start by plane bed (no motion) and ripplee. Meanwhile, for the same discharge at the various opening gate occurs the ripple bed configuration. The various velocity that occur during the runing process cause the changing of bed configuration. For the greater discharge at the same opening gate occur the highest velocity. This condition cause the grain sediment material of the bed channel lift up and start to moving. This result is suitable with equation approaches from the van Rijn, Simon Richardson and Garde Albertson.

TURBULENCE-RESOLVING NUMERICAL SIMULATION OF FINE SEDIMENT TRANSPORT OVER BEDFORMS

Wave-supported gravity currents in turbulent wave bottom boundary layer (WBBL) are one of the most important processes causing cross-continental shelf sediment transport. The high numerical accuracy 3D numerical model has been used to investigate the fine sediment transport in the WBBL and several different transport modes have been found due to sedimentinduced density stratification (Ozdemir et al., 2010; Cheng et al., 2015). However, laboratory experiments suggest the presence of a small amount of sand fraction and the formation of ripple bed alter the structure of WBBL significantly (Hooshmand, et al., 2015). The purpose of this study is to understand the interplay of fine sand, bedforms, and sediment-induced density stratification in determining the transport modes of fine sediments in WBBL through turbulence-resolving numerical simulations.

Developments in acoustics for studying wave-driven boundary layer flow and sediment dynamics over rippled sand-beds

The processes of sediment entrainment, transport, and deposition over bedforms are highly dynamic and temporally and spatially variable. Obtaining measurements to understand these processes has led to ongoing developments in instrumentation for studying near-bed sediment dynamics, with the outputs applied to the development and assessment of sediment transport modelling. In the present study results are reported from three acoustic systems deployed to make observations of bedforms, bedload, suspended concentration and horizontal and vertical velocity components. To evaluate the instruments a series of near-bed boundary layer measurements were collected in a large scale flume facility over a rippled bed of medium sand under regular waves. The observations were conducted as part of Joint Research Activities within the EU funded Hydralab project. The suite of acoustic instruments consisted of a Bedform And Suspended Sediment Imager, BASSI, a three dimensional acoustic ripple profiler, 3D-ARP, and three Acoustic Concentration and Velocity Profilers, ACVP's. Here results are reported from the deployment of the instruments, to illustrate the ongoing developments in acoustics and the expanding capability of the application of acoustics to the study of near-bed flow and sediment dynamics.

Critical Depths Derived for Three Distinct Modes of Coastal Sediment Transport

Shi, H.Y.; You, Z.J.; Yin, B.S., and Bai, Y.C., 2018. Critical Depths Derived for Three Distinct Modes of Coastal Sediment Transport. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 271–275. Coconut Creek (Florida), ISSN 0749-0208.A unified criterion is developed for three distinct modes of coastal sediment transport: incipient movement of sediment (only bedload), initiation of bedripple formation (bedload and suspended load), and inception of bed ripple disappearance or sheet flow (mainly bed load) based on three unique laboratory datasets collected on a horizontal bed of sediment under regular waves. The onset velocity criterion on the three distinct sediment transport modesis derived to be of the same simple form, U0 = 2πC (1 − T0/T), where U0 is the maximum on set wave orbital velocity close to the bed, T is the wave period, and C and T0 are the coefficients dependent of sediment property only. The newly developed criterion is then extended to calculate critical depths for the distinct modes of sediment transport under coastal waves by replacing regular wave height H and period T with statistical wave height Hrms and period Trms according to the recently developed “zero-crossing and energy balance” wave analysis method and linear wave theory. The critical depth calculated from this unified criterion is shown to be a function of sediment grain size and density, and wave height and period, but more sensitive to wave period. The critical depth estimated for the initiation of bed sediment ripple formation is found to be much larger than the depth of closure derived for beach-fill designs.

Direct Numerical Simulation of Transverse Ripples: 2. Self‐Similarity, Bedform Coarsening, and Effect of Neighboring Structures

AbstractCoupled bed‐flow direct numerical simulations investigating the early stages of pattern formation and bedform (ripple) interactions were examined in a previous paper (Part 1), making use of the resolved flow field. In this paper (Part 2), we compare our results to published experimental data and provide an extensive quantitative analysis of the bed using spectral analysis and two‐point correlations. The effect of the mobile rippled bed on the flow structure and turbulence is investigated locally (at specific streamwise locations) and over the entire computational domain. We show that developing ripples attain a self‐similar profile in both the shape and the corresponding bed shear stress. We demonstrate the importance of neighboring structures, especially upstream neighbors, on bedform dynamics in terms of the growth, decay, and speed of ripples. Finally, we examine the defect‐free interactions in the later stages of bed evolution, which primarily lead to wave coarsening.

