Predicting bed form roughness: the influence of lee side angle

Flow transverse bedforms (ripples and dunes) are ubiquitous in rivers and coastal seas. Local hydrodynamics and transport conditions depend on the size and geometry of these bedforms, as they constitute roughness elements at the bed. Bedform influence on flow energy must be considered for the understanding of flow dynamics, and in the development and application of numerical models. Common estimations or predictors of form roughness (friction factors) are based mostly on data of steep bedforms (with angle-of-repose lee slopes), and described by highly simplified bedform dimensions (heights and lengths). However, natural bedforms often are not steep, and differ in form and hydraulic effect relative to idealised bedforms. Based on systematic numerical model experiments, this study shows how the hydraulic effect of bedforms depends on the flow structure behind bedforms, which is determined by the bedform lee side angle, aspect ratio and relative height. Simulations reveal that flow separation behind bedform crests and, thus, a hydraulic effect is induced at lee side angles steeper than 11 to 18° depending on relative height, and that a fully developed flow separation zone exists only over bedforms with a lee side angle steeper than 24°. Furthermore, the hydraulic effect of bedforms with varying lee side angle is evaluated and a reduction function to common friction factors is proposed. A function is also developed for the Nikuradse roughness (k _s), and a new equation is proposed which directly relates k _s to bedform relative height, aspect ratio and lee side angle.     

Evolution of the Nearshore Bed Envelope

The temporal growth of the envelope of bed motion owing to the migration of bedforms, which can be considered a proxy for maximum object burial depth, is examined using five different data sets. These data sets support the hypothesis that the envelope of bed motion will grow as an exponential taper, quickly at first, tapering off and approaching an asymptotic value. This growth is largest and fastest in the surf zone where wave and current flows are strong. Within the surf zone, envelopes owing solely to the migration of megaripples (bedforms with heights from 20 to 40 cm and lengths from 1 to 5 m) grow for about 8 d and reach an asymptote of about 40 cm. When wave energy becomes larger ( 1 m), bed envelopes are dominated by migrating sand bars and approach an asymptote of 3-4 m, but only after 2-12 years (depending on the beach). In addition, the frequency of object burial (the percentage of time that an object would be buried by the crests of migrating bedforms) is highest in the surf zone and grows rapidly with time.     

Direct bed shear stress measurements in bore-driven swash

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

Suspended sediment transport in the swash zone of a dissipative beach

Simultaneous high frequency field measurements of water depth, flow velocity and suspended sediment concentration were made at three fixed locations across the high tide swash and inner surf zones of a dissipative beach. The dominant period of the swash motion was 30–50 s and the results are representative of infragravity swash motion. Suspended sediment concentrations, loads and transport rates in the swash zone were almost one order of magnitude greater than in the inner surf zone. The vertical velocity gradient near the bed and the resulting bed shear stress at the start of the uprush was significantly larger than that at the end of the backwash, despite similar flow velocities. This suggests that the bed friction during the uprush was approximately twice that during the backwash.The suspended sediment profile in the swash zone can be described reasonably well by an exponential shape with a mixing length scale of 0.02–0.03 m. The suspended sediment transport flux measured in the swash zone was related to the bed shear stress through the Shields parameter. If the bed shear stress is derived from the vertical velocity gradient, the proportionality coefficient between shear stress and sediment transport rate is similar for the uprush and the backwash. If the bed shear stress is estimated using the free-stream flow velocity and a constant friction factor, the proportionality factor for the uprush is approximately twice that of the backwash. It is suggested that the uprush is a more efficient transporter of sediment than the backwash, because the larger friction factor during the uprush causes larger bed shear stresses for a given free-stream velocity. This increased transport competency of the uprush is necessary for maintaining the beach, otherwise the comparable strength and greater duration of the backwash would progressively remove sediment from the beach.     

