The Blind Spot of Scale-Invariant Residual Metrics: Why Off-Diagonal Autocorrelation Fails to Detect Intermittent Turbulent Bursts

Atmospheric turbulence near wind turbines and aerodynamic surfaces is intermittent: long quiescent periods are interrupted by rare, energetic coherent structures (vortex strikes). Standard FFT smears these localized events over the window, and the peak spectral density may appear benign. We test the hypothesis that the autocorrelation matrix of AR residuals detects the "instantaneous phase locking" of such bursts: a nearly diagonal matrix (white noise) during calm periods should become strongly off-diagonal during a strike. Using a synthetic signal (AR(1) background plus sparse Gabor bursts with heavy-tailed amplitudes), we compute the normalized off-diagonal energy E_off in a sliding window. The result is negative: E_off remains essentially flat, while both total FFT energy and peak PSD spike at the burst times. We explain the failure through three mechanisms: (i) scale invariance of E_off (normalization by total residual energy makes it blind to amplitude events), (ii) in-window AR whitening (the model adapts to the burst), and (iii) the nature of the bursts (amplitude transients rather than persistent phase coherence). The negative result delineates the limits of scale-invariant correlation metrics and reinforces the need for energy-based or time-frequency detectors in intermittency monitoring.