Bedforms

Introduction

Bedforms are the repeating surface features that develop on a sandy bed under fluid flow - ripples, dunes, flat surfaces, and the upstream-migrating antidunes that form under the most energetic conditions. They are not random. Their character is controlled systematically by flow velocity, grain size, and water depth, and the sequence in which they appear as flow strengthens is predictable and well documented. Because bedforms leave internal structures in the sedimentary record - mainly cross-lamination and planar lamination - understanding bedforms is inseparable from interpreting ancient sandstones.

The Bedform Sequence Under Unidirectional Flow

Flume experiments have established that under unidirectional flow over medium to coarse sand (approximately 0.25-0.7 mm), bedforms develop in a predictable sequence as flow velocity increases.

Ripples are the smallest bedform, ranging in length from about 5 to 20 cm and in height from about 0.5 to 3 cm. They therefore have a ripple index (the ratio of ripple length to ripple height) ranging from about 8 for coarse sand to 20 for fine sand. Ripples form in sediment ranging in size from silt (0.06 mm) to sand as coarse as 0.7 mm. ^[1]

Larger bedforms with spacing (wave length) ranging from under 1 m to over 1,000 m are called dunes. Dunes resemble ripples in general form but are larger. They form at higher flow velocities in sediment ranging from fine sand to gravel. The ripple index of dunes ranges from about 5 in finer sands to 50 in coarser sediment. In the lower part of the dune stability field, ripples may be superimposed on the backs of dunes. ^[1]

The hydraulic conditions that generate ripples and dunes take place at Froude numbers <~1. Under these conditions, the water surface shows little disturbance or the water waves are out of phase with bedforms, and flow is in the lower flow regime. Downstream migration of ripples and dunes produces cross-lamination dipping downstream at angles of up to about 30°. ^[1]

With further increase in flow velocity, dunes are destroyed and the flow enters the upper flow regime at Froude numbers >~1. Sheetlike, rapid flow generates surface water waves that are in phase with bedforms. Intense sediment transport takes place over an initially flat bed - the plane-bed stage - producing internal planar lamination with individual laminae ranging in thickness from a few millimeters to a few centimeters. At still higher velocities, plane beds give way to antidunes, which are low, undulating bedforms up to 5 m in length. Antidunes form in very fast, shallow flows and migrate upstream during flow, giving rise to low-angle (<10°) cross-bedding directed upstream. ^[1]

Two-dimensional dunes are generally straight-crested and their shapes can be described in a two-dimensional plane parallel to flow direction. Three-dimensional dunes are characterized by curved faces and scour pits, and their shapes must be described in three dimensions. ^[1]

Effects of Grain Size and Water Depth

The standard bedform sequence does not apply universally - it depends on grain size. The succession of bedforms at a given water depth depends not only on flow velocity but also on grain size. ^[1] In sediment coarser than about 0.9 mm, the ripple phase does not develop; a lower plane-bed stage forms just before dunes appear instead. Below a grain size of about 0.15 mm, dunes do not form at all - the ripple phase passes abruptly into the upper plane-bed phase.

These thresholds reflect the physics of how grain size controls the relationship between fluid forces and grain motion. In coarse sediment, the grains are large enough that the near-bed flow is always hydraulically rough, preventing the formation of the small-scale coherent structures that produce ripples. In very fine sediment, the cohesion and low settling velocity of the grains allow them to stay in suspension long enough to suppress the instability that generates dunes.

Most bedform data come from laboratory flumes or shallow natural environments (commonly less than about 1 m depth). In deeper water, small ripples behave approximately as in shallow water, but dunes can grow much larger. The hydraulic relationships remain the same - dunes form at higher velocities than ripples and lower velocities than plane beds and antidunes - but the exact grain size, flow velocity, and bedform phase relationships are not well documented for deep water. Exceedingly high velocities are required to produce antidunes at water depths greater than a few meters, so antidunes are unlikely under natural deep-water conditions, except perhaps under some turbidity currents. ^[1]

Flow Separation: The Mechanism Behind Bedform Movement

The formation and migration of transverse bedforms is controlled by a mechanism called flow separation. As sediment is transported in suspension or by traction up the stoss (upstream) side of a bedform to the brink or crest, the flow separates from the bed at the brink, creating a zone of reverse circulation or backflow - the separation eddy. ^[1] A zone of diffusion exists between the backflow and the main flow above, produced by turbulent mixing. Downstream from the separation point - at a distance several times the height of the bedform - the flow reattaches to the bed.

Flow separation sorts the transported sediment into bedload and suspended load fractions. The bedload fraction accumulates at the ripple crest until the lee slope exceeds the angle of repose, at which point avalanching occurs and sediment cascades down the lee face. The suspended load fraction is carried downcurrent, where coarser particles settle through the diffusion zone into the backflow and are deposited in the lee of the ripple. It is these combined processes that drive bedform development and migration. ^[1]

Each avalanche event deposits a foreset lamina - the individual layer that dips downstream on the lee face. This is the direct origin of cross-lamination and cross-bedding: every dipping internal layer in a cross-stratified unit represents one avalanche event on the lee face of a migrating bedform. The geometry of cross-stratification therefore records not just the presence of a bedform, but the direction of flow that drove it.

Preservation Potential

Dunes are even less commonly preserved than ripples; nonetheless, ancient dunes are present in some thick sandstone units. ^[1]

References

1. Boggs, S. Jr. (2012). Principles of Sedimentology and Stratigraphy, 5th ed. Pearson Prentice Hall.

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