Sediment Transport Simulator: Erosion, Entrainment, and Deposition

simulator intermediate ~10 min
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Saltation / Bedload — 1 mm sand grains bouncing along the bed

At 0.8 m/s flow velocity with 1 mm sand grains, the Shields parameter indicates active bedload transport. Grains are entrained and move by saltation — bouncing along the channel floor in short hops.

Formula

τ_bed = ρ_w × g × h × sin(S)
θ = τ / ((ρ_s - ρ_w) × g × D)
w_s = (ρ_s - ρ_w) × g × D² / (18 × μ) [Stokes law, D < 0.1 mm]

Rivers as Geological Agents

Rivers are the primary conveyor belts of the rock cycle, transporting weathered material from mountains to ocean basins. The physics of sediment entrainment, transport, and deposition governs the formation of alluvial fans, floodplains, deltas, and ultimately the sedimentary rocks that cover most of Earth's surface. Understanding these processes requires linking fluid mechanics to particle behavior at every scale.

The Hjulström Curve

Filip Hjulström's 1935 diagram elegantly captures the relationship between flow velocity and grain fate. Medium sand requires the least velocity to erode because it lacks both the cohesion of clay and the weight of gravel. The curve reveals a critical insight: once entrained, fine particles remain suspended at velocities far below those needed to dislodge them — explaining why muddy river water stays turbid for days after a flood recedes.

Shields Criterion and Bedload

Albert Shields formalized the threshold for grain motion using dimensional analysis. The Shields parameter compares the fluid force trying to move a grain to the gravitational force holding it in place. Above the critical value, grains begin rolling, sliding, and saltating along the bed. The total bedload flux increases with the cube of the excess shear stress — a nonlinear response that makes flood events disproportionately important for sediment budgets.

From Transport to Rock

When carrying capacity drops — at a river bend, estuary, or lake floor — sediment settles according to grain size: gravel first, then sand, silt, and finally clay. This sorting process creates the layered deposits visible in outcrop as sandstone, shale, and conglomerate. Billions of years of sediment transport and deposition have produced the vast sedimentary sequences that record Earth's climate, evolution, and tectonic history.

FAQ

What is the Hjulström curve?

The Hjulström curve relates flow velocity to grain size for erosion, transport, and deposition. It shows that medium sand (0.1–1 mm) is easiest to erode, while both finer (cohesive) and coarser (heavy) grains need higher velocities. Deposition velocities are always lower than erosion velocities for a given grain size.

What is the Shields parameter?

The Shields parameter (θ) is a dimensionless ratio of fluid shear stress to the gravitational force on a grain. When θ exceeds a critical threshold (approximately 0.047 for turbulent flow), grains begin to move. It was introduced by Albert Shields in 1936 and remains the standard criterion for sediment entrainment.

What determines whether sediment is suspended or rolls along the bed?

The ratio of shear velocity to settling velocity determines transport mode. When shear velocity exceeds settling velocity, grains are held in suspension. When they are comparable, grains saltate (bounce). When shear velocity is much less, grains roll or slide as bedload.

How does sediment transport create sedimentary rocks?

When flow velocity drops — at river mouths, floodplains, or ocean basins — sediment settles and accumulates in layers. Over geological time, burial pressure and cementation lithify these deposits into sandstone, siltstone, mudstone, and conglomerate, preserving records of ancient environments.

Sources

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