Magnitude and cross-shore distribution of bed return flow measured on natural beaches

Field measurements of cross-shore currents 0.25 m from the bed were made on two natural beaches under a range of incident wave conditions. The results indicated the presence of a relatively strong, offshore-directed mean current, both within and seaward of the surf zone. Typical velocities within the surf zone were of the order of 0.2–0.3 m/s. This bed return flow, or “undertow”, represents a mass conservation response, returning water seaward that was initially transported onshore in the upper water column, primarily above the trough of the incident waves. The measurements demonstrated that the bed return flow velocity increases with the incident wave height. In addition, the crossshore distribution of the bed return flow is characterised by a mid-surf zone maximum, which exhibits a strong decrease in velocity towards the shoreline and a more gradual decay in the offshore direction. Several bed return flow models based on mass continuity were formulated to predict the cross-shore distribution of the bed return flow under an irregular wave field and were compared with the field data. Best agreement was obtained using shallow water linear wave theory, after including the mass transport associated with unbroken waves. The contribution of the unbroken waves enables net offshore-directed bottom currents to persist outside the region of breaking waves, providing a mechanism, other than rip currents, to transport sediment offshore beyond the surf zone.     

Mine Burial Experiments at the Martha's Vineyard Coastal Observatory

Several experiments to measure postimpact burial of seafloor mines by scour and fill have been conducted near the Woods Hole Oceanographic Institution's Martha's Vineyard Coastal Observatory (MVCO, Edgartown, MA). The sedimentary environment at MVCO consists of a series of rippled scour depressions (RSDs), which are large scale bedforms with alternating areas of coarse and fine sand. This allows simultaneous mine burial experiments in both coarse and fine sand under almost identical hydrodynamic forcing conditions. Two preliminary sets of mine scour burial experiments were conducted during winters 2001-2002 in fine sand and 2002-2003 in coarse sand with a single optically instrumented mine in the field of view of a rotary sidescan sonar. From October 2003 to April of 2004, ten instrumented mines were deployed along with several sonar systems to image mine behavior and to characterize bedform and oceanographic processes. In fine sand, the sonar imagery of the mines revealed that large scour pits form around the mines during energetic wave events. Mines fell into their own scour pits, aligned with the dominant wave crests and became level with the ambient seafloor after several energetic wave events. In quiescent periods, after the energetic wave events, the scour pits episodically infilled with mud. After several scour and infilling events, the scour pits were completely filled and a layer of fine sand covered both the mines and the scour pits, leaving no visible evidence of the mines. In the coarse sand, mines were observed to bury until the exposed height above the ripple crests was approximately the same as the large wave orbital ripple height (wavelengths of 50-125 cm and heights of 10-20 cm). A hypothesis for the physical mechanism responsible for this partial burial in the presence of large bedforms is that the mines bury until they present roughly the same hydrodynamic roughness as the orbital-scale bedforms present in coarse sand.     

An analytic solution to the wave bottom boundary layer governing equation under arbitrary wave forcing

Existing models of the wave bottom boundary layer have focused on the vertical and temporal dynamics associated with monochromatic forcing. While these models have made significant advances, they do not address the more complicated dynamics of random wave forcing, commonly found in natural environments such as the surf zone. In the closed form solution presented here, the eddy viscosity is assumed to vary temporally with the bed shear velocity and linearly with depth, however, the solution technique is valid for any eddy viscosity which is separable in time and space. A transformation of the cross-shore velocity to a distorted spatial domain leads to time-independent boundary conditions, allowing for the derivation of an analytic expression for the temporal and vertical structure of the cross-shore velocity under an arbitrary wave field. The model is compared with two independent laboratory observations. Model calculations of the bed shear velocity are in good agreement with laboratory measurements made by Jonsson and Carlsen (1976, J. Hydraul. Res., 14, 45–60). A variety of monochromatic, skewed, and asymmetric wave forcing conditions, characteristic of those found in the surf zone, are used to evaluate the relative effects on the bed shear. Because the temporal variation of the eddy viscosity is assumed proportional to the bottom shear, a weakly nonlinear interaction is created, and a fraction of the input monochromatic wave energy is transferred to the odd harmonics. For a monochromatic input wave, the ratio of the third harmonic of velocity at the bed to the first is <10%. However, for a skewed and asymmetric input wave, this ratio can be as large as 30% and is shown to increase with increasing root-mean-square input wave acceleration. The work done by the fluid on the bed is shown to be a maximum under purely skewed waves and is directed onshore. Under purely asymmetric waves, the work done is significantly smaller and directed offshore.     

