The dimensions of sand ripples in full-scale oscillatory flows

New large-scale experiments have been carried out in two oscillatory flow tunnels to study ripple regime sand suspension and net sand transport processes in full-scale oscillatory flows. The paper focuses on ripple dimensions and the new data are combined with existing data to make a large dataset of ripple heights and lengths for flows with field-scale amplitudes and periods. A feature of the new experiments is a focus on the effect of flow irregularity. The combined dataset is analysed to examine the range of hydraulic conditions under which oscillatory flow ripples occur, to examine the effects of flow irregularity and ripple three-dimensionality on ripple dimensions and to test and improve existing methods for predicting ripple dimensions.The following are the main conclusions. (1) The highest velocities in a flow time-series play an important role in determining the type of bedform occurring in oscillatory flow. Bedform regime is well characterised by mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth peak velocities in the case of irregular flow. (2) For field-scale flows, sand size is the primary factor determining whether equilibrium ripples will be 2D or 3D. 2D ripples occur when the sand D₅₀ ≥ 0.30 mm and 3D ripples occur when D₅₀ ≤ 0.22 mm (except when the flow orbital diameter is low). (3) Ripple type (2D or 3D) is the same for regular and irregular flows and ripple dimensions produced by equivalent regular and irregular flows follow a similar functional dependence on mobility number, with mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth velocities in the case of irregular flow. For much of the ripple regime, ripple dimensions have weak dependency on mobility number and ripple dimensions are similar for regular and irregular flows with the same flow orbital amplitude. However, differences in ripples produced by equivalent regular and irregular flows become significant at the high mobility end of the ripple regime. (4) Ripple dimensions predicted using the Wiberg and Harris formulae are in poor agreement with measured ripple dimensions from the large-scale experiments. Predictions based on the Mogridge et al. and the Nielsen formulae show better overall agreement with the data but also show systematic differences in cases of 3D ripples and ripples generated by irregular flows. (5) Based on the combined large-scale data, modifications to the Nielsen ripple dimension equations are proposed for the heights and lengths of 2D ripples. The same equations apply to regular and irregular flows, but with mobility number appropriately defined. 3D ripples are generally smaller than 2D ripples and estimates of 3D ripple height and length may be obtained by applying multipliers of 0.55 and 0.73 respectively to the 2D formulae. The proposed modified Nielsen formulae provide an improved fit to the large-scale data, accounting for flow irregularity and ripple three-dimensionality.     

Modelling ripple development under non-uniform flow and sediment supply-limited conditions in a laboratory flume

Results are reported herein of an open channel flow laboratory based study of the development of ripples on a fine silica sand bed, and under non-uniform turbulent subcritical flow conditions. The hydraulic model used included a diverging channel, which resulted in a variation of hydraulic and sediment transport parameters along the channel. Sediment supply limitation occurred during experimentation, impacting bed form development. The overall aim of this study was to improve the understanding and modelling capability of the development of bed forms under limited sediment supply and non-uniform flow conditions. In particular, the applicability of an existing empirical model capable of predicting ripple development was tested for the conditions of this study, using measured ripple dimensions. The ripple height and length results were extracted from detailed bed profile records, obtained using an acoustic Doppler probe traversed longitudinally over the sediment bed, at various experimentation time intervals. It was found that the non-uniform flow conditions affected the development rate of the bed forms, while sediment supply limitation impacted their steady state dimensions. The measured steady state ripple dimensions were lower, on average, than the corresponding equilibrium dimensions predicted using existing empirical equations. Non-uniform flow also caused the simultaneous occurrence of bed forms at different stages of development along the hydraulic model, where 3D and 2D ripples and incipient bed forms were recorded. Such a scenario can occur in estuarine and coastal flows, due to changing hydraulic conditions and/or a limitation of sediment supply. The ripple development model tested was verified for the conditions of this study, with its accuracy being shown to depend on an accurate determination of steady state parameters.     

