Category: Ecology

Summary: Estimating when stronger branch-floodplain exchange makes a directed river-network operator transiently reactive and relocates its dominant mode onto a branch-floodplain bridge.

Floodplains and off-channel storage can strongly reshape how water, nutrients, and tracers move through river networks. This experiment asks when increasing exchange between the main branching network and floodplain storage pushes the system into a transiently amplifying regime, with the dominant mode relocating onto a branch-floodplain bridge instead of remaining trunk-dominated.

The code builds dense operators for directed river transport, forms the associated numerical-abscissa problem, and uses iterative deepening with repeated eigensolves to bisect the critical exchange threshold across larger network sizes. It records reactivity, bridge dominance, floodplain mass, and a connectivity proxy to distinguish a genuine structural transition from a smooth quantitative change.

That makes the project relevant to transport and storage dynamics rather than only to steady flow. The value is in identifying the onset of transient amplification, where floodplain coupling begins to reorganize the dominant transport pattern of the network.

Method: Dense symmetric eigensolves of numerical-abscissa matrices with iterative deepening and bisection on branch-floodplain exchange strength across N=64 to 2048.

What is measured: Critical exchange estimate, reactive eigenvalue, bridge ratio, floodplain mass, connectivity proxy, passes completed, and bracket width.