Implications of bedform dimensions for the prediction of local scour in tidal inlets: a case study from the southern North Sea

The bedforms and the local scour at the base of a cylindrical pile were studied in a tidal inlet in the Wadden Sea, southern North Sea, using high-resolution multibeam bathymetry data from four surveys. The observed changes in scour and bedform dimensions were interpreted in terms of hydraulic forcings varying periodically at different time scales. It appears that bedform orientation reacts to changing flow conditions on a semidiurnal basis, whereas bedform height and steepness reflect the spring-neap cycle as well as seasonal signals. The scour depth carries a strong overprint of the semidiurnal tidal cycle, which is at a maximum during the strongest tidal flow. Subtler variations in scour depth can possibly be attributed to the spring-neap tidal cycle. Based on these data on bedform and scour dimensions, correlation functions were established between scour depth and dune height as well as dune length. In measuring the scour depth under mobile bed conditions, establishing the seabed level based on the trough level of the bedforms nearest to the scour proved useful. These findings suggest that the dimensions of bedforms in dynamic equilibrium with prevailing hydraulic flow conditions can be used to estimate scouring in tidal environments.     

Small-scale sediment transport patterns and bedform morphodynamics: new insights from high-resolution multibeam bathymetry

New multibeam echosounder and processing technologies yield sub-meter-scale bathymetric resolution, revealing striking details of bedform morphology that are shaped by complex boundary-layer flow dynamics at a range of spatial and temporal scales. An inertially aided post processed kinematic (IAPPK) technique generates a smoothed best estimate trajectory (SBET) solution to tie the vessel motion-related effects of each sounding directly to the ellipsoid, significantly reducing artifacts commonly found in multibeam data, increasing point density, and sharpening seafloor features. The new technique was applied to a large bedform field in 20–30 m water depths in central San Francisco Bay, California (USA), revealing bedforms that suggest boundary-layer flow deflection by the crests where 12-m-wavelength, 0.2-m-amplitude bedforms are superimposed on 60-m-wavelength, 1-m-amplitude bedforms, with crests that often were strongly oblique (approaching 90°) to the larger features on the lee side, and near-parallel on the stoss side. During one survey in April 2008, superimposed bedform crests were continuous between the crests of the larger features, indicating that flow detachment in the lee of the larger bedforms is not always a dominant process. Assessment of bedform crest peakedness, asymmetry, and small-scale bedform evolution between surveys indicates the impact of different flow regimes on the entire bedform field. This paper presents unique fine-scale imagery of compound and superimposed bedforms, which is used to (1) assess the physical forcing and evolution of a bedform field in San Francisco Bay, and (2) in conjunction with numerical modeling, gain a better fundamental understanding of boundary-layer flow dynamics that result in the observed superimposed bedform orientation.     

Morphodynamics of a bar-trough surf zone

A field study was made of the distinguishing morphodynamic processes operating in a surf zone which perennially exhibits accentuated bar-trough topography (the “longshore-bar-trough” and “rhytmic-bar-and-beach” states as described by Wright and Short, 1984). Characteristic features of the morphology include a shallow bar with a steep shoreward face, a deep trough, and a steep beach face. This morphology, which is favored by moderate breaker heights and small tidal ranges, strongly controls the coupled suite of hydrodynamic processes. In contrast to fully dissipative surf zones, the bar-trough surf zone is not at all saturated and oscillations at incident wave frequency remain dominant from the break point to the subaerial beach. The degree of incident wave groupiness does not change appreciably across the surf zone. Infragravity standing waves which, in dissipative surf zones, dominate the inshore energy, remain energetically secondary and occur at higher frequencies in the bar trough surf zone. Analyses of the field data combined with numerical simulations of leaky mode and edge wave nodal—antinodal positions over observed surf-zone profiles, indicate that the frequencies which prevail are favored by the resonant condition of antinodes over the bar and nodes in the trough. Standing waves which would have nodes over the bar are suppressed. Sediment resuspension in the surf zone appears to be largely attributable to the incident waves which are the main source of bed shear stress. In addition, the extra near-bottom eddy viscosity provided by the reformed, non-breaking waves traversing the trough significantly affects the vertical velocity profile of the longshore current. Whereas the bar is highly mobile in terms of onshore—offshore migration rates, the beach face and inner regions of the trough are remarkably stable over time.     