Modelling and measurement of sand transport processes over full-scale ripples in oscillatory flow

A new series of laboratory experiments was performed in the Aberdeen Oscillatory Flow Tunnel (AOFT) and the Large Oscillating Water Tunnel (LOWT) to investigate time-averaged suspended sand concentrations and transport rates over rippled beds in regular and irregular oscillatory flow. The wave-induced oscillatory near-bed flows were simulated at full-scale. Five series of experiments were carried out. During the two AOFT experimental series, ripple dimensions, ripple migration rates and net sand transport rates were measured under regular and irregular asymmetric flow for two different sand types. The three LOWT experimental series focussed on measurements of the ripple dimensions, ripple migration rates, time-averaged suspended sand concentrations and net sand transport rates under regular asymmetric and irregular weakly asymmetric flow for two different sand types. From analysis of new and other full-scale data, it is concluded that the lower part of the time- and bed-averaged concentration profile (up to two times the ripple height above the ripple crest level) has an exponential profile. A new reference concentration formula is proposed based on the formula of Bosman and Steetzel [Bosman, J.J., Steetzel, H.J., 1986. Time- and bed-averaged concentration under waves. Proc. 20th ICCE Taipei, ASCE, pp. 986–1000], which includes the grain-size influence. Furthermore, it is shown that the concentration decay length is strongly related to the ripple height and that the simple formula R_c = 1.27η gives good agreement with the data. A new transport model is proposed for the wave-related net transport over full-scale ripples based on a modified half wave cycle concept of Dibajnia and Watanabe [Dibajnia, M., Watanabe, A., 1992. Sheet flow under nonlinear waves and currents. Proc. 23rd ICCE Venice, ASCE, pp. 2015–2028; Dibajnia, M., Watanabe, A., 1996. A transport rate formula for mixed sands. Proc. 25th ICCE Orlando, ASCE, pp. 3791–3804]. The magnitudes of the half wave cycle transport contributions are related to the grain-related Shields parameter, the degree of wave asymmetry and a newly defined vortex suspension parameter P, which is the ratio between the ripple height and the median grain-size. The new model has been calibrated using transport data from the new regular flow experiments and has subsequently been validated using other data, including measurements from irregular flow experiments. The new model is seen to perform better overall than existing practical models for ripple regime net sand transport.     

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.     

The formation of offshore ripples in the zone under irregular waves

In this article, results obtained from an experimental investigation conducted to determine the wave-induced geometric characteristics of offshore ripples and bars are presented. The experiments were performed using irregular waves. Natural beach sand was used in the study, where the mean diameter was 0.35 mm and the specific gravity was 2.63. The initial slope of the beach was 1:5. Different wave groups were generated over the initially flat beach, and a number of characteristics were determined. These include the ripple number, individual and average ripple heights, individual and average ripple lengths and the length of the offshore bar. The results of the experimental study were evaluated and empirical expressions based on the results were formulated.     

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…     

Reconstruction of ancient sea conditions with an example from the Swiss Molasse

Ancient sea conditions can be estimated from the grain size, spacing and steepness of preserved ripple-marks. The element of greatest uncertainty in such reconstructions is the relationship between near-bed orbital diameter of water particles and the ripple spacing. This relationship is simple for vortex ripples of high steepness but is problematical for the low-steepness forms known as post-vortex, rolling-grain or anorbital ripples.

The existence field for wave ripples is between the threshold velocity for sediment movement and the onset of sheet flow, most low-steepness forms occurring close to the bed planation threshold. A range of maximum period of formative waves can be obtained using combinations of orbital diameter and orbital velocity, assuming linear wave theory to be a reasonable approximation.

Probable wave heights, wave lengths and water depths can be investigated using the transformation of wave parameters in shallowing waters and the constraints on wave dimensions provided by the wave-breaking condition. Given reasonable estimates of wave height, crude estimates of wave power allow a comparison of ancient wave-influenced sequences with modern counterparts.

Wave ripple-marks preserved in the Upper Marine Molasse of western Switzerland have been investigated. Results, which are in agreement with regional geology, suggest deposition in a seaway of approximately 100 km width, where moderate period waves (T = 3–6 s) were generated. The depositional facies belts were adjusted to the prevailing waves, tides and fluvial outflows.     

Database of full-scale laboratory experiments on wave-driven sand transport processes

A new database of laboratory experiments involving sand transport processes over horizontal, mobile sand beds under full-scale non-breaking wave and non-breaking wave-plus-current conditions is described. The database contains details of the flow and bed conditions, information on which quantities were measured and the value of the measured net sand transport rate for 298 experiments conducted in 7 large-scale laboratory facilities. Analysis of the coverage of the experiments and the measured net sand transport rates identified the following gaps in the range of test conditions and/or the type of measurements: (i) graded sand experiments, (ii) wave-plus-current experiments and (iii) intra-wave velocity and concentration measurements in the ripple regime. Furthermore, it highlights two areas requiring further research: (i) the differences in sand transport processes and sand transport rates between real waves and tunnel flows with nominally similar near-bed oscillatory flow conditions and (ii) the effects of acceleration skewness on transport rates. The database is a useful resource for the development and validation of sand transport models for coastal applications.     