Waves plus currents crossing at a right angle: near-bed velocity statistics

ABSTRACTWave–current flow over a bottom covered with different roughness elements was analysed to provide new insights into the statistical properties of the near-bed velocity. Experimental data of three different experimental campaigns, with orthogonal waves and currents over a sandy bed, a gravel bed and a rippled bed were used. Velocity profiles were acquired by means of a micro-ADV. The paper focuses on the effects that the waves have on the statistics of the velocity in the current direction. In particular, in the case of a steady current only, the near-bed velocities closely follow a Gaussian distribution. When waves are added, the distribution becomes double-peaked. In order to get single-peaked velocity distributions the total velocity events in the current direction were split in two classes according to the sign of the wave directed velocities. The nature of the distribution functions is influenced by the mass conservation principle and, in the rippled bed case, by the vorticity dynamics.

Effect of bottom topography on wave scattering by multiple porous barriers

Scattering of obliquely incident surface gravity waves by multiple porous barriers is studied in the presence of step type varying bottom topography. The bottom bed consists of a finite interval of uneven geometry which is connected by two semi-infinite intervals of uniform water depths. An array of porous barriers are located on water of uniform depth on the lee side of bottom variations. Using small amplitude wave theory and Darcy’s law for flow past porous structure, the physical problem is converted into a boundary value problem which is handled for solution using coupled eigenfunction expansion in uniform bottom regions and modified mild-slope equation in varying bottom region. Further, certain jump conditions are used for the conservation of mass flux at slope discontinuities in bottom profile. To understand the effect of variations in bottom topography on wave scattering by multiple porous barriers, physical quantities such as reflection and transmission coefficients, wave forces on the barriers are computed and analyzed for different values of depth ratio, varying bottom parameter, porous-effect parameter, incident wave angle, spacing between the barriers and slope length of varying bottom. In the presence of ripple bottom bed, effect of multiple porous barriers on Bragg scattering is analyzed. Certain drift in Bragg reflection is noticed due to propagation of oblique incident waves over step type ripple beds.

Modeling of suspended sediment concentrations under combined wave-current flow over rippled bed

Ripples appear and disappear dynamically on coastal bed. The bottom stress can significantly be enhanced when ripples appear, and then the sediment transport will be influenced by the ripple-enhanced stress. However, ripples’ impact on suspended sediments is seldom discussed. In this study, a bedform (ripples) module based on combined wave and current flow is coupled with a bottom boundary layer (BBL) model. This BBL model outputs our improved bottom shear stress (BSS) to both the sediment model (UNSW-sed) and the hydrodynamic model (POM). Model results in Jervis Bay of Australia show that the simulated suspended sediment concentration (SSC) of an abrupt rising is significantly improved by considering ripples rather than setting a uniform roughness (Kb) without ripples. However, the SSC is still underestimated by using previous schemes. Differently from the previous estimation of ripple-enhanced shear velocity U∗cwe, noted as U∗cwe_NL, we introduce an U∗cwe improved by calculating through ripple-enhanced ripple-enhanced Kb, which is noted as U∗cwe_Kb. Simulation shows that U∗cwe_Kb produces significantly increased SSC under high wave conditions, resulting in reasonable agreements with the measurements. The wave friction factor fw is shown to play a crucial role in causing the difference between U∗cwe_Kb and U∗cwe_NL.

LARGE-EDDY SIMULATION OF OSCILLATORY FLOW AND MORPHODYNAMICS OVER RIPPLES

The objective of the present study was to study the morphodynamical development of ripples in a movable bed. The methodology is based on the coupling of fluid flow, sediment transport and morphodynamics. A well-resolved large-eddy simulation (LES) is employed for the simulation of the three-dimensional turbulent oscillatory flow and the corresponding bed and suspended sediment transport over a rippled bed. The evolution of the bed form is obtained by the numerical solution of the Exner equation based on the spanwise-mean flow and sediment transport conditions. The Immersed Boundary method is implemented for the imposition of fluid and sediment boundary conditions on the moving bed surface. Results are presented for ripple creation and propagation from a quasi-flat bed, as well as results of initially sinusoidal ripples adapting to water conditions, based on the mobility number, ψ. The numerical model demonstrates phenomena of ripple creation, propagation and migration, resulting in ripple lengths in agreement with those predicted by empirical equations. It was shown that under the same hydrodynamic forcing, the bed tends to reach the same equilibrium state, regardless of the initial bed form.