Characterization of bedform morphology generated under combined flows and currents using wavelet analysis

The wavelet transform (WT) has been successfully implemented in many fields such as signal and image processing, communication theory, optics, numerical analysis, and fluid mechanics. However, the application of WT to describe bedform morphology in coastal areas, oceans, and rivers is rare. The present study demonstrates the capability of WT analysis to fully represent the space–frequency characteristics of signals describing bed topography generated in marine and river environments. In this study WT is used to examine the morphological characteristics of bedforms generated in two separate laboratory facilities: a wave tank and a meandering channel. In the wave tank a set of ripples superimposed upon large wave ripples were generated; while in the meandering channel, 2D and 3D migrating ripples and dunes were observed. The WT proved to be a useful tool in detecting the complex variability of the generated bedform structures. The size distribution of the bottom features such as ripples, large wave ripples and sandbars were first examined along a 2D bed profile. Later analysis studied the variability of features in the transverse direction by using the power Hovmöller. Experiments in the wave tank were conducted for a mobility number of ψ=(10, 28), and a Reynolds wave number of R_ew=(17,500, 83,500) which correspond to waves alone (WA) and to combined flow (CF) scenarios, respectively. Experiments in the meandering channel were conducted under a morphological regime that produced mainly migrating sandbars.     

Extraction of morphometric bedform characteristics from profiling sonar datasets recorded in shallow coastal waters of China

The morphological characteristics of small-scale bedforms were measured by means of an acoustic profiling sonar on the Dafeng tidal flat,Jiangsu,in 2009,and in the Jiulong Estuary,Xiamen,in 2010,respectively.The "multi-threshold value" method was utilized to reveal the morphological undulations along which bedforms were present.Analyses of the datasets obtained show that:(1) sand ripples can have irregular shapes,and(2) changes in bedform morphology are small within a single tidal cycle but may be significant over several tidal cycles.Fractal and variogram analyses of the seabed roughness revealed the existence of a significant relationship between current speed and the fractal dimension of the seabed roughness.As current speed increases,seabed roughness increases with a trend of smaller-scale bottom structures being replaced by larger-scale structures.Furthermore,the surface of the larger-scale bottom structures can either become smooth due to the absence of smaller-scale features or become rougher due to the presence of superimposed smaller-scale structures.     

Surf zone characterization for integration with remote sensing data

A numerical model that solves the unsteady, incompressible, Reynolds averaged, Navier–Stokes equations has been utilized to simulate 57 cases of monochromatic, breaking waves over a sloping bed. The Volume of Fluid technique is used to track the complex, discontinuous free surface and the Renormalized Group turbulence model is used for closure. The model is validated by comparing predictions with Particle Image Velocimetry data and other empirical results. The model results are used to determine a relationship between the incipient wave breaking height and the maximum orbital velocity as well as a relationship between surf zone width and breaker type. Such expressions may be useful for remote sensing methods like Synthetic Aperture Radar to derive breaker height and classification from image data.     

Wave parameter gradients along the wave ray

Computer methods have been used to track selected deep-water waves along their orthogonals to the surf zone. Three bottom orbital parameters were computed at each step: diameter, maximum velocity and acceleration. These three parameters were then plotted along the several wave rays, thereby providing shoreward gradients.The three gradients have essentially the same geometry, so that any one can be taken as an indicator of the other two. Bottom slope changes are responsible for departure of the gradients from linearity. The bottom orbital gradients are quite different from gradients of wave height and wave length. These results from coasting waves cannot be applied directly to the case of forced, or wind-driven, waves.The non-linear nature of the bottom orbital gradients indicates that the near-shore bottom should exhibit a crude banding, more-or-less parallel with the coast, with different sediment transport and ripple-mark geometry from band to band.     