潮流及单向流作用下海底沙波形成和运移试验

基于量纲分析理论进行水槽试验,研究了潮流以及单向流作用下海底沙波的形成和发展过程。通过分析 海床地形数据,对海底沙波的特征尺度和发展过程进行定量描述,得出了潮流流速、周期、水深以及叠加单向流等因素对沙波特征尺度的影响。结果表明,潮流作用产生的海底地貌由大尺度的沙波和小尺度的沙纹共同组成,大尺度沙波在地貌形态塑造中占主导地位。从平坦海床开始,沙波波高和波长随水流作用逐渐增大,增长速度越来越慢,最终达到动态平衡。沙波特征波高和特征波长随流速和水深增大而增大,同时随往复流周期的增大而增大,并不断趋近于单向水流的情况。进一步对小尺度的沙纹地貌进行分析,得出了沙纹特征尺度随水流条件的变化规律。     

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.     

控制流水波痕的外部地质作用

流水波痕可以广泛发育在不同的海、陆相环境中。对流水波痕的研究不能仅仅注意沉积作用方面，更要注意作用于流水波痕的外部条件。     

Tidal-cycle changes in oscillation ripples on the inner part of an estuarine sand flat

Oscillation ripples form on subaqueous sand beds when wave-generated, near-bottom water motions are strong enough to move sand grains. The threshold of grain motion is the lower bound of the regime of oscillation ripples and the onset of sheet flow is the upper bound. Based on the relation between ripple spacing and orbital diameter, three types of symmetrical ripples occur within the ripple regime. In the lower part of the ripple regime (orbital ripples), spacing is proportional to orbital diameter; in the upper part (anorbital ripples) spacing is independent of orbital diameter. Between these regions occurs a transitional region (suborbital ripples).

Oscillation ripples develop on a sandy tidal flat in Willapa Bay, Washington, as a result of waves traversing the area when it is submerged. Because wave energy is usually low within the bay, the ripples are primarily orbital in type. This means that their spacing should respond in a systematic way to changes in wave conditions. During the high-water parts of some tidal cycles, ripples near the beach decrease in spacing during the latter stage of the ebb tide while ripples farther offshore do not change. Observations made over several tidal cycles show that the zone of active ripples shifts on- or offshore in response to different wave conditions.

Detailed bed profiles and current measurements taken during the high-water part of spring tides show the manner in which the oscillation ripples change with changes in orbital diameter. Changes in ripple spacing at the study site could be correlated with changes in orbital diameter in the manner suggested by the criterion for orbital ripples. However, there appeared to be a lag time between a decrease in orbital diameter and the corresponding decrease in ripple spacing. Absence of change during a tidal cycle could be attributed to orbital velocities below the threshold for grain motion that negated the effects of changes in orbital diameter.

Because changes in sand-flat ripples depend both upon changes in orbital diameter and upon the magnitude of the orbital velocity, exposed ripples were not necessarily produced during the preceding high tide. In fact, some ripples may have been just produced, while others, farther offshore, may have been produced an unknown number of tides earlier. Therefore, when interpreting past wave conditions over tidal flats from low-tide ripples, one must remember that wave periods have to be short enough to produce velocities greater than the threshold velocity for the orbital diameters calculated from the observed ripple spacings.     

Measurements of sheet flow transport in acceleration-skewed oscillatory flow and comparison with practical formulations

Near-bed oscillatory flows with acceleration skewness are characteristic of steep and breaking waves in shallow water. In order to isolate the effects of acceleration skewness on sheet flow sand transport, new experiments are carried out in the Aberdeen Oscillatory Flow Tunnel. The experiments have produced a dataset of net transport rates for full-scale oscillatory flows with varying degrees of acceleration skewness and three sand sizes. The new data confirm previous research that net transport in acceleration-skewed flow is non-zero, is always in the direction of the largest acceleration and increases with increasing acceleration skewness. Large transport rates for the fine sand conditions suggest that phase lag effects play an important role in augmenting positive net transport. A comparison of the new experimental data with a number of practical sand transport formulations that incorporate acceleration skewness shows that none of the formulations performs well in predicting the measured net transport rates for both the fine and the coarser sands. The new experimental data can be used to further develop practical sand transport formulations to better account for acceleration skewness.     

