A Coupled Multi-Node Attractor Network Framework for Resolving Sediment Starvation and Regulating 3D Navier-Stokes Flows in the Nile River Basin

This expanded research addresses sediment starvation downstream of the Aswan High Dam (the “Hungry Water” effect) and the anthropogenic flattening of the natural hydrograph in the Nile River basin. By integrating classical fluvial geomorphology with nonlinear dynamical systems theory, we propose an enhanced management paradigm based on the Hala Attractor, now extended to a coupled multi-node attractor network that accounts for tributary interactions at the Khartoum confluence and multi-reservoir controls including the Grand Ethiopian Renaissance Dam (GERD). Unlike traditional static operations, this framework treats dams as tunable parameters (γ) in a hierarchical cascade, engineering the river’s chaoticity to optimize sediment transport across branches. We formulate a mathematical theory asserting that 3D Navier-Stokes regularity can be preserved by maintaining flows within finite-dimensional global attractors (A3D), mitigating destructive hydraulic jumps and shear stress exceedances. Through an expanded 2k Factorial Design of Experiment (DoE) incorporating GERD filling scenarios, we demonstrate that “Chaos Compression” via nonlinear feedback prevents silt settling and enables “Successive Controlled Collapse” of trajectories onto Delta coordinates. Results show that Hala-tuned operations can deliver up to 92% of injected sediment to the Nile Delta, with GERD reducing downstream siltation by 92–97% while enhancing Sudanese reservoir lifespans. This study provides rigorous evidence that the Nile basin can be operated as a programmable discrete-chaotic engine, bridging hydraulic engineering, turbulence physics, and basin-scale governance.