Does this include bars, width variation, or floodplain stratigraphy?

No. It is a single-line cartoon with smoothing λ to mimic unresolved subgrid dissipation; there is no cross-section, no Exner bed update, and no bank-height physics.

Why pin y=0 at both ends?

It fixes the reach length and prevents rigid translation of the whole thread, making relative bend growth easier to see in a small canvas.

River Meandering (Toy)

Natural river meanders arise from feedbacks among flow, sediment transport, and erodible banks — often summarized in reduced models (e.g. Ikeda–Parker–Sawai) where bend curvature and its streamwise gradient steer lateral migration. This page collapses that story to a pinned-end centerline y(x,t) on a fixed downstream reach: curvature κ is approximated by ∂²y/∂x² (gentle slopes), streamwise curvature gradient by ∂κ/∂x, and a toy evolution ∂y/∂t = k₁ ∂κ/∂s + λ ∂²y/∂x² with ∂κ/∂s ≈ ∂κ/∂x. Parameters are chosen for visible bend growth and numerical stability, not field calibration.

Who it's for: Introductory geomorphology or PDE-motivation labs after basic derivatives.

Key terms

Meander
Curvature
Centerline migration
Semi-empirical model
Numerical diffusion

Real meanders couple hydraulics, sediment, banks, and floodplain memory; this page keeps a single semi-empirical PDE-like rule so the “k₁ ∂c/∂s” bend-talk from notes becomes a visible curve.

Live graphs

How it works

Pinned-end centerline of a river reach: curvature κ drives lateral migration via a gradient term k₁ ∂κ/∂s plus smoothing — a classroom cartoon of why bends can sharpen and propagate along valley floors.

Key equations

κ ≈ ∂²y/∂x²; ∂y/∂t = k₁ ∂κ/∂s + λ ∂²y/∂x² (with ∂κ/∂s ≈ ∂κ/∂x here).

Frequently asked questions

Does this include bars, width variation, or floodplain stratigraphy?: No. It is a single-line cartoon with smoothing λ to mimic unresolved subgrid dissipation; there is no cross-section, no Exner bed update, and no bank-height physics.
Why pin y=0 at both ends?: It fixes the reach length and prevents rigid translation of the whole thread, making relative bend growth easier to see in a small canvas.

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