Practical sand transport formula for non-breaking waves and currents

Many existing practical sand transport formulae for the coastal marine environment are restricted to a limited range of hydrodynamic and sand conditions. This paper presents a new practical formula for net sand transport induced by non-breaking waves and currents. The formula is especially developed for cross-shore sand transport under wave-dominated conditions and is based on the semi-unsteady, half wave-cycle concept, with bed shear stress as the main forcing parameter. Unsteady phase-lag effects between velocities and concentrations, which are especially important for rippled bed and fine sand sheet-flow conditions, are accounted for through parameterisations. Recently-recognised effects on the net transport rate related to flow acceleration skewness and progressive surface waves are also included. To account for the latter, the formula includes the effects of boundary layer streaming and advection effects which occur under real waves, but not in oscillatory tunnel flows. The formula is developed using a database of 226 net transport rate measurements from large-scale oscillatory flow tunnels and a large wave flume, covering a wide range of full-scale flow conditions and uniform and graded sands with median diameter ranging from 0.13 mm to 0.54 mm. Good overall agreement is obtained between observed and predicted net transport rates with 78% of the predictions falling within a factor 2 of the measurements. For several distinctly different conditions, the behaviour of the net transport with increasing flow strength agrees well with observations, indicating that the most important transport processes in both the rippled bed and sheet flow regime are well captured by the formula. However, for some flow conditions good quantitative agreement could only be obtained by introducing separate calibration parameters. The new formula has been validated against independent net transport rate data for oscillatory flow conditions and steady flow conditions.     

Sand waves and other bedforms in lower Cook Inlet,Alaska

Abstract

Lower Cook Inlet in Alaska has high‐ tidal currents that average 3–4 knots and normally reach a peak of 6–8 knots. The bottom has an average depth of about 60–70 m in the central part of the inlet that deepens toward the south. Several types of bedforms, such as sand waves, dunes, ripples, sand ribbons, and lag deposits form a microtopography on the otherwise smooth seafloor. Each bedform type covers a small field, normally a few hundred to a few thousand meters wide, and usually several kilometers long parallel to the tidal flow. High‐resolution seismic systems, side‐scan sonar and bottom television were used to study these bedforms. Large sand waves with wavelengths over 300 m and wave heights up to 10 m were observed. Fields of ebb‐oriented or flood‐oriented asymmetric bedforms commonly grade into more symmetric shapes. Several orders of smaller sand waves and dunes cover the flanks of the very large bedforms. The crest directions of both size groups are normally parallel, but deviations of up to 90° have been observed; local deviations may occur where smaller forms approach the crests of the larger sand waves. Bottom television observations demonstrated active bedload transport in a northerly direction on crests and midflanks of southward asymmetric large sand waves, but not in their troughs. Movement of bedload occurs in the form of small ripples. Although the asymmetry of the large bedforms suggests that migration has taken place in the ebb or flood directions, the very low surface angles (2.5°‐8°) of these bedforms do not indicate regular movements. The large bedforms are probably relict features, or they migrate only under severe conditions, whereas active sand transport by ripples and smaller sand waves and dunes moves bedload back and forth with the tides. An understanding of such movements is essential for determining design criteria for offshore installations and in benthic‐faunal studies.     

Sea ripple formation: the heterogeneous sediment case

Ripple formation beneath sea waves is analyzed both by experimental and analytical means when the bottom is made up of a mixture of sands. An oscillatory flow is obtained in a closed duct by the oscillations of two rigidly connected pistons located at the ends of the duct. The amplitude and period of the oscillations can be continuously varied. A fixed tray, located at the bottom of the duct and filled with different types of sediments, allows ripple formation to be observed. The presence of graded sediments is found to have a stabilizing effect and causes longer ripples to appear. Moreover a selective sediment transport is observed and quantified which tends to pile up the coarse grains at ripple crests leaving the fine ones in the troughs. As in the companion paper, the theory is based on a linear stability analysis of a flat sandy bottom subject to an oscillatory flow. Because of the presence of a mixture, a modified version of Exner equation is used and an “hiding” factor should be inserted in the sediment transport rate formula. The flow regime in the bottom boundary layer is assumed to be turbulent. The conditions for ripple appearance are determined along with their wavelengths as they form. Good agreement is found between experimental data and theoretical findings.     

