Coherence and Breakdown in Aircraft Airflows: A Classical Mathematical Diagnostic Framework for Aerodynamic Organisation, Separation, Wave Persistence, and Flow Stability

This manuscript presents a classical mathematical diagnostic framework for interpreting aircraft airflows in terms of coherent organisation, breakdown, reorganisation, wake persistence, and flow stability. The paper does not propose a replacement for established fluid dynamics. Instead, it provides a bounded diagnostic language built from established aerodynamic quantities, including velocity, vorticity, circulation, pressure, turbulence intensity, and finite-volume conservation measures. The framework is intended as a conceptual and computational aid for analysing attached flow, separation, stall development, vortex persistence, wake evolution, and aerodynamic loss. It introduces normalised diagnostic indices for coherence, breakdown, reorganisation, and wake persistence, and discusses their possible use in computational fluid dynamics interpretation and aerodynamic design review. The manuscript is explicitly preliminary. No new wind-tunnel, flight-test, or computational fluid dynamics dataset is presented. The proposed diagnostic framework requires calibration, sensitivity analysis, benchmarking against existing coherent-structure methods, and validation against experimental or high-fidelity numerical datasets before it can be treated as an operational aerodynamic method.