Laboratory measurements of large-scale near-bed turbulent flow structures under spilling regular waves

The instantaneous turbulent velocity field created by the breaking of spilling regular waves on a plane slope was measured in a plane running parallel to the slope using particle image velocimetry. The measurement plane was located at a height of about 1 mm above the bed. The measurement area encompassed the region where the large eddies generated at incipient wave breaking impinged on the bottom inside the surf zone. A total of 30 trials were conducted under identical experimental conditions. In each trial, six consecutive wave cycles were recorded. The measured velocity fields were separated into a mean flow and a turbulence component by ensemble averaging. The instantaneous turbulent velocity fields were analyzed to determine the occurrence frequency, location, geometry and evolution of the large eddies, and their contributions to instantaneous shear stresses, turbulent kinetic energy and turbulence energy fluxes. The motion of single glass spheres along the bed was also investigated. The two-phase flow measurements showed that the velocity and displacement of large solid particles on a smooth bed were significantly affected by the magnitude and direction of turbulence velocities. Overall, this study has examined the kinematic and dynamic properties of large eddies impinging on the bed and the interaction of these large-scale turbulent flow structures with the mean flow. The study has also highlighted the important role of large eddies in sediment transport.     

Geomorphology of a sand wave in lower Chesapeake Bay,Virginia, U.S.A.

Morphologic and sedimentologic studies of a single sand wave within a sand wave field in the lower Chesapeake Bay suggest that the bedform was originally formed by ebb currents, and is presently in static equilibrium with the circulation pattern. In this report, the concept of solitary sand wave is introduced to describe the state of a sand wave when further evolution of the sedimentary structure is mostly independent of adjacent bedforms. This concept can be applied to several bedforms in the area that are isolated from others by flats. A particular sand wave that is included in this category is discussed.Contribution number 79, Instituto Argentino de Oceanografia.     

On low-frequency waves in the surf and swash

Low-frequency waves in the surf and swash zones on various beach slopes are discussed using numerical simulations. Simulated surface elevations of both primary waves and low-frequency waves across the surf zone were first compared with experimental data and good agreement found. Low-frequency wave characteristics are then discussed in terms of their physical nature and their relationship to the primary wave field on a series of sea bottom slopes. Unlike primary waves, low-frequency wave energy increases towards the shoreline. Low-frequency waves in the surf and swash are a function of incident waves and the sea bottom slope and hence the saturation level of the surf zone. Wave energy on a gently sloping beach is dominated by low-frequency waves while primary waves play a significant role on a steep beach. Low-frequency wave radiation from the surf zone on a given beach depends on primary wave frequency and beach slope. However, a very poor correlation was found between surf similarity parameter and low-frequency wave radiation.     

Wave-formed structures and paleoenvironmental reconstruction

Wave-formed sedimentary structures can be powerful interpretive tools because they reflect not only the velocity and direction of the oscillatory currents, but also the length of the horizontal component of orbital motion and the presence of velocity asymmetry within the flow. Several of these aspects can be related through standard wave theories to combinations of wave dimensions and water depth that have definable natural limits. For a particular grain size, threshold of particle movement and that of conversion from a rippled to flat bed indicate flow-velocity limits. The ratio of ripple spacing to grain size provides an estimate of the length of the near-bottom orbital motion. The degree of velocity asymmetry is related to the asymmetry of the bedforms, though it presently cannot be estimated with confidence. A plot of water depth versus wave height (h—H diagram) provides a convenient approach for showing the combination of wave parameters and water depths capable of generating any particular structure in sand of a given grain size. Natural limits on wave height and inferences or assumptions regarding either water depth or wave period based on geologic evidence allow refinement of the paleoenvironmental reconstruction. The assumptions and the degree of approximation involved in the different techniques impose significant constraints. Inferences based on wave-formed structures are most reliable when they are drawn in the context of other evidence such as the association of sedimentary features or progradational sequences.     

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.