An investigation of the velocity field under regular and irregular waves over a sand beach

Near-bed horizontal (cross-shore) and vertical velocity measurements were acquired in a laboratory wave flume over a 1:8 sloping sand beach of finite depth. Data were acquired using a three-component acoustic Doppler velocimeter to measure the velocity field close to, but at a fixed distance from the bed. The near-bed velocity field is examined as close as 1.5 cm above a trough and crest of a ripple under three different types of wave forcing (Stokes waves, Stokes groups, and irregular waves). Although both horizontal and vertical velocity measurements were made, attention is focused primarily on the vertical velocity. The results clearly indicate that the measured near-bed vertical velocity (which was outside the wave-bottom boundary layer) is distinctly nonzero and not well predicted by linear theory. Spectral and bispectral analysis techniques indicate that the vertical velocity responds differently depending on the location over a ripple, and that ripple-induced effects on the velocity field are present as high as 4–8 cm above the bed (for vortex ripples with wavelengths on the order of 8 cm and amplitudes on the order of 2 cm). At greater heights above the bed, the observed wave-induced motion is adequately predicted by the linear theory.     

A two-phase numerical model for sediment transport prediction under oscillatory sheet flows

To predict sediment transport under oscillatory sheet flow condition, especially for fine sand, is still a challenging research subject in coastal engineering. This paper describes a newly-developed numerical model based on two-phase theory with the use of a one-equation turbulence closure, and its applications in predicting fine sediment suspension in near-prototype oscillatory sheet flow conditions. Model results were compared with comprehensive laboratory measurements of flow velocity and sediment concentration under both symmetrical and asymmetrical oscillatory sheet flows from a large-scale water tunnel. Good agreements between the model results and measurements were achieved and the results demonstrated that the model is capable of reproducing detailed characteristics of sediment entrainment process in the sheet flow regime. The comparisons also revealed the fact that the concentration peaks at flow reversal is associated with the strong vertical sediment transport flux in the pickup layer, which has been widely observed in many laboratory experiments. The effects of flow reversal events on total sediment transport were also discussed.     

A two-phase flow model for asymmetric sheetflow conditions

A newly developed two-phase flow model was applied to simulate the sediment movement under 2nd-order Stokes wave sheetflow conditions with different sediment sizes and wave periods. As for the distribution of eddy viscosity and sediment diffusion coefficient, the difference between onshore and offshore phases was considered by using an equivalent sinusoidal velocity amplitude for the asymmetric velocity profile. Sophisticated comparisons between laboratory measurements [O'Donoghue, T., Wright, S., 2004b. Flow tunnel measurements of velocities and sand flux in oscillatory sheetflow for well-sorted and graded sands. Coast. Eng., 51 (11–12), 1163–1184.] and the present numerical simulation were performed for sediment concentration, sediment velocity, sand flux and net transport rate. Four existing engineering models, together with the present two-phase flow model, were introduced for net transport rate prediction. Taking both the net sand transport rate magnitude and direction into account, the present process-based two-phase flow model provided the best estimations, which can simulate both the onshore net transport for medium/coarse sand cases and offshore net transport for fine sand cases with the agreement by a factor of 2 for almost all the considered cases.     

Generation of tidal bedding in a circular flume experiment: formation process and preservation potential of mud drapes

Flume experiments aimed to produce flaser bedding were conducted using fine sand and clay in a circular flume. The formation process of mud drapes during the slack-water stage was revealed in detail. When the tidal current declines, a uniform mobile mud layer initially settles from suspension and drapes the entire rippled sand bed (type A mud). When the remaining flow velocity is very low, a more fluid mud begins to settle out (type B mud) that preferentially fills the ripple troughs, the ripples and mud together forming a flat surface. At slack tide, the two-phase mud drape is temporarily stationary. After the onset of the reversed flow phase, most of the type B mud is resuspended, while the type A mud is eroded from the crests, leaving behind a remnant mud drape (flaser) in the troughs that is subsequently buried by migrating ripples. Type B mud generally contains variable amounts of sand derived from eroded ripple crests, but does not show any visible internal sedimentary structures. Type A mud represents the ‘mud drapes’ commonly described in the literature, the temporary existence of type B mud having gone unnoticed because of its low preservation potential. When present, it can be recognized by its sand content and the occurrence of flame structures in ripple troughs. Tidal deposits reflecting the existence and depositional characteristics of both type A and type B mud are found in, for example, the macrotidal Oligocene Ashiya Group, Japan.