Why do the bends move downstream as well as outward?

Because the fastest water in a bend arrives *after* the bend. The near-bank velocity that erodes the outer bank responds to the curvature upstream of it, with a lag of a few channel widths — so the erosion maximum sits downstream of the curvature maximum, and the whole train of bends walks downstream.

What are the stripes on the floodplain?

Scroll bars: the record of where the channel used to be. Every cell carries the year the river last occupied or flooded it, so the age layer is the floodplain’s stratigraphy seen from above. Cutting a section through it is how a geologist reads a river’s history.

Why does my delta shrink even though the river is still flowing?

Deltas survive by being fed faster than they sink. Subsidence, compaction and sea-level rise all lower the plain; only new sediment raises it. Take the sediment away — with a dam — or stop the river from switching channels — with levees — and the arithmetic stops working.

Meander & Delta — Five centuries of a river deciding where to be.

You are the river-basin engineer. A river left alone does not stay put. Watch a channel grow meanders, cut them off, leave oxbow lakes and lay down the striped floodplain that records every one of its old positions — while at the far end its delta is built, drowned or starved depending on what you do upstream. Five hundred years, at up to two centuries a minute.

Timescale: 500 years. Model: Ikeda–Parker–Sawai bank migration on a resampled centreline, with a raster floodplain and a DeltaRCM-style cellular delta

What you will learn

Why a meander grows and then destroys itself, and why the floodplain is striped.
Why levees protect a town and starve the land behind them at the same time.
Why a dam a hundred kilometres upstream makes a delta sink.
Why a delta needs its river to keep switching channels to survive.

Scenarios

Wild River — Five hundred years, no engineering, no objectives.
Keep the Town Dry — A town on the floodplain, two centuries, and $260M of works.
Rebuild the Delta — 9 mm/yr of subsidence, a rising sea and a dam upstream. Maximise land at year 100.
Dam Upstream — The dam closes in year 50. Watch what happens for the next two centuries.

What you control

Mean annual discharge (m³/s) — Sets the channel width through hydraulic geometry — and a wider channel makes longer meanders.
Flood variability (σ) — Log-space spread of annual discharge. A river that floods rarely and hugely builds a very different floodplain from one that floods every year.
Sediment supply (Mt/yr) — What arrives from upstream, for a mid-sized river. It builds the floodplain first and the delta with whatever is left.
Sand fraction — Sandy banks are weak and migrate fast; muddy banks are cohesive and hold. It also sets how far overbank deposits reach from the channel.
Bank vegetation — Roots bind banks. Clearing the riparian forest can double the migration rate.
Valley slope (m/km) — How high the valley head stands above the sea. Steep valleys give straight rivers; gentle ones give tight meanders.
Bend lag length (channel widths) — How far downstream the near-bank velocity remembers the curvature. Short lags give fat symmetrical bends, long lags give skewed, downstream-migrating ones.
Sea-level rise (mm/yr) — A delta must build upward at least this fast simply to stay where it is.
Delta subsidence (mm/yr) — Compaction of the delta’s own deposits, plus whatever is being pumped out from under it. It adds to sea-level rise and it is often the larger of the two.
Wave energy — Waves straighten a delta’s shoreline and spread its sediment along the coast. High wave energy gives a smooth arcuate delta; low energy gives a bird’s foot.

Questions

Why do the bends move downstream as well as outward?: Because the fastest water in a bend arrives *after* the bend. The near-bank velocity that erodes the outer bank responds to the curvature upstream of it, with a lag of a few channel widths — so the erosion maximum sits downstream of the curvature maximum, and the whole train of bends walks downstream.
What are the stripes on the floodplain?: Scroll bars: the record of where the channel used to be. Every cell carries the year the river last occupied or flooded it, so the age layer is the floodplain’s stratigraphy seen from above. Cutting a section through it is how a geologist reads a river’s history.
Why does my delta shrink even though the river is still flowing?: Deltas survive by being fed faster than they sink. Subsidence, compaction and sea-level rise all lower the plain; only new sediment raises it. Take the sediment away — with a dam — or stop the river from switching channels — with levees — and the arithmetic stops working.

What this model cannot do

Bend theory is linear. It is derived for gentle curvature and is being used here on tight bends, where it overstates how fast the tightest ones migrate.
The channel has one width everywhere and no bed. Real rivers widen in bends, have pools and riffles, and aggrade or incise their beds — the "sediment-hungry river below a dam" is asserted in the sediment budget rather than emerging from a bed model.
Avulsion — the river abandoning its whole course for a new one across the floodplain — is not modelled upstream of the delta. Real rivers do this every few centuries and it dominates floodplain architecture.
The delta router is a reduced-complexity model, not hydrodynamics. It has no waves computed from a wind field, no tides, no salt wedge and no vegetation holding the marsh together.
Compaction is a fixed subsidence rate, not a function of what has been deposited.
A fictional valley. It is not a model of any real river, and nothing here should be used to plan works on one.

Sources

Ikeda, S., Parker, G. & Sawai, K. (1981), Bend theory of river meanders — the linear bend theory behind the migration rule
Howard, A. D. & Knutson, T. R. (1984), Sufficient conditions for river meandering — the practical weighted-curvature form used here
Liang, M., Voller, V. R. & Paola, C. (2015), A reduced-complexity model for river delta formation — DeltaRCM, which the delta router is a simplified version of
Sylvester, Z., Durkin, P. & Covault, J. (2019), High curvatures drive river meandering
Blum, M. D. & Roberts, H. H. (2009), Drowning of the Mississippi Delta due to insufficient sediment supply and global sea-level rise
Hudson, P. F. & Kesel, R. H. (2000), Channel migration and meander-bend curvature in the lower Mississippi River prior to major human modification