Meandering River Valley Erosion

Fluvial Controls

Erosion rate 1.0

Meander mobility 1.0

Time speed 1.0x

Elapsed time

0 kyr

Sinuosity

1.00

Valley width

–

Oxbow lakes

How it works

The terrain starts as an almost-flat plateau with a river running across it. Every bend in the channel migrates in the direction it already curves — the outer bank of a bend is where flow velocity and shear stress are highest, so it erodes, while the inner bank accretes as a point bar. That single feedback rule (migration ∝ local curvature) is enough to grow gentle wiggles into full meander loops on its own, exactly as in real alluvial rivers. As the channel sweeps sideways over and over, it scours a wide, flat-bottomed valley into what was once solid plateau — the valley you see is the *accumulated footprint* of centuries of the river's past positions, not something carved once and left alone.

dz/dt(bend) = k · curvature(bend) · migration_rate
height(x,z,t) -= erosion_rate · Gaussian(z − river_z(x,t))

Erosion rate — how fast the channel cuts down and the floodplain around it lowers; higher values deepen and widen the valley faster.
Meander mobility — how strongly curvature drives lateral bank migration; at zero the river stays straight and only downcuts, at high values loops swing wildly and cut themselves off quickly.
Time speed — how fast simulated geologic time passes; the physics is unchanged, only the clock.

Watch for a neck cutoff: when a growing loop swings around far enough that two bends nearly touch, the river punches straight through the neck, abandoning the loop as a crescent-shaped oxbow lake stranded on the floodplain — a real, common event in meandering rivers like the Mississippi or the Amazon.

River channel Floodplain Valley wall / plateau Oxbow lake

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