Bedforms and roughness
Bed forms are relief features initiated by the fluid motions generated downstream of small local obstacles at the bottom consisting of movable (alluvial) sediment materials.
Many types of bed forms can be observed in nature. The bed form regimes for steady flow over a sand bed can be classified into (see Figure 1):
- lower transport regime with flat bed, ribbons and ridges, ripples, dunes and bars,
- transitional regime with washed-out dunes and sand waves,
- upper transport regime with flat mobile bed and sand waves (anti-dunes).
When the bed form crest is perpendicular (transverse) to the main flow direction, the bed forms are called transverse bed forms, such as ripples, dunes and anti-dunes. Ripples have a length scale much smaller than the water depth, whereas dunes have a length scale much larger than the water depth. The crest lines of the bed forms may be straight, sinuous, linguoid or lunate. Ripples and dunes travel downstream by erosion at the upstream face (stoss-side) and deposition at the downstream face (lee-side). Antidunes travel upstream by lee-side erosion and stoss-side deposition. Bed forms with their crest parallel to the flow are called longitudinal bed forms such as ribbons and ridges.
In the literature, various bed-form classification methods for sand beds are presented. The types of bed forms are described in terms of basic parameters (Froude number, suspension parameter, particle mobility parameter; dimensionless particle diameter).
A flat immobile bed may be observed just before the onset of particle motion, while a flat mobile bed will be present just beyond the onset of motion. The bed surface before the onset of motion may also be covered with relict bed forms generated during stages with larger velocities.
Small-scale ribbon and ridge type bed forms parallel to the main flow direction have been observed in laboratory flumes and small natural channels, especially in case of fine sediments (grainsize typically smaller than 0.1 mm). They are probably generated by secondary flow phenomena and near-bed turbulence effects (burst-sweep cycle) in the lower and transitional flow regime. These bed forms are also known as parting lineations because of the streamwise ridges and hollows with a vertical scale equal to about 10 grain diameters. These bed forms are mostly found in fine sediments ().
When the velocities are somewhat larger (10%-20%) than the critical velocity for initiation of motion and the median particle size is smaller than about 0.5 mm, small (mini) ripples are generated at the bed surface. Ripples that are developed during this stage remain small with a ripple length much smaller than the water depth. The characteristics of mini ripples are commonly assumed to be related to the turbulence characteristics near the bed (burst-sweep cycle). Current ripples have an asymmetric profile with a relatively steep downstream face (lee-side) and a relatively gentle upstream face (stoss-side). As the velocities near the bed become larger, the ripples become more irregular in shape, height and spacing yielding strongly three-dimensional ripples. In this case the variance of the ripple length and height becomes rather large. These ripples are known as lunate ripples when the ripple front has a concave shape in the current direction (crest is moving slower than wing tips) and are called linguoid ripples when the ripple front has a convex shape (crest is moving faster than wing tips). The largest ripples may have a length up to the water depth and are commonly called mega-ripples.
Another typical bed form type of the lower regime is the dune-type bed form. Dunes have an asymmetrical (triangular) profile with a rather steep lee-side and a gentle stoss-side. A general feature of dune type bed forms is lee-side flow separation resulting in strong eddy motions downstream of the dune crest. The length of the dunes is strongly related to the water depth () with values in the range of . Extremely large dunes with heights () of the order of 7 m and lengths () of the order of 500 m have been observed in the Rio Parana River (Argentina) at water depths of about 25 m, velocities of about 2 m/s and bed material sizes of about 0.3 mm. The formation of dunes may be caused by large-scale fluid velocity oscillations generating regions at regular intervals with decreased and increased bed-shear stresses, resulting in the local deposition and erosion of sediment particles.
The largest bed forms in the lower regime are sand bars (such as alternate bars, side bars, point bars, braid bars and transverse bars), which usually are generated in areas with relatively large transverse flow components (bends, confluences, expansions). Alternate bars are features with their crests near alternate banks of the river. Braid bars actually are alluvial "islands" which separate the anabranches of braided streams. Numerous bars can be observed distributed over the cross-sections. These bars have a marked streamwise elongation. Transverse bars are diagonal shoals of triangular-shaped plan along the bed. One side may be attached to the channel bank. These type of bars generally are generated in steep slope channels with a large width-depth ratio. The flow over transverse bars is sinuous (wavy) in plan. Side bars are bars connected to river banks in a meandering channel. There is no flow over the bar. The planform is roughly triangular. Special examples of side bars are point bars and scroll bars.
It is a well-known phenomenon that the bed forms generated at low velocities are washed out at high velocities. It is not clear, however, whether the disappearance of the bed forms is accomplished by a decrease of the bed form height, by an increase of the bed form length or both. Flume experiments with sediment material of about 0.45 mm show that the transition from the lower to the upper regime is effectuated by an increase of the bed form length and a simultaneous decrease of the bed form height. Ultimately, relatively long and smooth sand waves with a roughness equal to the grain roughness were generated .
In the transition regime the sediment particles will be transported mainly in suspension. This will have a strong effect on the bed form shape. The bed forms will become more symmetrical with relatively gentle lee-side slopes. Flow separation will occur less frequently and the effective bed roughness will approach to that of a plane bed. Large-scale bed forms with a relative height () of 0.1 to 0.2 and a relative length () of 5 to 15 were present in the Mississippi river at high velocities in the upper regime.
In the supercritical upper regime the bed form types will be plane bed and/or anti-dunes. The latter type of bed forms are sand waves with a nearly symmetrical shape in phase with the water surface waves. The anti-dunes do not exist as a continuous train of bed waves, but they gradually build up locally from a flat bed. Anti-dunes move upstream due to strong lee-side erosion and stoss-side deposition. Anti-dunes are bed forms with a length scale of less than 10 times the water depth. When the flow velocity further increases, finally a stage with chute and pools may be generated.
Nikuradse introduced the concept of an equivalent or effective sand roughness height, , to simulate the roughness of arbitrary roughness elements of the bottom boundary. In case of a movable bed consisting of sediments the effective bed roughness mainly consists of grain roughness () generated by skin friction forces and of form roughness () generated by pressure forces acting on the bed forms. Similarly, a grain-related bed-shear stress () and a form-related bed-shear stress () can be defined. The effective bed roughness for a given bed material size is not constant but depends on the flow conditions. Analysis results of -values computed from Mississippi River data (USA) show that strongly decreases from about 0.5 m at low velocities (0.5 m/s) to about 0.001 m at high velocities (2 m/s), probably because the bed forms become more rounded or are washed out at high velocities. The fundamental problem of bed roughness prediction is that the bed characteristics (bed forms) and hence the bed roughness depend on the main flow variables (depth, velocity) and sediment transport rate (sediment size). These hydraulic variables are, however, in turn strongly dependent on the bed configuration and its roughness. Another problem is the almost continuous variation of the discharge during rising and falling stages. Under these conditions the bed form dimensions and hence the Chézy-coefficient are not constant but vary with the flow conditions. See further Bed roughness and friction factors in estuaries.
- Van Rijn, L.C., 1993, 2012. Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publications, Amsterdam, The Netherlands (WWW.AQUAPUBLICATIONS.NL)
- Nikuradse, J., 1932. Gesetzmässigkeiten der turbulente Strömung in glatten Rohren. Ver. Deut. Ing. Forschungsheft 356
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